Equivalent Fractions Worksheet 1: Name the equivalent fractions and draw a bar diagram to show a different equivalent fraction.

Let’s solve each problem step by step. We’re looking for equivalent fractions — that means different fractions that represent the same amount.

We’ll look at each pair of bars, figure out what fraction each shaded part represents, and then find a third equivalent fraction (and imagine drawing a bar diagram for it).

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Problem 1:

Top bar: 2 red parts out of 4 total → 2/4

Bottom bar: 4 red parts out of 8 total → 4/8

Are they equal? Yes! Because 2 ÷ 2 = 1, 4 ÷ 2 = 2 → so 2/4 = 1/2
And 4 ÷ 4 = 1, 8 ÷ 4 = 2 → so 4/8 = 1/2

So both are equal to 1/2

Another equivalent fraction? Let’s try 3/6 (because 3÷3=1, 6÷3=2 → also 1/2)

✔ So answers for #1:
First box: 2/4
Second box: 4/8
Third box: 1/2 or 3/6 (we’ll use 1/2 as simplest form)

But wait — the worksheet says “Name the equivalent fractions below” — meaning name the two shown, then draw/show a *different* one.

So we write the two given, then pick another equivalent.

Actually, let’s re-read: “Name the equivalent fractions below. Draw a bar diagram to show a different equivalent fraction?”

So for each number, there are two bars already drawn — we name those two fractions, then in the third box, we write a *different* equivalent fraction (and presumably draw a bar for it — but since we can’t draw here, we just write the fraction).

So for #1:

Bar 1: 2/4
Bar 2: 4/8
Different equivalent: 1/2 (or 3/6, 5/10, etc.)

We’ll go with 1/2 as the simplest.

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Problem 2:

Top bar: 2 yellow out of 3 → 2/3

Bottom bar: 6 yellow out of 9 → 6/9

Check if equal: 2/3 = ? 6/9 → divide numerator and denominator of 6/9 by 3 → 2/3 → yes!

Another equivalent? Try 4/6 (divide by 2 → 2/3) or 8/12, etc.

Let’s use 4/6

✔ Answers for #2:
2/3, 6/9, 4/6

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Problem 3:

Top bar: 2 yellow out of 8 → 2/8

Bottom bar: 1 yellow out of 4 → 1/4

Are they equal? 2/8 simplifies to 1/4 → yes!

Another equivalent? Try 3/12 (since 3÷3=1, 12÷3=4 → 1/4) or 4/16

Use 3/12

✔ Answers for #3:
2/8, 1/4, 3/12

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Problem 4:

Top bar: 3 green out of 4 → 3/4

Bottom bar: 9 green out of 12 → 9/12

Check: 9÷3=3, 12÷3=4 → 3/4 → yes!

Another equivalent? Try 6/8 (6÷2=3, 8÷2=4 → 3/4)

✔ Answers for #4:
3/4, 9/12, 6/8

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Problem 5:

Top bar: 1 blue out of 5 → 1/5

Bottom bar: 2 blue out of 10 → 2/10

Check: 2÷2=1, 10÷2=5 → 1/5 → yes!

Another equivalent? Try 3/15 or 4/20

Use 3/15

✔ Answers for #5:
1/5, 2/10, 3/15

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Problem 6:

Top bar: 8 purple out of 10 → 8/10

Bottom bar: 12 purple out of 15 → 12/15

Simplify both:

8/10 → divide by 2 → 4/5
12/15 → divide by 3 → 4/5 → yes, equal!

Another equivalent? Try 16/20 (16÷4=4, 20÷4=5 → 4/5) or 20/25

Use 16/20

✔ Answers for #6:
8/10, 12/15, 16/20

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Now, let’s compile all final answers clearly.

Final Answer:

1. 2/4, 4/8, 1/2
2. 2/3, 6/9, 4/6
3. 2/8, 1/4, 3/12
4. 3/4, 9/12, 6/8
5. 1/5, 2/10, 3/15
6. 8/10, 12/15, 16/20