Math worksheet for practicing equivalent proportions with fraction equations.

You’ve uploaded a math worksheet titled “Completing Equivalent Proportions”. The goal is to find the missing number in each proportion so that both sides are equal (i.e., the fractions are equivalent).

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🔢 How to Solve Equivalent Proportions

A proportion is an equation stating that two ratios are equal:

> a/b = c/d

To solve for a missing value, we use cross-multiplication:

> a × d = b × c

Then solve for the unknown variable.

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Let’s go through each problem one by one.

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## ✔ Problem 1:
88 / 24 = 22 / ?

Cross-multiply:
88 × ? = 24 × 22
→ 88x = 528
→ x = 528 ÷ 88
→ x = 6

✔ Answer: 6

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## ✔ Problem 2:
33 / 7 = 11 / ?

Cross-multiply:
33 × ? = 7 × 11
→ 33x = 77
→ x = 77 ÷ 33
→ x = 7/3 ≈ 2.333...

But since this is likely expecting a simplified fraction or whole number, let’s check:

Actually, 33/7 = 11/x → divide both numerator and denominator on left by 3 → 11/(7/3) → so x = 7/3.

✔ Answer: 7/3 (or 2 1/3)

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## ✔ Problem 3:
20 / 15 = 48 / ?

Cross-multiply:
20 × ? = 15 × 48
→ 20x = 720
→ x = 720 ÷ 20
→ x = 36

✔ Answer: 36

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## ✔ Problem 4:
18 / 8 = 9 / ?

Cross-multiply:
18 × ? = 8 × 9
→ 18x = 72
→ x = 72 ÷ 18
→ x = 4

✔ Answer: 4

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## ✔ Problem 5:
35 / 42 = 7 / ?

Simplify 35/42 first → divide numerator and denominator by 7 → 5/6.

So 5/6 = 7/x → cross-multiply:
5x = 42
→ x = 42 ÷ 5
→ x = 8.4 or 42/5

Alternatively, from original:
35x = 42×7 = 294
→ x = 294 ÷ 35 = 8.4 → same.

✔ Answer: 42/5 or 8.4

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## ✔ Problem 6:
66 / 96 = 22 / ?

Simplify 66/96 → divide by 6 → 11/16 → so 11/16 = 22/x → multiply numerator by 2 → denominator must be 32.

Or cross-multiply:
66x = 96 × 22 = 2112
→ x = 2112 ÷ 66 = 32

✔ Answer: 32

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## ✔ Problem 7:
? / 16 = 22 / 64

Cross-multiply:
x × 64 = 16 × 22
→ 64x = 352
→ x = 352 ÷ 64 = 5.5 or 11/2

✔ Answer: 11/2 or 5.5

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## ✔ Problem 8:
4 / 10 = 36 / ?

Cross-multiply:
4x = 10 × 36 = 360
→ x = 360 ÷ 4 = 90

✔ Answer: 90

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## ✔ Problem 9:
15 / 40 = 9 / ?

Simplify 15/40 → 3/8 → so 3/8 = 9/x → multiply numerator by 3 → denominator must be 24.

Cross-multiply:
15x = 40 × 9 = 360
→ x = 360 ÷ 15 = 24

✔ Answer: 24

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## ✔ Problem 10:
45 / 25 = 81 / ?

Simplify 45/25 → 9/5 → so 9/5 = 81/x → 81 is 9×9 → so x = 5×9 = 45

Cross-multiply:
45x = 25 × 81 = 2025
→ x = 2025 ÷ 45 = 45

✔ Answer: 45

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## ✔ Problem 11:
48 / 24 = 20 / ?

Simplify 48/24 = 2 → so 2 = 20/x → x = 20 ÷ 2 = 10

✔ Answer: 10

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## ✔ Problem 12:
14 / 28 = 1 / ?

Simplify 14/28 = 1/2 → so 1/2 = 1/x → x = 2

✔ Answer: 2

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## 📝 Final Answers Summary:

1. 6
2. 7/3
3. 36
4. 4
5. 42/5 or 8.4
6. 32
7. 11/2 or 5.5
8. 90
9. 24
10. 45
11. 10
12. 2

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💡 Tip: You can also simplify fractions first before solving — it often makes the numbers easier!

Let me know if you’d like a printable version or step-by-step work shown for any specific problem!