Math worksheet for solving simple proportions, including equivalent fraction checks and algebraic proportion problems.

Let’s solve each problem step by step. We’ll check if two ratios form a proportion (Part A), and then solve for x in proportions (Part B).

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Part A: Determine whether or not each pair of ratios is a proportion.

A proportion means the two fractions are equal — we can check by cross-multiplying. If the products are equal, it’s a proportion.

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1.) 3/5 and 8/24

Cross multiply:
3 × 24 = 72
5 × 8 = 40
72 ≠ 40 → Not a proportion

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2.) 9/6 and 9/10

Cross multiply:
9 × 10 = 90
6 × 9 = 54
90 ≠ 54 → Not a proportion

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3.) 18/44 and 9/2

Cross multiply:
18 × 2 = 36
44 × 9 = 396
36 ≠ 396 → Not a proportion

*(Wait — let me double-check that. Maybe I misread the numbers? The image says “18 over 44” and “9 over 2”. Yes, that’s correct. Not a proportion.)*

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4.) 3/2 and 27/18

Cross multiply:
3 × 18 = 54
2 × 27 = 54
54 = 54 → Yes, it IS a proportion

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5.) 4/2 and 28/14

Cross multiply:
4 × 14 = 56
2 × 28 = 56
56 = 56 → Yes, it IS a proportion

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6.) 5/8 and 15/18

Cross multiply:
5 × 18 = 90
8 × 15 = 120
90 ≠ 120 → Not a proportion

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7.) 8/6 and 4/3

Cross multiply:
8 × 3 = 24
6 × 4 = 24
24 = 24 → Yes, it IS a proportion

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8.) 24/32 and 27/36

Cross multiply:
24 × 36 = 864
32 × 27 = 864
864 = 864 → Yes, it IS a proportion

*(Note: You could also simplify both fractions first: 24/32 = 3/4, 27/36 = 3/4 — same thing!)*

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Part B: Solve for x in each proportion.

We use cross multiplication again, then solve for x.

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9.) 1/2 = x/50

Cross multiply:
1 × 50 = 2 × x
50 = 2x
Divide both sides by 2:
x = 25

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10.) 3/x = 10/20

First, simplify 10/20 to 1/2 → so 3/x = 1/2
Cross multiply:
3 × 2 = 1 × x
6 = x
→ x = 6

*(Or without simplifying: 3×20 = 10×x → 60 = 10x → x=6 — same answer.)*

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11.) 5/x = 22/33

Simplify 22/33 → divide numerator and denominator by 11 → 2/3
So 5/x = 2/3
Cross multiply:
5 × 3 = 2 × x
15 = 2x
x = 15 ÷ 2 = 7.5

*(Or as fraction: x = 15/2)*

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12.) 1/x = 7/63

Simplify 7/63 → divide by 7 → 1/9
So 1/x = 1/9 → x = 9

*(Or cross multiply: 1×63 = 7×x → 63 = 7x → x=9)*

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13.) 3/5 = x/60

Cross multiply:
3 × 60 = 5 × x
180 = 5x
x = 180 ÷ 5 = 36

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14.) 10/x = 13/26

Simplify 13/26 → 1/2
So 10/x = 1/2
Cross multiply:
10 × 2 = 1 × x
20 = x
→ x = 20

*(Without simplifying: 10×26 = 13×x → 260 = 13x → x=20 — same.)*

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15.) 5/7 = 48/54

Wait — this one doesn’t have an x? Let me check the original image.

Looking back: Problem 15 is written as “5/7 = 48/54” — but there’s no variable. That might be a typo? Or maybe it’s asking if it’s a proportion?

But Part B says “Solve for x”, so likely it should be “5/7 = x/54” or something similar.

Wait — looking at the image again (from your upload description):

Actually, in the user’s image, problem 15 is:

> 15.) 5/7 = 48/54

That has no x. But Part B says “Solve for x”. So perhaps it’s a mistake? Or maybe it’s meant to be checked like Part A?

But since it’s listed under Part B (“Solve for x”), and there’s no x, I think it’s likely a typo. However, looking closely at the original image you provided (in text form), problem 15 is:

> 15.) 5/7 = 48/54

This is probably meant to be solved as a proportion check — but since it’s in Part B, maybe it’s supposed to be “5/7 = x/54”? Let me assume that’s the case, because otherwise it doesn’t make sense.

Alternatively, maybe it’s “5/x = 48/54”? Let me check standard patterns.

Looking at other problems: #14 is “10/x = 13/26”, #16 is “5/x = 10/22”

So likely, #15 is meant to be “5/x = 48/54” — that would fit.

I’ll go with that assumption: 5/x = 48/54

Simplify 48/54 → divide by 6 → 8/9

So 5/x = 8/9

Cross multiply:
5 × 9 = 8 × x
45 = 8x
x = 45 ÷ 8 = 5.625 or 45/8

But let’s verify with original numbers:

5/x = 48/54
Cross multiply: 5 × 54 = 48 × x
270 = 48x
x = 270 ÷ 48

Simplify: divide numerator and denominator by 6 → 45/8 → same as above.

So x = 45/8 or 5.625

But wait — maybe the problem was written correctly as “5/7 = 48/54” and it’s actually a trick question? Let’s check if it’s a proportion:

5/7 vs 48/54 → cross multiply: 5×54=270, 7×48=336 → not equal → not a proportion.

But again, Part B says “solve for x”, so unless x is missing, it doesn’t fit.

Given the pattern, I believe it’s a typo and should be “5/x = 48/54”. I’ll proceed with that.

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16.) 5/x = 10/22

Simplify 10/22 → 5/11

So 5/x = 5/11 → x = 11

*(Or cross multiply: 5×22 = 10×x → 110 = 10x → x=11)*

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Now, compiling all answers:

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Final Answer:

Part A:
1.) No
2.) No
3.) No
4.) Yes
5.) Yes
6.) No
7.) Yes
8.) Yes

Part B:
9.) x = 25
10.) x = 6
11.) x = 7.5 or 15/2
12.) x = 9
13.) x = 36
14.) x = 20
15.) x = 45/8 or 5.625 *(assuming problem is 5/x = 48/54)*
16.) x = 11

*(Note: For problem 15, if the original was indeed "5/7 = 48/54" with no x, then it's not solvable for x — but given context, I assumed a typo. If your teacher wrote it differently, please clarify.)*