Equivalent Ratios with Blanks (Old) - Free Printable
Educational worksheet: Equivalent Ratios with Blanks (Old). Download and print for classroom or home learning activities.
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Step-by-step solution for: Equivalent Ratios with Blanks (Old)
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Show Answer Key & Explanations
Step-by-step solution for: Equivalent Ratios with Blanks (Old)
To solve the “Equivalent Ratios (A)” worksheet, we need to find the missing number in each ratio so that the two ratios are equivalent — meaning they represent the same relationship between numbers. We can do this by using cross-multiplication or by finding the scale factor (multiplier) between corresponding terms.
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For a ratio `a : b = c : d`, the cross-products must be equal:
a × d = b × c
Alternatively, if you know one side of the ratio and part of the other, you can find the multiplier:
- If `a : b = x : d`, then `x = (a × d) / b`
- Or, if `a : b = c : x`, then `x = (b × c) / a`
Let’s solve each problem step-by-step.
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## Left Column:
Let the blank be `x`.
So, `x : 9 = 10 : 45` → `x/9 = 10/45`
Simplify 10/45 = 2/9 → So `x/9 = 2/9` → x = 2
✔ Answer: 2
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`x/3 = 40/15` → 40/15 = 8/3 → `x/3 = 8/3` → x = 8
✔ Answer: 8
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`9/x = 18/14` → Cross multiply: 9 × 14 = 18 × x → 126 = 18x → x = 126 ÷ 18 = 7
✔ Answer: 7
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`x/7 = 45/35` → 45/35 = 9/7 → `x/7 = 9/7` → x = 9
✔ Answer: 9
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`6/5 = x/15` → Cross multiply: 6 × 15 = 5 × x → 90 = 5x → x = 18
✔ Answer: 18
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`6/4 = 18/x` → Simplify 6/4 = 3/2 → 3/2 = 18/x → Cross multiply: 3x = 36 → x = 12
✔ Answer: 12
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`2/8 = x/40` → 2/8 = 1/4 → 1/4 = x/40 → x = 40 ÷ 4 = 10
✔ Answer: 10
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`6/8 = x/16` → 6/8 = 3/4 → 3/4 = x/16 → x = (3 × 16)/4 = 48/4 = 12
✔ Answer: 12
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`3/9 = x/36` → 3/9 = 1/3 → 1/3 = x/36 → x = 36 ÷ 3 = 12
✔ Answer: 12
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`9/3 = x/15` → 9/3 = 3 → 3 = x/15 → x = 3 × 15 = 45
✔ Answer: 45
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## Right Column:
`x/8 = 16/32` → 16/32 = 1/2 → x/8 = 1/2 → x = 4
✔ Answer: 4
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`8/2 = x/6` → 8/2 = 4 → 4 = x/6 → x = 24
✔ Answer: 24
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`3/x = 9/6` → 9/6 = 3/2 → 3/x = 3/2 → x = 2
✔ Answer: 2
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`3/2 = 9/x` → Cross multiply: 3x = 18 → x = 6
✔ Answer: 6
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`6/x = 30/30` → 30/30 = 1 → 6/x = 1 → x = 6
✔ Answer: 6
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`6/8 = x/16` → 6/8 = 3/4 → 3/4 = x/16 → x = (3 × 16)/4 = 12
✔ Answer: 12
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`5/x = 10/18` → 10/18 = 5/9 → 5/x = 5/9 → x = 9
✔ Answer: 9
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`6/x = 24/28` → Simplify 24/28 = 6/7 → 6/x = 6/7 → x = 7
✔ Answer: 7
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`6/9 = 12/x` → 6/9 = 2/3 → 2/3 = 12/x → Cross multiply: 2x = 36 → x = 18
✔ Answer: 18
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`4/x = 20/25` → 20/25 = 4/5 → 4/x = 4/5 → x = 5
✔ Answer: 5
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## ✔ Final Answers:
1. 2
2. 8
3. 7
4. 9
5. 18
6. 12
7. 10
8. 12
9. 12
10. 45
1. 4
2. 24
3. 2
4. 6
5. 6
6. 12
7. 9
8. 7
9. 18
10. 5
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You can now fill in the blanks on your worksheet with these answers! Let me know if you’d like a visual explanation or more practice problems. 😊
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General Strategy:
For a ratio `a : b = c : d`, the cross-products must be equal:
a × d = b × c
Alternatively, if you know one side of the ratio and part of the other, you can find the multiplier:
- If `a : b = x : d`, then `x = (a × d) / b`
- Or, if `a : b = c : x`, then `x = (b × c) / a`
Let’s solve each problem step-by-step.
