Grade 5 Fractions Worksheets: Multiplying mixed numbers | Worsheets library - Free Printable

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

---

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} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} = \frac{9}{7} $
- Second row: Four $\frac{1}{7}$ parts → $ \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} = \frac{4}{7} $

So, the expression is:
$$
\frac{9}{7} + \frac{4}{7} = \frac{13}{7}
$$

Answer: $ \boxed{\frac{13}{7}} $

> This is an improper fraction. It can also be written as a mixed number: $ 1 \frac{6}{7} $, but unless asked, we keep it as an improper fraction.

---

#### b.
Two circles divided into 8 equal parts (since both have 8 sections).

- First circle: 3 shaded parts → $ \frac{3}{8} $
- Second circle: 2 shaded parts → $ \frac{2}{8} $

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

Answer: $ \boxed{\frac{5}{8}} $

---

Problem 2: Find the sum.

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

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

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

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

#### d. $ \frac{9}{16} + \frac{11}{16} = \frac{20}{16} = \frac{5}{4} $ (simplify: divide numerator and denominator by 4)

#### e. $ \frac{15}{18} + \frac{17}{18} = \frac{32}{18} = \frac{16}{9} $ (divide by 2)

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

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

---

Problem 3: Which of the following expressions will evaluate to $ \frac{3}{5} $?

Let’s evaluate each option:

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

First simplify: $ \frac{3}{6} = \frac{1}{2} $, $ \frac{3}{4} $ remains.

Find common denominator: LCD of 2 and 4 is 4.

$ \frac{1}{2} = \frac{2}{4} $, so:
$$
\frac{2}{4} + \frac{3}{4} = \frac{5}{4} \neq \frac{3}{5}
$$

✘ Not correct.

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

✔ Yes! This equals $ \frac{3}{5} $

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

LCD of 3 and 5 is 15.

$ \frac{1}{3} = \frac{5}{15}, \frac{1}{5} = \frac{3}{15} $

Sum: $ \frac{5}{15} + \frac{3}{15} = \frac{8}{15} \neq \frac{3}{5} $

✘ No.

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

✘ No.

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

---

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}} $

---

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

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

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

Answer: $ \boxed{\frac{16}{27}} $

---

✔ Final Answers Summary:

1. a. $ \frac{13}{7} $
b. $ \frac{5}{8} $

2. a. $ \frac{3}{4} $
b. $ \frac{8}{7} $
c. $ \frac{9}{11} $
d. $ \frac{5}{4} $
e. $ \frac{16}{9} $
f. $ \frac{5}{2} $

3. B. $ \frac{2}{10} + \frac{4}{10} $

4. $ \frac{2}{3} $

5. $ \frac{16}{27} $

Let me know if you'd like this formatted for printing or with visual models!