Adding fractions: bar models - Fraction Worksheets for Year 3 (age ... - Free Printable

Let's solve each of the fraction addition problems using the bar models provided in the worksheet. The bar models visually represent fractions, where each bar is divided into equal parts, and colored sections show the value of each fraction.

We will go through each problem step by step, determine the fractions from the bar model, add them, and fill in the blanks.

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1.

Bar: 5 parts total → 2 blue + 1 yellow = 3 shaded
$$
\frac{2}{5} + \frac{1}{5} = \frac{3}{5}
$$

✔ Answer: $ \frac{3}{5} $

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2.

Bar: 5 parts total → 2 blue + 2 yellow = 4 shaded
$$
\frac{2}{5} + \frac{2}{5} = \frac{4}{5}
$$

✔ Answer: $ \frac{4}{5} $

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3.

Bar: 6 parts total → 2 blue + 1 yellow = 3 shaded
So:
$$
\frac{2}{6} + \frac{1}{6} = \frac{3}{6}
$$

✔ Answer: $ \frac{3}{6} $ (can simplify to $ \frac{1}{2} $, but keep as $ \frac{3}{6} $ unless asked)

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4.

Bar: 5 parts total → 3 blue + 2 yellow = 5 shaded
$$
\frac{3}{5} + \frac{2}{5} = \frac{5}{5} = 1
$$

✔ Answer: $ \frac{5}{5} $ or $ 1 $

But since it's a fraction addition, write $ \frac{5}{5} $

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5.

Bar: 8 parts total → 1 blue + 4 yellow = 5 shaded
$$
\frac{1}{8} + \frac{4}{8} = \frac{5}{8}
$$

✔ Answer: $ \frac{5}{8} $

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6.

Bar: 7 parts total → 1 blue + 4 yellow = 5 shaded
$$
\frac{1}{7} + \frac{4}{7} = \frac{5}{7}
$$

✔ Answer: $ \frac{5}{7} $

Wait — let’s double-check: the bar has 7 parts? Let's count:

- Blue: 1 part
- Yellow: 4 parts
- Total shaded: 5 parts
- So yes: $ \frac{1}{7} + \frac{4}{7} = \frac{5}{7} $

✔ Answer: $ \frac{5}{7} $

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7.

Bar: 9 parts total → 4 blue + 3 yellow = 7 shaded
$$
\frac{4}{9} + \frac{3}{9} = \frac{7}{9}
$$

✔ Answer: $ \frac{7}{9} $

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8.

Bar: 8 parts total → 3 blue + 4 yellow = 7 shaded
$$
\frac{3}{8} + \frac{4}{8} = \frac{7}{8}
$$

✔ Answer: $ \frac{7}{8} $

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9.

Bar: 8 parts total → 4 blue + 2 yellow = 6 shaded
$$
\frac{4}{8} + \frac{2}{8} = \frac{6}{8}
$$

✔ Answer: $ \frac{6}{8} $ (can simplify to $ \frac{3}{4} $, but again, keep as $ \frac{6}{8} $ if not simplified)

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10.

Bar: 8 parts total → 3 blue + 5 yellow = 8 shaded
$$
\frac{3}{8} + \frac{5}{8} = \frac{8}{8} = 1
$$

✔ Answer: $ \frac{8}{8} $

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✔ Final Answers:

| Problem | Addition | Answer |
|--------|--------------------|------------|
| 1 | $ \frac{2}{5} + \frac{1}{5} $ | $ \frac{3}{5} $ |
| 2 | $ \frac{2}{5} + \frac{2}{5} $ | $ \frac{4}{5} $ |
| 3 | $ \frac{2}{6} + \frac{1}{6} $ | $ \frac{3}{6} $ |
| 4 | $ \frac{3}{5} + \frac{2}{5} $ | $ \frac{5}{5} $ |
| 5 | $ \frac{1}{8} + \frac{4}{8} $ | $ \frac{5}{8} $ |
| 6 | $ \frac{1}{7} + \frac{4}{7} $ | $ \frac{5}{7} $ |
| 7 | $ \frac{4}{9} + \frac{3}{9} $ | $ \frac{7}{9} $ |
| 8 | $ \frac{3}{8} + \frac{4}{8} $ | $ \frac{7}{8} $ |
| 9 | $ \frac{4}{8} + \frac{2}{8} $ | $ \frac{6}{8} $ |
| 10 | $ \frac{3}{8} + \frac{5}{8} $ | $ \frac{8}{8} $ |

> 💡 Note: All fractions are added with like denominators, so we just add the numerators. The bar models help visualize how many parts are being added.

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✔ How to Fill in the Blanks:

For each question, you need to fill in the missing numerator and denominator based on the bar model.

Example for #1:
- First fraction: $ \frac{2}{5} $
- Second: $ \frac{1}{5} $
- Sum: $ \frac{3}{5} $

So, the blank is filled as:
$ \frac{2}{5} + \frac{1}{5} = \frac{3}{5} $

Similarly for others.

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Let me know if you'd like this formatted as a completed worksheet!