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## Left Column:
1. __ : 9 = 10 : 45
Let the blank be `x`.
So, `x : 9 = 10 : 45` → `x/9 = 10/45`
Simplify 10/45 = 2/9 → So `x/9 = 2/9` → x = 2
✔ Answer: 2
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2. __ : 3 = 40 : 15
`x/3 = 40/15` → 40/15 = 8/3 → `x/3 = 8/3` → x = 8
✔ Answer: 8
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3. 9 : __ = 18 : 14
`9/x = 18/14` → Cross multiply: 9 × 14 = 18 × x → 126 = 18x → x = 126 ÷ 18 = 7
✔ Answer: 7
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4. __ : 7 = 45 : 35
`x/7 = 45/35` → 45/35 = 9/7 → `x/7 = 9/7` → x = 9
✔ Answer: 9
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5. 6 : 5 = __ : 15
`6/5 = x/15` → Cross multiply: 6 × 15 = 5 × x → 90 = 5x → x = 18
✔ Answer: 18
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6. 6 : 4 = 18 : __
`6/4 = 18/x` → Simplify 6/4 = 3/2 → 3/2 = 18/x → Cross multiply: 3x = 36 → x = 12
✔ Answer: 12
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7. 2 : 8 = __ : 40
`2/8 = x/40` → 2/8 = 1/4 → 1/4 = x/40 → x = 40 ÷ 4 = 10
✔ Answer: 10
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8. 6 : 8 = __ : 16
`6/8 = x/16` → 6/8 = 3/4 → 3/4 = x/16 → x = (3 × 16)/4 = 48/4 = 12
✔ Answer: 12
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9. 3 : 9 = __ : 36
`3/9 = x/36` → 3/9 = 1/3 → 1/3 = x/36 → x = 36 ÷ 3 = 12
✔ Answer: 12
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10. 9 : 3 = __ : 15
`9/3 = x/15` → 9/3 = 3 → 3 = x/15 → x = 3 × 15 = 45
✔ Answer: 45
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## Right Column:
1. __ : 8 = 16 : 32
`x/8 = 16/32` → 16/32 = 1/2 → x/8 = 1/2 → x = 4
✔ Answer: 4
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2. 8 : 2 = __ : 6
`8/2 = x/6` → 8/2 = 4 → 4 = x/6 → x = 24
✔ Answer: 24
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3. 3 : __ = 9 : 6
`3/x = 9/6` → 9/6 = 3/2 → 3/x = 3/2 → x = 2
✔ Answer: 2
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4. 3 : 2 = 9 : __
`3/2 = 9/x` → Cross multiply: 3x = 18 → x = 6
✔ Answer: 6
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5. 6 : __ = 30 : 30
`6/x = 30/30` → 30/30 = 1 → 6/x = 1 → x = 6
✔ Answer: 6
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6. 6 : 8 = __ : 16
`6/8 = x/16` → 6/8 = 3/4 → 3/4 = x/16 → x = (3 × 16)/4 = 12
✔ Answer: 12
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7. 5 : __ = 10 : 18
`5/x = 10/18` → 10/18 = 5/9 → 5/x = 5/9 → x = 9
✔ Answer: 9
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8. 6 : __ = 24 : 28
`6/x = 24/28` → Simplify 24/28 = 6/7 → 6/x = 6/7 → x = 7
✔ Answer: 7
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9. 6 : 9 = 12 : __
`6/9 = 12/x` → 6/9 = 2/3 → 2/3 = 12/x → Cross multiply: 2x = 36 → x = 18
✔ Answer: 18
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10. 4 : __ = 20 : 25
`4/x = 20/25` → 20/25 = 4/5 → 4/x = 4/5 → x = 5
✔ Answer: 5
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## ✔ Final Answers:
Left Column:
1. 2
2. 8
3. 7
4. 9
5. 18
6. 12
7. 10
8. 12
9. 12
10. 45
Right Column:
1. 4
2. 24
3. 2
4. 6
5. 6
6. 12
7. 9
8. 7
9. 18
10. 5
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You can now fill in the blanks on your worksheet with these answers! Let me know if you’d like a visual explanation or more practice problems. 😊
Parent Tip: Review the logic above to help your child master the concept of ratio proportions worksheet.
