- 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
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# Product of a Unit Fraction and a Whole Number

A unit **fraction **is a fraction whose numerator is always 1 and whose denominator is a positive integer.

For **example**, following are some **unit fractions** $\frac{1}{2}$, $\frac{1}{9}$, $\frac{1}{16}$, $\frac{1}{47}$ and so on.

**Rules to find the product of a unit fraction and a whole number**

We first write the whole number as a fraction, i.e., writing it divided by one; for example: 7 is written as $\frac{7}{1}$

We then multiply the numerators

We multiply the denominators

If any simplification is required, it is done and then we write the final fraction.

What is $\frac{1}{2}$ of 6

### Solution

**Step 1:**

$\frac{1}{2}$ of 6 is $\frac{1}{2}$ × 6

**Step 2:**

First, we write the whole number 6 as a fraction $\frac{6}{1}$

$\frac{1}{2}$ × 6 = $\frac{1}{2}$ × $\frac{6}{1}$

**Step 3:**

As 2 and 6 are multiples of 2, cross cancelling 2 and 6, we get

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

**Step 4:**

Multiply the numerators and denominators of both fractions as follows.

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

**Step 5:**

So $\frac{1}{2}$ of 6 = 3

What is $\frac{1}{4}$ of 16

### Solution

**Step 1:**

$\frac{1}{4}$ of 16 is $\frac{1}{4}$ × 16

**Step 2:**

First, we write the whole number 16 as a fraction $\frac{16}{1}$

$\frac{1}{4}$ × 16 = $\frac{1}{4}$ × $\frac{16}{1}$

**Step 3:**

As 4 and 16 are multiples of 4, cross cancelling 4 and 16, we get

$\frac{1}{4}$ × $\frac{16}{1}$ = $\frac{1}{1}$ × $\frac{4}{1}$

**Step 4:**

Multiply the numerators and denominators of both fractions as follows.

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

**Step 5:**

So $\frac{1}{4}$ of 16 = 4