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

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.

(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

= \(\frac{3 ×15}{4}\)

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

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

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

= \(\frac{4 × 2 + 1}{2}\) of 3

= \(\frac{9}{2}\) × 3

= \(\frac{9 × 3}{2}\)

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

= 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

= \(\frac{29 × 7}{2}\)

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

= 101\(\frac{1}{2}\)**5.** 6\(\frac{2}{7}\) of 4

= \(\frac{6 × 7 + 2}{7}\) of 4

= \(\frac{44}{7}\) × 4

= \(\frac{44 × 4}{7}\)

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

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

**6.** 18\(\frac{1}{4}\) × 12

= \(\frac{18 × 4 + 1}{4}\) × 12

= \(\frac{73}{4}\) × 12

= \(\frac{73 × 12}{4}\)

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

= 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.**

**● ****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.**

**● ****Worksheet
on Word Problems on Fractions.**

**5th Grade Numbers **

**5th Grade Math Problems **

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