- Multiply and Divide Fractions
- Home
- Product of a Unit Fraction and a Whole Number
- Product of a Fraction and a Whole Number: Problem Type 1
- Introduction to Fraction Multiplication
- Fraction Multiplication
- Product of a Fraction and a Whole Number Problem Type 2
- Determining if a Quantity is Increased or Decreased When Multiplied by a Fraction
- Modeling Multiplication of Proper Fractions
- Multiplication of 3 Fractions
- Word Problem Involving Fractions and Multiplication
- The Reciprocal of a Number
- Division Involving a Whole Number and a Fraction
- Fraction Division
- Fact Families for Multiplication and Division of Fractions
- Modeling Division of a Whole Number by a Fraction
- Word Problem Involving Fractions and Division

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Product of a Fraction and a Whole Number: Problem Type 1

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 $\frac{5}{4}$ × 8

**Solution**

**Step 1:**

First, we write the whole number 8 as a fraction $\frac{8}{1}$

**Step 2:**

$\frac{5}{4}$ × 8 = $\frac{5}{4}$ × $\frac{8}{1}$

**Step 3:**

As 4 and 8 are multiples of 8, cross cancelling 4 and 8, we get

$\frac{5}{4}$ × $\frac{8}{1}$ = $\frac{5}{1}$ × $\frac{2}{1}$

**Step 4:**

Multiply the numerators and denominators of both fractions as follows.

$\frac{5}{1}$ × $\frac{2}{1}$ = $\frac{(5 × 2)}{(1 × 1)}$ = $\frac{10}{1}$ = 10

**Step 5:**

So $\frac{5}{4}$ × 8 = 10

Multiply $\frac{4}{5}$ × 15

### Solution

**Step 1:**

First, we write the whole number 15 as a fraction $\frac{15}{1}$

**Step 2:**

$\frac{4}{5}$ × 15 = $\frac{4}{5}$ × $\frac{15}{1}$

**Step 3:**

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

$\frac{4}{5}$ × $\frac{15}{1}$ = $\frac{4}{1}$ × $\frac{3}{1}$

**Step 4:**

We multiply the numerators and denominators of both fractions as follows.

$\frac{4}{1}$ × $\frac{3}{1}$ = $\frac{(4 × 3)}{(1 × 1)}$ = $\frac{12}{1}$ = 12

**Step 5:**

So $\frac{4}{5}$ × 15 = 12

Multiply $\frac{3}{7}$ × 14

### Solution

**Step 1:**

First, we write the whole number 14 as a fraction $\frac{14}{1}$

**Step 2:**

$\frac{3}{7}$ × 14 = $\frac{3}{7}$ × $\frac{14}{1}$

**Step 3:**

As 7 and 14 are multiples of 7, cross cancelling 7 and 14, we get

$\frac{3}{7}$ × $\frac{14}{1}$ = $\frac{3}{1}$ × $\frac{2}{1}$

**Step 4:**

Multiply the numerators and denominators of both fractions as follows.

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

**Step 5:**

So $\frac{3}{7}$ × 14 = 6