# Product of a Fraction and a Whole Number: Problem Type 2

In this lesson, we solve problems where we find the product of a fraction and a whole number.

**Rules for finding the product of a fraction and a whole number**

We first write the whole number as a fraction, i.e., we write it divided by one; for example 5 is written as 5/1.

We then multiply the numerators and then the denominators of both fractions to get the product fraction.

If any simplification or cross cancelling is required, it is done and final answer is written.

**Example**

Multiply $\frac{3}{8}$ × 5

**Solution**

**Step 1:**

First, we write the whole number 5 as a fraction $\frac{5}{1}$

**Step 2:**

$\frac{3}{8}$ × 5 = $\frac{3}{8}$ × $\frac{5}{1}$

**Step 3:**

Multiply the numerators and denominators of both fractions as follows.

$\frac{3}{8}$ × $\frac{5}{1}$ = $\frac{(3 × 5)}{(8 × 1)}$ = $\frac{15}{8}$

**Step 4:**

So $\frac{3}{8}$ × 5 = $\frac{15}{8}$

Multiply $\frac{2}{15}$ × 5

### Solution

**Step 1:**

First, we write the whole number 5 as a fraction $\frac{5}{1}$

$\frac{2}{15}$ × 5 = $\frac{2}{15}$ × $\frac{5}{1}$

**Step 2:**

As 5 and 15 are multiples of 5, cross cancelling 5 and 15, we get

$\frac{2}{3}$ × $\frac{1}{1}$

**Step 3:**

Multiply the numerators and denominators of both fractions as follows.

$\frac{2}{3}$ × $\frac{1}{1}$ = $\frac{(2 × 1)}{(3 × 1)}$ = $\frac{2}{3}$

**Step 4:**

So $\frac{2}{15}$ × 5 = $\frac{2}{3}$

Multiply $\frac{3}{7}$ × 2

### Solution

**Step 1:**

First, we write the whole number 2 as a fraction $\frac{2}{1}$

$\frac{3}{7}$ × 2 = $\frac{3}{7}$ × $\frac{2}{1}$

**Step 2:**

Multiply the numerators and denominators of both fractions as follows.

$\frac{3}{7}$ × $\frac{2}{1}$ = $\frac{(3 × 2)}{(7 × 1)}$ = $\frac{6}{7}$

**Step 3:**

So $\frac{3}{7}$ × 2 = $\frac{6}{7}$