Ratio Worksheets | Ratio Worksheets for Teachers - Free Printable

Let’s go through each problem step by step.

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Section 1: Write two equivalent ratios.

Equivalent ratios are made by multiplying or dividing both numbers in the ratio by the same number.

For example, if you have 5/11, you can multiply top and bottom by 2 → 10/22, and by 3 → 15/33.

We’ll do this for each:

1) 5/11
→ Multiply by 2: (5×2)/(11×2) = 10/22
→ Multiply by 3: (5×3)/(11×3) = 15/33
✔ Two equivalent ratios: 10/22, 15/33

2) 7/8
→ ×2: 14/16
→ ×3: 21/24
✔ 14/16, 21/24

3) 7/4
→ ×2: 14/8
→ ×3: 21/12
✔ 14/8, 21/12

4) 11/5
→ ×2: 22/10
→ ×3: 33/15
✔ 22/10, 33/15

5) 4/5
→ ×2: 8/10
→ ×3: 12/15
✔ 8/10, 12/15

6) 8/5
→ ×2: 16/10
→ ×3: 24/15
✔ 16/10, 24/15

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Section 2: Determine whether the ratios are equivalent.

To check if two fractions are equivalent, cross-multiply:

If a/b and c/d are equivalent → a×d should equal b×c.

7) 8/7 and 9/7
Cross multiply: 8×7 = 56, 7×9 = 63 → 56 ≠ 63 → ✘ Not equivalent

8) 4/7 and 3/4
4×4 = 16, 7×3 = 21 → 16 ≠ 21 → ✘ Not equivalent

9) 7/5 and 11/3
7×3 = 21, 5×11 = 55 → 21 ≠ 55 → ✘ Not equivalent

10) 11/10 and 5/6
11×6 = 66, 10×5 = 50 → 66 ≠ 50 → ✘ Not equivalent

11) 5/7 and 9/2
5×2 = 10, 7×9 = 63 → 10 ≠ 63 → ✘ Not equivalent

12) 5/12 and 4/3
5×3 = 15, 12×4 = 48 → 15 ≠ 48 → ✘ Not equivalent

Wait — let me double-check #12. Maybe I misread?

5/12 vs 4/3 → 5×3=15, 12×4=48 → still not equal. So all are NOT equivalent? That seems odd, but mathematically correct.

Actually, looking again — maybe some ARE equivalent? Let me recheck #8: 4/7 and 3/4 → no. #9: 7/5 and 11/3 → no. All seem correctly calculated as not equivalent.

But wait — perhaps I made a mistake in interpretation? The question says “determine whether” — so answer is either “yes” or “no”.

So answers:

7) No
8) No
9) No
10) No
11) No
12) No

Hmm… that’s unusual for a worksheet to have all “no”, but based on calculation, it’s correct.

Alternatively, maybe I should write “not equivalent” for each.

But since the blank is just a line, probably expects “yes” or “no”.

I’ll stick with calculations.

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Section 3: Use equivalent ratios to find the unknown value.

Set up proportion and solve.

13) 2/9 = r/36

Cross multiply: 2 × 36 = 9 × r → 72 = 9r → r = 72 ÷ 9 = 8

✔ r = 8

14) k/24 = 11/8

Cross multiply: k × 8 = 24 × 11 → 8k = 264 → k = 264 ÷ 8 = 33

✔ k = 33

15) 2/5 = 8/z

Cross multiply: 2 × z = 5 × 8 → 2z = 40 → z = 40 ÷ 2 = 20

✔ z = 20

16) 3/2 = 15/z

Cross multiply: 3 × z = 2 × 15 → 3z = 30 → z = 30 ÷ 3 = 10

✔ z = 10

17) 9/8 = r/16

Cross multiply: 9 × 16 = 8 × r → 144 = 8r → r = 144 ÷ 8 = 18

✔ r = 18

18) 77/f = 11/7

Cross multiply: 77 × 7 = f × 11 → 539 = 11f → f = 539 ÷ 11 = 49

Check: 11 × 49 = 539? 10×49=490, 1×49=49 → 490+49=539 ✔

✔ f = 49

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Now compiling final answers:

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Final Answer:

1) 10/22, 15/33
2) 14/16, 21/24
3) 14/8, 21/12
4) 22/10, 33/15
5) 8/10, 12/15
6) 16/10, 24/15
7) No
8) No
9) No
10) No
11) No
12) No
13) 8
14) 33
15) 20
16) 10
17) 18
18) 49