Equivalent Ratio Worksheets - Math Monks - Free Printable
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Step-by-step solution for: Equivalent Ratio Worksheets - Math Monks
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Show Answer Key & Explanations
Step-by-step solution for: Equivalent Ratio Worksheets - Math Monks
Let’s solve each equivalent ratio problem step by step. Remember: two ratios are equivalent if you can multiply or divide both parts of one ratio by the same number to get the other ratio.
We’ll go one by one:
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[1] 12 : ___ = 24 : 30
Look at the right side: 24 : 30
What do we divide 24 by to get 12? → 24 ÷ 2 = 12
So divide 30 by 2 too → 30 ÷ 2 = 15
✔ Answer: 15
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[2] 27 : 72 = 3 : ___
Left side: 27 : 72
Divide 27 by 9 to get 3 → so divide 72 by 9 → 72 ÷ 9 = 8
✔ Answer: 8
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[3] 3.6 : ___ = 12 : 2
Right side: 12 : 2 → simplify by dividing both by 2 → 6 : 1
But let’s think differently: What do we multiply 3.6 by to get 12?
12 ÷ 3.6 = 120 ÷ 36 = 10/3 ≈ 3.333…
Better way: Cross-multiply!
Set up: 3.6 / x = 12 / 2
→ 3.6 / x = 6
→ x = 3.6 ÷ 6 = 0.6
Check: 3.6 : 0.6 = 6 : 1, and 12 : 2 = 6 : 1 → yes!
✔ Answer: 0.6
---
[4] 6.25 : 5 = 25 : ___
Cross-multiply: 6.25 / 5 = 25 / x
→ 1.25 = 25 / x
→ x = 25 ÷ 1.25 = 20
Check: 6.25 × 4 = 25, 5 × 4 = 20 → yes!
✔ Answer: 20
---
[5] 25 : ___ = 5 : 8
Cross-multiply: 25 / x = 5 / 8
→ 5x = 25 × 8 = 200
→ x = 200 ÷ 5 = 40
Check: 25 ÷ 5 = 5, 40 ÷ 5 = 8 → yes!
✔ Answer: 40
---
[6] 8 : 28 = ___ : 7
Simplify left: 8 : 28 → divide both by 4 → 2 : 7
So blank is 2
Check: 8 ÷ 4 = 2, 28 ÷ 4 = 7 → yes!
✔ Answer: 2
---
[7] 3 : ___ = 27 : 72
Simplify right: 27 : 72 → divide both by 9 → 3 : 8
So blank is 8
Check: 3 × 9 = 27, 8 × 9 = 72 → yes!
✔ Answer: 8
---
[8] 1.2 : ___ = 30 : 150
Simplify right: 30 : 150 → divide both by 30 → 1 : 5
So 1.2 : x = 1 : 5 → x = 1.2 × 5 = 6
Check: 1.2 × 25 = 30, 6 × 25 = 150 → yes!
✔ Answer: 6
---
[9] 9 : 21 = ___ : 7
Simplify left: 9 : 21 → divide both by 3 → 3 : 7
So blank is 3
Check: 9 ÷ 3 = 3, 21 ÷ 3 = 7 → yes!
✔ Answer: 3
---
[10] 6 : 13 = ___ : 52
Right side denominator: 52 ÷ 13 = 4
So multiply 6 by 4 → 6 × 4 = 24
Check: 6×4=24, 13×4=52 → yes!
✔ Answer: 24
---
[11] 15 : 54 = 5 : ___
Left: 15 ÷ 3 = 5 → so 54 ÷ 3 = 18
Check: 15:54 = 5:18 → yes!
✔ Answer: 18
---
[12] 9 : ___ = 3 : 20
Cross-multiply: 9/x = 3/20
→ 3x = 9 × 20 = 180
→ x = 180 ÷ 3 = 60
Check: 9÷3=3, 60÷3=20 → yes!
✔ Answer: 60
---
[13] 15 : 55 = ___ : 11
Simplify left: 15 : 55 → divide both by 5 → 3 : 11
So blank is 3
Check: 15÷5=3, 55÷5=11 → yes!
✔ Answer: 3
---
[14] 48 : 45 = ___ : 75
Cross-multiply: 48/45 = x/75
→ x = (48 × 75) ÷ 45
Calculate: 48 × 75 = 3600
3600 ÷ 45 = 80
Check: 48:45 = 16:15, 80:75 = 16:15 → yes!
