Multiplication of Fractional Number by a Whole Number

We will discuss here about the multiplication of fractional number by a whole number.

\(\frac{1}{4}\) is multiplied by 4 or 4 \(\frac{1}{4}\) = 4 of \(\frac{1}{4}\)

This is Whole Part

Suppose this is whole (1)

This is One Fourth Part

This is the one fourth of 1 that is  \(\frac{1}{4}\)

This is 1 Part

So, this figure shows 4 of \(\frac{1}{4}\) or \(\frac{1}{4}\). (Since, 4 × \(\frac{1}{4}\) = \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\))

Therefore, 4 × \(\frac{1}{4}\) = \(\frac{4}{1}\) × \(\frac{1}{4}\) = \(\frac{4 × 1}{1 × 4}\) = \(\frac{4}{4}\) = 1

Hence we conclude that, to multiply a fraction by a whole number, the numerator of the fraction is multiplied by the whole number. This becomes the numerator of the product. The denominator does not change.

The following rules are given below for the multiplication of a fraction by a whole number:

(a) If the fraction is a mixed fraction, convert it to improper fraction.

Multiplication of Fractional Number by a Whole Number



(c) Always write the answer as a mixed fraction if it is not a proper fraction/whole number.


Solved examples on multiplication of fractional number by a whole number:

1. \(\frac{3}{4}\) × 15

Multiplication of Fractional Number by a Whole Number



= \(\frac{3 ×15}{4}\)

= \(\frac{45}{4}\)

Multiplication of Fractional Number by a Whole Number








= 11\(\frac{1}{4}\)



2. 4\(\frac{1}{2}\) of 3

= \(\frac{4 × 2 + 1}{2}\) of 3

= \(\frac{9}{2}\) × 3

= \(\frac{9 × 3}{2}\)

= \(\frac{27}{2}\)

Multiplication of Fractional Number by a Whole Number








= 13\(\frac{1}{2}\)

Note: ‘Of‘ stands for multiplication.


3. \(\frac{9}{3}\) × 5

= \(\frac{9 × 5}{3}\)

= \(\frac{45}{3}\)

= 15



4. 14\(\frac{1}{2}\) of 7

= \(\frac{14 × 2 + 1}{2}\) of 7

= \(\frac{29}{2}\) × 7

= \(\frac{29 × 7}{2}\)

= \(\frac{203}{2}\)

Multiplication of Fractional Number by a Whole Number







= 101\(\frac{1}{2}\)



5. 6\(\frac{2}{7}\) of 4

= \(\frac{6 × 7 + 2}{7}\) of 4

= \(\frac{44}{7}\) × 4

= \(\frac{44 × 4}{7}\)

= \(\frac{176}{7}\)

Multiplication of Fractional Number by a Whole Number








= 25\(\frac{1}{7}\)



6. 18\(\frac{1}{4}\) × 12

= \(\frac{18 × 4 + 1}{4}\) × 12

= \(\frac{73}{4}\) × 12

= \(\frac{73 × 12}{4}\)

= \(\frac{876}{4}\)

Multiplication of Fractional Number by a Whole Number










= 219



Multiplication is Repeated Addition.

Multiplication of Fractional Number by a Whole Number.

Multiplication of a Fraction by Fraction.

Properties of Multiplication of Fractional Numbers.

Multiplicative Inverse.

Worksheet on Multiplication on Fraction.

Division of a Fraction by a Whole Number.

Division of a Fractional Number.

Division of a Whole Number by a Fraction.

Properties of Fractional Division.

Worksheet on Division of Fractions.

Simplification of Fractions.

Worksheet on Simplification of Fractions.

Word Problems on Fraction.

Worksheet on Word Problems on Fractions.





5th Grade Numbers

5th Grade Math Problems

From Multiplication of Fractional Number by a Whole Number to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Dec 01, 23 01:16 AM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  2. Days of the Week | 7 Days of the Week | What are the Seven Days?

    Nov 30, 23 10:59 PM

    Days of the Weeks
    We know that, seven days of a week are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. A day has 24 hours. There are 52 weeks in a year. Fill in the missing dates and answer the questi…

    Read More

  3. Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical

    Nov 30, 23 01:08 PM

    Types of Lines
    What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver…

    Read More