Absolutely! Let’s solve this
Equivalent Ratios worksheet step by step.
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🔍 What is an Equivalent Ratio?
An
equivalent ratio is a ratio that expresses the same relationship between two quantities as another ratio. You can find equivalent ratios by
multiplying or dividing both parts of the ratio by the same number.
For example:
- 1:2 is equivalent to 2:4, 3:6, 5:10, etc., because you multiply both numbers by the same value.
- You can also think of ratios as fractions: 1:2 = 1/2, so any fraction equal to 1/2 (like 5/10 or 9/18) represents the same ratio.
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We’ll go problem by problem.
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##
✔ Problem 1: `1 : 2 = ___ : 10 = 9 : ___`
We want to find numbers that make these ratios equivalent to 1:2.
- First blank: `? : 10`
- Since 2 × 5 = 10, multiply 1 by 5 →
5
- So, 1:2 =
5:10
- Second blank: `9 : ?`
- Since 1 × 9 = 9, multiply 2 by 9 →
18
- So, 1:2 = 9:
18
✔ Answer:
5 : 10 = 9 : 18
→ In fraction:
1/2
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##
✔ Problem 2: `1 : 3 = ___ : 15 = 2 : ___`
- First blank: `? : 15`
- 3 × 5 = 15 → 1 × 5 =
5
- So, 1:3 =
5:15
- Second blank: `2 : ?`
- 1 × 2 = 2 → 3 × 2 =
6
- So, 1:3 = 2:
6
✔ Answer:
5 : 15 = 2 : 6
→ In fraction:
1/3
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##
✔ Problem 3: `1 : 4 = ___ : 24 = 5 : ___`
- First blank: `? : 24`
- 4 × 6 = 24 → 1 × 6 =
6
- So, 1:4 =
6:24
- Second blank: `5 : ?`
- 1 × 5 = 5 → 4 × 5 =
20
- So, 1:4 = 5:
20
✔ Answer:
6 : 24 = 5 : 20
→ In fraction:
1/4
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##
✔ Problem 4: `1 : 5 = ___ : 35 = 3 : ___`
- First blank: `? : 35`
- 5 × 7 = 35 → 1 × 7 =
7
- So, 1:5 =
7:35
- Second blank: `3 : ?`
- 1 × 3 = 3 → 5 × 3 =
15
- So, 1:5 = 3:
15
✔ Answer:
7 : 35 = 3 : 15
→ In fraction:
1/5
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##
✔ Problem 5: `1 : 6 = ___ : 12 = 4 : ___`
- First blank: `? : 12`
- 6 × 2 = 12 → 1 × 2 =
2
- So, 1:6 =
2:12
- Second blank: `4 : ?`
- 1 × 4 = 4 → 6 × 4 =
24
- So, 1:6 = 4:
24
✔ Answer:
2 : 12 = 4 : 24
→ In fraction:
1/6
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##
✔ Problem 6: `1 : 7 = ___ : 21 = 6 : ___`
- First blank: `? : 21`
- 7 × 3 = 21 → 1 × 3 =
3
- So, 1:7 =
3:21
- Second blank: `6 : ?`
- 1 × 6 = 6 → 7 × 6 =
42
- So, 1:7 = 6:
42
✔ Answer:
3 : 21 = 6 : 42
→ In fraction:
1/7
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##
✔ Problem 7: `1 : 8 = ___ : 16 = 7 : ___`
- First blank: `? : 16`
- 8 × 2 = 16 → 1 × 2 =
2
- So, 1:8 =
2:16
- Second blank: `7 : ?`
- 1 × 7 = 7 → 8 × 7 =
56
- So, 1:8 = 7:
56
✔ Answer:
2 : 16 = 7 : 56
→ In fraction:
1/8
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##
✔ Problem 8: `1 : 9 = ___ : 72 = 6 : ___`
- First blank: `? : 72`
- 9 × 8 = 72 → 1 × 8 =
8
- So, 1:9 =
8:72
- Second blank: `6 : ?`
- 1 × 6 = 6 → 9 × 6 =
54
- So, 1:9 = 6:
54
✔ Answer:
8 : 72 = 6 : 54
→ In fraction:
1/9
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## 📝 Final Answers Summary:
| # | Ratio Completed | In Fraction |
|---|----------------------------------|-------------|
| 1 | 1 : 2 =
5 : 10 = 9 :
18 | 1/2 |
| 2 | 1 : 3 =
5 : 15 = 2 :
6 | 1/3 |
| 3 | 1 : 4 =
6 : 24 = 5 :
20 | 1/4 |
| 4 | 1 : 5 =
7 : 35 = 3 :
15 | 1/5 |
| 5 | 1 : 6 =
2 : 12 = 4 :
24 | 1/6 |
| 6 | 1 : 7 =
3 : 21 = 6 :
42 | 1/7 |
| 7 | 1 : 8 =
2 : 16 = 7 :
56 | 1/8 |
| 8 | 1 : 9 =
8 : 72 = 6 :
54 | 1/9 |
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💡
Tip for Students: Always check your work by simplifying the completed ratios back to the original. For example, 5:10 simplifies to 1:2 — perfect!
Let me know if you’d like a printable version or more practice problems! 😊
Parent Tip: Review the logic above to help your child master the concept of ratios and proportions worksheet.
