# Multiply Whole Number by Fraction

In this post we will learn how to multiply a whole number by a fraction.

For this topic you should first have clear understanding of concept of whole numbers and fraction.

In this post we will discuss two method of multiplication. Understand both the method and start practicing each of them

## Multiplying Fractions and Whole Numbers

Understand that multiplication is a form of repeated addition

If we have to multiply 2 x 3, we can get answer by adding number 2 three times
⟹ 2 + 2 + 2
⟹ 6

we will use the same technique for multiplication with fraction

Let us understand the method with example

Example 01
Multiply 6 x \frac{1}{3}

To solve this, we add number \frac{1}{3} six times

\Longrightarrow \ \frac{1}{3} +\frac{1}{3} +\frac{1}{3} +\frac{1}{3} +\frac{1}{3} +\frac{1}{3} \\\ \\ \Longrightarrow \ \frac{6}{3}\\\ \\ \Longrightarrow \ \frac{1}{2}\

Hence \frac{1}{2} is the solution

Let us look at another example for conceptual clarity

Example 02
Multiply 4 x \frac{5}{3}

The question can be easily solved by adding \frac{5}{3} four times

\Longrightarrow \ \frac{5}{3} +\frac{5}{3} +\frac{5}{3} +\frac{5}{3}\\\ \\ \Longrightarrow \ \frac{20}{3}\\\ \\

Hence \frac{20}{3} is the solution

I hope you understood this method. Let’s move on to learn method 2.

### Fraction Simplification Method

You can multiply the fraction with whole number using following steps:

Step 01
Represent whole number as fraction by putting denominator 1

Step 02
Multiply the numerators of given numbers

Step 03
Multiply the denominator of given numbers

Step 04
Do the simplification of final number (if required)

Let us understand the multiplication of fraction with whole number using examples

Example 01
8 x \frac{1}{2}

Here whole number 8 is given to you.

We can represent the number 8 in the form of 8 boxes

Now multiply 8 by fraction \frac{1}{2}

To multiply the above number, do the following steps

(a) Represent whole number 8 in form of Fraction by putting denominator 1

⟹ 8 will be written as \frac{8}{1}

(b) write the math expression

\frac{8}{1} \times \frac{1}{2}

(c) Multiply the top numbers (numerator) and bottom number separately (denominator)

\Longrightarrow \frac{8}{1} \times \frac{1}{2}\\\ \\ \Longrightarrow \ \ \frac{8\times 1}{1\times 2}\\\ \\ \Longrightarrow \ \frac{8}{2}

(d) Simplify the expression further

\frac{8}{2} \ =\frac{4}{1}\

Number of boxes left after multiplication with fraction are:

Let us take another example for conceptual clarity

Example 02
Multiply 7 x \frac{3}{28}

Step 01:
Write the whole number as fraction
\frac{7}{1}

Step 02:
Multiply the numerator and denominator separately

\Longrightarrow \ \frac{7}{1} \ \times \frac{3}{28}\\\ \\ \Longrightarrow \ \frac{7\times \ 3}{1\times 28}\\\ \\ \Longrightarrow \ \frac{21}{28}

Step 03:
Further Simplification

Divide Numerator and Denominator by 7 to simplify the number

Hence \frac{3}{4} is the solution of given multiplication

I have explained both the method of multiplication of whole number with fraction.

In my opinion, method 2 is easy and straightforward as it requires less calculation. Try to practice both the method and then move on to solve worksheet questions given below

## Multiply Fractions by Whole Numbers Worksheets

Here we will solve some questions related to this topic.

All the questions are of Grade 5 Level.

Solution for each question is provided for your reference

### Simple Multiplication

A Whole number and a fraction is provided in the question.

You have to multiply the numbers and find the solution

(1) 9 x \frac{7}{10} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1

\frac{9}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{9}{1} \ \times \frac{7}{10}\\\ \\ \Longrightarrow \ \ \frac{63}{10}

Step 03: Simplify the result

The fraction cannot be simplified further

Hence \frac{63}{10} is the solution

(2) 3 x \frac{5}{6} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{3}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{3}{1} \ \times \frac{5}{6}\\\ \\ \Longrightarrow \ \ \frac{15}{6}

Step 03: Simplify the result

Divide numerator and denominator by 3

Hence \frac{5}{2} is the solution

(3) 11 x \frac{9}{22} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{11}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{11}{1} \ \times \frac{9}{22}\\\ \\ \Longrightarrow \ \ \frac{99}{22}

Step 03: Simplify the result

Divide numerator and denominator by 11

Hence \frac{9}{2} is the solution

(4) 9 x \frac{4}{6} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{9}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{9}{1} \ \times \frac{4}{6}\\\ \\ \Longrightarrow \ \ \frac{36}{6}

Step 03: Simplify the result

Divide numerator and denominator by 6

Hence \frac{6}{1} is the solution

(05) 20 x \frac{25}{4} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{20}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{20}{1} \ \times \frac{25}{4}\\\ \\ \Longrightarrow \ \ \frac{500}{4}

