5th Grade Common Core Math Worksheets - Free Printable

Let's solve each problem step by step and provide clear explanations.

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Problem 1: Use the model shown below to write an addition or subtraction expression. Find the value of the expression.

#### a.
We are given two rows of fractions:

- First row: Nine $\frac{1}{7}$ parts → $ \frac{1}{7} + \frac{1}{7} + \cdots + \frac{1}{7} $ (9 times)
- Second row: Four $\frac{1}{7}$ parts → $ \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} $

So, the expression is:
$$
\frac{9}{7} + \frac{4}{7}
$$

Since they have the same denominator, add the numerators:
$$
\frac{9 + 4}{7} = \frac{13}{7}
$$

This can be written as a mixed number:
$$
\frac{13}{7} = 1 \frac{6}{7}
$$

✔ Answer for 1a: $ \boxed{\frac{13}{7}} $ or $ \boxed{1 \frac{6}{7}} $

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#### b.
Two circles divided into 8 equal parts.

- First circle: 5 out of 8 parts shaded → $ \frac{5}{8} $
- Second circle: 2 out of 8 parts shaded → $ \frac{2}{8} $

Expression:
$$
\frac{5}{8} + \frac{2}{8} = \frac{7}{8}
$$

✔ Answer for 1b: $ \boxed{\frac{7}{8}} $

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Problem 2: Find the sum.

All these are like fractions (same denominators), so just add numerators.

#### a. $ \frac{2}{4} + \frac{1}{4} = \frac{3}{4} $

#### b. $ \frac{5}{7} + \frac{3}{7} = \frac{8}{7} = 1 \frac{1}{7} $

#### c. $ \frac{4}{11} + \frac{5}{11} = \frac{9}{11} $

#### d. $ \frac{9}{16} + \frac{11}{16} = \frac{20}{16} = \frac{5}{4} = 1 \frac{1}{4} $

#### e. $ \frac{15}{18} + \frac{17}{18} = \frac{32}{18} = \frac{16}{9} = 1 \frac{7}{9} $

#### f. $ \frac{1}{2} + \frac{4}{2} = \frac{5}{2} = 2 \frac{1}{2} $

✔ Answers:
- a. $ \boxed{\frac{3}{4}} $
- b. $ \boxed{\frac{8}{7}} $ or $ \boxed{1 \frac{1}{7}} $
- c. $ \boxed{\frac{9}{11}} $
- d. $ \boxed{\frac{5}{4}} $ or $ \boxed{1 \frac{1}{4}} $
- e. $ \boxed{\frac{16}{9}} $ or $ \boxed{1 \frac{7}{9}} $
- f. $ \boxed{\frac{5}{2}} $ or $ \boxed{2 \frac{1}{2}} $

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Problem 3: Which expression evaluates to $ \frac{3}{5} $?

Let’s evaluate each option:

#### A. $ \frac{3}{6} + \frac{3}{4} $

Simplify: $ \frac{1}{2} + \frac{3}{4} = \frac{2}{4} + \frac{3}{4} = \frac{5}{4} $ → Not $ \frac{3}{5} $

#### B. $ \frac{2}{10} + \frac{4}{10} = \frac{6}{10} = \frac{3}{5} $ ✔

This matches!

#### C. $ \frac{1}{3} + \frac{1}{5} $

LCM of 3 and 5 is 15:
$$
\frac{5}{15} + \frac{3}{15} = \frac{8}{15} \neq \frac{3}{5}
$$

#### D. $ \frac{2}{10} + \frac{3}{10} = \frac{5}{10} = \frac{1}{2} \neq \frac{3}{5} $

✔ Answer: B. $ \boxed{\frac{2}{10} + \frac{4}{10}} $

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Problem 4: Fraction of trees that are mango or apple trees

Given:
- Mango trees: $ \frac{5}{12} $
- Apple trees: $ \frac{3}{12} $

Add them:
$$
\frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3}
$$

✔ Answer: $ \boxed{\frac{2}{3}} $

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Problem 5: What fraction of the story book was already read by Olivia?

She read:
- Morning: $ \frac{5}{27} $
- Evening: $ \frac{11}{27} $

Total read:
$$
\frac{5}{27} + \frac{11}{27} = \frac{16}{27}
$$

✔ Answer: $ \boxed{\frac{16}{27}} $

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✔ Final Answers Summary:

1a. $ \frac{13}{7} $ or $ 1 \frac{6}{7} $
1b. $ \frac{7}{8} $
2a. $ \frac{3}{4} $
2b. $ \frac{8}{7} $ or $ 1 \frac{1}{7} $
2c. $ \frac{9}{11} $
2d. $ \frac{5}{4} $ or $ 1 \frac{1}{4} $
2e. $ \frac{16}{9} $ or $ 1 \frac{7}{9} $
2f. $ \frac{5}{2} $ or $ 2 \frac{1}{2} $
3. B
4. $ \frac{2}{3} $
5. $ \frac{16}{27} $

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