✔ Answer: 80
---
[15] 2 : 5 = ___ : 30
5 × 6 = 30 → so 2 × 6 = 12
Check: 2×6=12, 5×6=30 → yes!
✔ Answer: 12
---
[16] 42 : ___ = 63 : 54
Cross-multiply: 42/x = 63/54
Simplify 63/54 = 7/6
So 42/x = 7/6
→ 7x = 42 × 6 = 252
→ x = 252 ÷ 7 = 36
Check: 42:36 = 7:6, 63:54 = 7:6 → yes!
✔ Answer: 36
---
[17] 2.2 : ___ = 33 : 135
Cross-multiply: 2.2/x = 33/135
Simplify 33/135 = 11/45
So 2.2/x = 11/45
→ 11x = 2.2 × 45 = 99
→ x = 99 ÷ 11 = 9
Check: 2.2 × 15 = 33, 9 × 15 = 135 → yes!
✔ Answer: 9
---
[18] ___ : 12 = 15 : 40
Cross-multiply: x/12 = 15/40
Simplify 15/40 = 3/8
So x/12 = 3/8
→ 8x = 36
→ x = 36 ÷ 8 = 4.5
Check: 4.5 : 12 = 45:120 = 3:8, 15:40 = 3:8 → yes!
✔ Answer: 4.5
---
[19] 40 : 30 = ___ : 48
Simplify left: 40:30 = 4:3
So x:48 = 4:3 → x = (4 × 48) ÷ 3 = 192 ÷ 3 = 64
Check: 40:30 = 4:3, 64:48 = 4:3 → yes!
✔ Answer: 64
---
[20] 45 : 120 = 15 : ___
Simplify left: 45:120 → divide by 3 → 15:40
So blank is 40
Check: 45÷3=15, 120÷3=40 → yes!
✔ Answer: 40
---
Final Answer:
[1] 15
[2] 8
[3] 0.6
[4] 20
[5] 40
[6] 2
[7] 8
[8] 6
[9] 3
[10] 24
[11] 18
[12] 60
[13] 3
[14] 80
[15] 12
[16] 36
[17] 9
[18] 4.5
[19] 64
[20] 40
We’ll go one by one:
---
[1] 12 : ___ = 24 : 30
Look at the right side: 24 : 30
What do we divide 24 by to get 12? → 24 ÷ 2 = 12
So divide 30 by 2 too → 30 ÷ 2 = 15
✔ Answer: 15
---
[2] 27 : 72 = 3 : ___
Left side: 27 : 72
Divide 27 by 9 to get 3 → so divide 72 by 9 → 72 ÷ 9 = 8
✔ Answer: 8
---
[3] 3.6 : ___ = 12 : 2
Right side: 12 : 2 → simplify by dividing both by 2 → 6 : 1
But let’s think differently: What do we multiply 3.6 by to get 12?
12 ÷ 3.6 = 120 ÷ 36 = 10/3 ≈ 3.333…
Better way: Cross-multiply!
Set up: 3.6 / x = 12 / 2
→ 3.6 / x = 6
→ x = 3.6 ÷ 6 = 0.6
Check: 3.6 : 0.6 = 6 : 1, and 12 : 2 = 6 : 1 → yes!
✔ Answer: 0.6
---
[4] 6.25 : 5 = 25 : ___
Cross-multiply: 6.25 / 5 = 25 / x
→ 1.25 = 25 / x
→ x = 25 ÷ 1.25 = 20
Check: 6.25 × 4 = 25, 5 × 4 = 20 → yes!
✔ Answer: 20
---
[5] 25 : ___ = 5 : 8
Cross-multiply: 25 / x = 5 / 8
→ 5x = 25 × 8 = 200
→ x = 200 ÷ 5 = 40
Check: 25 ÷ 5 = 5, 40 ÷ 5 = 8 → yes!
✔ Answer: 40
---
[6] 8 : 28 = ___ : 7
Simplify left: 8 : 28 → divide both by 4 → 2 : 7
So blank is 2
Check: 8 ÷ 4 = 2, 28 ÷ 4 = 7 → yes!
