- Mixed numbers
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- Writing a mixed number and an improper fraction for a shaded region
- Writing an improper fraction as a mixed number
- Writing a mixed number as an improper fraction
- Mixed number multiplication
- Multiplication of a mixed number and a whole number
- Division with a mixed number and a whole number
- Mixed number division
- Word problem involving multiplication or division with mixed numbers

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In this lesson, we are dealing with multiplication of a mixed number with another fraction.

**Rules for mixed number multiplication**

First, the mixed number is converted into an improper fraction and then multiplied with the given fraction.

The numerators of the two fractions are multiplied at the top and the denominators are multiplied at the bottom to get the resulting fraction.

Simplification is done, if required, the fraction is converted into a mixed fraction in simplest form.

Multiply. Write your answer as a mixed number in simplest form.

$2\frac{2}{5} \times \frac{3}{4}$

**Step 1:**

First, we write the mixed number $2\frac{2}{5}$ as an improper fraction

$2\frac{2}{5} = \frac{\left ( 2 \times 5 + 2 \right )}{5} = \frac{12}{5}$

**Step 2:**

$2\frac{2}{5} \times \frac{3}{4} = \frac{12}{5} \times \frac{3}{4}$

**Step 3:**

Cross cancelling 12 and 4 we get

$\frac{12}{5} \times \frac{3}{4} = \frac{3}{5} \times \frac{3}{1} = \frac{(3 \times 3)}{(5 \times 1)} = \frac{9}{5}$

**Step 4:**

$\frac{9}{5}$ can be written as a mixed number as follows

$\frac{9}{5} = 1\frac{4}{5}$

**Step 5:**

So, $2\frac{2}{5} \times \frac{3}{4} = 1\frac{4}{5}$

Multiply. Write your answer as a mixed number in simplest form.

$1\frac{4}{5} \times \frac{2}{3}$

**Step 1:**

First, we write the mixed number $1\frac{4}{5}$ as an improper fraction $1\frac{4}{5} = \frac{\left ( 1 \times 5 + 4 \right )}{5} = \frac{9}{5}$

**Step 2:**

$1\frac{4}{5} \times \frac{2}{3} = \frac{9}{5} \times \frac{2}{3}$

**Step 3:**

Cross cancelling 9 and 3 we get

$\frac{9}{5} \times \frac{2}{3} = \frac{3}{5} \times \frac{2}{1} = \frac{(3 \times 2)}{(5 \times 1)} = \frac{6}{5}$

**Step 4:**

$\frac{6}{5}$ can be written as a mixed number as follows

$\frac{6}{5} = 1\frac{1}{5}$

**Step 5:**

So, $1\frac{4}{5} \times \frac{2}{3} = 1\frac{1}{5}$

Multiply. Write your answer as a mixed number in simplest form.

$3\frac{2}{5} \times \frac{1}{4}$

**Step 1:**

First, we write the mixed number $3\frac{2}{5}$ as an improper fraction $3\frac{2}{5} = \frac{\left ( 3 \times 5 + 2 \right )}{5} = \frac{17}{5}$

**Step 2:**

$3\frac{2}{5} \times \frac{1}{4} = \frac{17}{5} \times \frac{1}{4}$

**Step 3:**

Simplifying

$\frac{17}{5} \times \frac{1}{4} = \frac{(17 \times 1)}{(5 \times 4)} = \frac{17}{20}$

**Step 4:**

So, $3\frac{2}{5} \times \frac{1}{4} = \frac{17}{20}$

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