Step 03: Simplify the result

Divide numerator and denominator by 4

Hence \frac{125}{1} is the solution

(06) 7 x \frac{5}{10} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{7}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{7}{1} \ \times \frac{5}{10}\\\ \\ \Longrightarrow \ \ \frac{35}{10}

Step 03: Simplify the result

Divide numerator and denominator by 5

Hence \frac{7}{2} is the solution

(07) 9 x \frac{7}{10} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{9}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{9}{1} \ \times \frac{7}{10}\\\ \\ \Longrightarrow \ \ \frac{63}{10}

Step 03: Simplify the result

The fraction cannot be simplified further

Hence \frac{63}{10} is the solution

(08) 15 x \frac{5}{3} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{15}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{15}{1} \ \times \frac{5}{3}\\\ \\ \Longrightarrow \ \ \frac{75}{3}

Step 03: Simplify the result

Divide numerator and denominator by 3

Hence \frac{25}{1} is the solution

(09) 12 x \frac{12}{6}\\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{12}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{12}{1} \ \times \frac{12}{6}\\\ \\ \Longrightarrow \ \ \frac{144}{6}

Step 03: Simplify the result
Divide numerator and denominator by 6

Hence \frac{24}{1} is the solution

(10) 6 x \frac{3}{2} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{6}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{6}{1} \ \times \frac{3}{2}\\\ \\ \Longrightarrow \ \ \frac{18}{2}

Step 03: Simplify the result

Divide numerator and denominator by 2

Hence \frac{9}{1} is the solution

(11) 7 x \frac{5}{7} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{7}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{7}{1} \ \times \frac{5}{7}\\\ \\ \Longrightarrow \ \ \frac{35}{7}

Step 03: Simplify the result

Divide numerator and denominator by 7

Hence \frac{5}{1} is the solution

(12) 25 x \frac{5}{10} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{25}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{25}{1} \ \times \frac{5}{10}\\\ \\ \Longrightarrow \ \ \frac{125}{10}

Step 03: Simplify the result

Divide numerator and denominator by 5

Hence \frac{25}{2} is the solution

(13) 9 x \frac{10}{90} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{9}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{9}{1} \ \times \frac{10}{90}\\\ \\ \Longrightarrow \ \ \frac{90}{90}

Step 03: Simplify the result

Divide numerator and denominator by 90

Hence \frac{1}{1} is the solution

(14) 4 x \frac{3}{8} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{4}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{4}{1} \ \times \frac{3}{8}\\\ \\ \Longrightarrow \ \ \frac{12}{8}

Step 03: Simplify the result

Divide numerator and denominator by 4

Hence \frac{3}{2} is the solution

(15) 20 x \frac{1}{20} \\\ \\ Read Solution

Step 01: Convert whole number into fraction by showing denominator 1
\frac{20}{1}

Step 02: Multiply numerators and denominators separately

\Longrightarrow \ \ \frac{20}{1} \ \times \frac{1}{20}\\\ \\ \Longrightarrow \ \ \frac{20}{20}

Step 03: Simplify the result

Divide numerator and denominator by 20

Hence 1 is the solution

### Multiplication of fraction by whole number using number line

In the question a multiplication set is provided along with the number line.

You have to do the multiplication and find the final answer

(01) Below is the number line model of multiplication of 5 x \frac{1}{3}
Show the multiplication step by step

We know that multiplication is form of repeated addition

\Longrightarrow \ \ 5\ \times \frac{1}{3}\\\ \\ \Longrightarrow \ \ \frac{1}{3} +\frac{1}{3} +\frac{1}{3} +\frac{1}{3} +\frac{1}{3}\\\ \\ \Longrightarrow \ \ \frac{5}{3}\

(02) The model show product of 6 x \frac{1}{5}
Show the multiplication step by step and find the right answer

\Longrightarrow \ \ 6\ \times \frac{1}{5}\\\ \\ \Longrightarrow \ \ \frac{1}{5} +\frac{1}{5} +\frac{1}{5} +\frac{1}{5} +\frac{1}{5} +\frac{1}{5}\\\ \\ \Longrightarrow \ \ \frac{6}{5}\

(03) The model show following product on number line
⟹ 3 x \frac{1}{7}
Do the multiplication step by step

\Longrightarrow \ \ 3\ \times \frac{1}{7}\\\ \\ \Longrightarrow \ \ \frac{1}{7} +\frac{1}{7} +\frac{1}{7}\\\ \\ \Longrightarrow \ \ \frac{3}{7}

(04) Below is the number line model of following multiplication
⟹ 10 x \frac{1}{4}
Solve the multiplication step by step

\Longrightarrow \ \ 10\ \times \frac{1}{4}\\\ \\ \Longrightarrow \ \ \frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\ \frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\ \frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\ \frac{1}{4}\\\ \\ \Longrightarrow \ \ \frac{10}{4}\

(05) The model shows product of 5 x \frac{1}{9}
Solve the multiplication step by step