✔ Answer: 2
---
[7] 3 : ___ = 27 : 72
Simplify right: 27 : 72 → divide both by 9 → 3 : 8
So blank is 8
Check: 3 × 9 = 27, 8 × 9 = 72 → yes!
✔ Answer: 8
---
[8] 1.2 : ___ = 30 : 150
Simplify right: 30 : 150 → divide both by 30 → 1 : 5
So 1.2 : x = 1 : 5 → x = 1.2 × 5 = 6
Check: 1.2 × 25 = 30, 6 × 25 = 150 → yes!
✔ Answer: 6
---
[9] 9 : 21 = ___ : 7
Simplify left: 9 : 21 → divide both by 3 → 3 : 7
So blank is 3
Check: 9 ÷ 3 = 3, 21 ÷ 3 = 7 → yes!
✔ Answer: 3
---
[10] 6 : 13 = ___ : 52
Right side denominator: 52 ÷ 13 = 4
So multiply 6 by 4 → 6 × 4 = 24
Check: 6×4=24, 13×4=52 → yes!
✔ Answer: 24
---
[11] 15 : 54 = 5 : ___
Left: 15 ÷ 3 = 5 → so 54 ÷ 3 = 18
Check: 15:54 = 5:18 → yes!
✔ Answer: 18
---
[12] 9 : ___ = 3 : 20
Cross-multiply: 9/x = 3/20
→ 3x = 9 × 20 = 180
→ x = 180 ÷ 3 = 60
Check: 9÷3=3, 60÷3=20 → yes!
✔ Answer: 60
---
[13] 15 : 55 = ___ : 11
Simplify left: 15 : 55 → divide both by 5 → 3 : 11
So blank is 3
Check: 15÷5=3, 55÷5=11 → yes!
✔ Answer: 3
---
[14] 48 : 45 = ___ : 75
Cross-multiply: 48/45 = x/75
→ x = (48 × 75) ÷ 45
Calculate: 48 × 75 = 3600
3600 ÷ 45 = 80
Check: 48:45 = 16:15, 80:75 = 16:15 → yes!
✔ Answer: 80
---
[15] 2 : 5 = ___ : 30
5 × 6 = 30 → so 2 × 6 = 12
Check: 2×6=12, 5×6=30 → yes!
✔ Answer: 12
---
[16] 42 : ___ = 63 : 54
Cross-multiply: 42/x = 63/54
Simplify 63/54 = 7/6
So 42/x = 7/6
→ 7x = 42 × 6 = 252
→ x = 252 ÷ 7 = 36
Check: 42:36 = 7:6, 63:54 = 7:6 → yes!
✔ Answer: 36
---
[17] 2.2 : ___ = 33 : 135
Cross-multiply: 2.2/x = 33/135
Simplify 33/135 = 11/45
So 2.2/x = 11/45
→ 11x = 2.2 × 45 = 99
→ x = 99 ÷ 11 = 9
Check: 2.2 × 15 = 33, 9 × 15 = 135 → yes!
✔ Answer: 9
---
[18] ___ : 12 = 15 : 40
Cross-multiply: x/12 = 15/40
Simplify 15/40 = 3/8
So x/12 = 3/8
→ 8x = 36
→ x = 36 ÷ 8 = 4.5
Check: 4.5 : 12 = 45:120 = 3:8, 15:40 = 3:8 → yes!
✔ Answer: 4.5
---
[19] 40 : 30 = ___ : 48
Simplify left: 40:30 = 4:3
So x:48 = 4:3 → x = (4 × 48) ÷ 3 = 192 ÷ 3 = 64
Check: 40:30 = 4:3, 64:48 = 4:3 → yes!
✔ Answer: 64
---
[20] 45 : 120 = 15 : ___
Simplify left: 45:120 → divide by 3 → 15:40
So blank is 40
Check: 45÷3=15, 120÷3=40 → yes!
✔ Answer: 40
---
Final Answer:
[1] 15
[2] 8
[3] 0.6
[4] 20
[5] 40
[6] 2
[7] 8
[8] 6
[9] 3
[10] 24
[11] 18
[12] 60
[13] 3
[14] 80
[15] 12
[16] 36
[17] 9
[18] 4.5
[19] 64
[20] 40
Parent Tip: Review the logic above to help your child master the concept of ratio worksheet with answers.
