PR.6B, SEC 1, invrs prpn (50)
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Question 1 of 50
1. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 12, y = 3.
Find x when y = 9.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 2 of 50
2. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 13, y = 5.
Find y when x = 26.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 3 of 50
3. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 10, y = 12.
Find x when y = 30.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 4 of 50
4. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 5, y = 7.
Find x when y = 35.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 5 of 50
5. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 6, y = 14.
Find x when y = 7.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 6 of 50
6. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 15, y = 9.
Find x when y = 3.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 7 of 50
7. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 15, y = 2.
Find x when y = 5.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 8 of 50
8. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 30, y = 2.
Find y when x = 12.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 9 of 50
9. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 7, y = 6.
Find y when x = 14.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 10 of 50
10. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 4, y = 11.
Find x when y = 22.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 11 of 50
11. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 25, y = 1.
Find x when y = 5.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 12 of 50
12. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 4, y = 20.
Find y when x = 10.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 13 of 50
13. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 7, y = 8.
Find x when y = 4.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 14 of 50
14. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable is inversely proportional to .
When , .
Find when .
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 15 of 50
15. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 21, y = 6.
Find x when y = 14.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 16 of 50
16. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 3, y = 12.
Find x when y = 6.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 17 of 50
17. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 6, y = 5.
Find x when y = 15.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 18 of 50
18. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 30, y = 7.
Find y when x = 15.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 19 of 50
19. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 10, y = 3.
Find x when y = 15.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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-
Question 20 of 50
20. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 8, y = 9.
Find x when y = 6.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 21 of 50
21. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 24, y = 8.
Find x when y = 16.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
-
-
Question 22 of 50
22. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 18, y = 5.
Find x when y = 9.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 23 of 50
23. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable is inversely proportional to .
When x = 9, y = 6.
Find y when x = 3.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 24 of 50
24. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 28, y = 3.
Find x when y = 6.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 25 of 50
25. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 14, y = 3.
Find x when y = 7.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 26 of 50
26. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 5, y = 12.
Find x when y = 4.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 27 of 50
27. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 32, y = 5.
Find y when x = 8.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 28 of 50
28. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 16, y = 5.
Find y when x = 8.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 29 of 50
29. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 18, y = 6.
Find x when y = 3.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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-
Question 30 of 50
30. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 18, y = 12.
Find x when y = 4.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 31 of 50
31. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 11, y = 6.
Find y when x = 22.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 32 of 50
32. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 6, y = 15.
Find y when x = 10.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 33 of 50
33. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 9, y = 15.
Find x when y = 5.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 34 of 50
34. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable is inversely proportional to .
When , .
Calculate when .
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 35 of 50
35. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 20, y = 4.
Find x when y = 10.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 36 of 50
36. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 14, y = 8.
Find x when y = 2.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 37 of 50
37. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 22, y = 9.
Find y when x = 11.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 38 of 50
38. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable is inversely proportional to .
When , .
Calculate when .
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 39 of 50
39. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 9, y = 10.
Find y when x = 18.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 40 of 50
40. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 3, y = 10.
Find x when y = 5.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 41 of 50
41. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 6, y = 4.
Find x when y = 8.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 42 of 50
42. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable is inversely proportional to .
When , .
Calculate when .
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 43 of 50
43. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 24, y = 3.
Find x when y = 8.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 44 of 50
44. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 25, y = 4.
Find y when x = 5.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 45 of 50
45. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 9, y = 4.
Find x when y = 6.
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x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 46 of 50
46. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable y is inversely proportional to x.
When x = 8, y = 9.
Find y when x = 12.
-
y =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 47 of 50
47. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 16, y = 9.
Find x when y = 18.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 48 of 50
48. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 6, y = 9.
Find x when y = 3.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 49 of 50
49. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 21, y = 2.
Find x when y = 14.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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Question 50 of 50
50. Question
Topic: Inverse Proportion.
Please have pen and paper handy to show workings out. 📝
🔗 The variable x is inversely proportional to y.
When x = 12, y = 8.
Find x when y = 2.
-
x =⌨️ Enter your answer in the field provided.
CorrectIncorrectHint
💡 Inverse proportion: quick method.
“Inverse” means use y = k⁄x.
Equivalently x · y = k.
How to find k.
Use any given pair and compute k = x × y.
You must find k first before finding y for any x or x for any y.
Turn it into a number machine.
x (input) ──▶ [ reciprocal (1⁄x) ] ──▶ [ × k ] ──▶ y (output)
A reciprocal flips the number or variable.
For example: x becomes 1⁄x, 2 becomes 1⁄2, and a⁄b becomes b⁄a (think of x as x⁄1 or 2 as 2⁄1 and just flip).
Forward through the number machine.
Start with x, make 1⁄x, then multiply by k to get y = k⁄x.
Backward through the number machine.
Start with y, divide by k to get y⁄k, then take the reciprocal to get k⁄y, so x = k⁄y.
Quick check: every answer should satisfy x · y = k.
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