## Arithmetic Chapter 5 Multiplication And Division Of A Number And By Fraction

**Arithmetic Chapter 5 the Rule Of Multiplication Of A Fraction By Whole Number**

**1. Multiplication of a proper fraction by the whole number**

- We know that 2/7 is a proper fraction (v the numerator < the denomination).
- Suppose we have to multiply this proper fraction by any whole number say 7.
- So the mathematical problem is 2/7 x 7 = What is the value?
- Here the rule is:

A proper fraction x the whole number = \(\frac{The number of the proper fraction x whole number}{The denominator of the proper fraction}\)

According to the above rule, \(\frac{2}{7} \times 7\)

= 2

**1. Similarly \(\frac{5}{6} \times 8\)**

= \(\frac{5 \times 8}{6}\)

= \(\frac{5 \times 4}{3}\)

= 20/3

= \(6 \frac{2}{3}\)

\(\frac{5}{6} \times 8\) = \(6 \frac{2}{3}\)

**2. similarly \(\frac{11}{14} \times 21\)**

= \(\frac{11}{14} \times 21\)

= \(\frac{11 \times 21}{14}\)

= \(\frac{11 \times 3}{2}\)

= 33/2

= \(16 \frac{1}{2}\)

\(\frac{11}{14} \times 21\) = \(16 \frac{1}{2}\)

**3. similarly \(\frac{17}{25} \times 35\)**

= \(\frac{17}{25} \times 35\)

= \(\frac{17 \times 35}{25}\)

= \(\frac{17 \times 7}{5}\)

= 119/5

= \(23 \frac{4}{5}\)

\(\frac{17}{25} \times 35\) = \(23 \frac{4}{5}\)

**2. ** **Multiplication of an improper fraction by the whole number :**

- We know that “ is an improper fraction (v the numerator > the denominator).
- Suppose we have to multiply this improper fraction by any whole number say 15.
- So the mathematical problem is:

Here also the rule is: The fraction x whole number = \(\frac{The numerator of the fraction x whole number}{The denominator of the fraction}\)

According to the above rule,

= \(\frac{8}{5} \times 15\)

= \(\frac{8 \times 15}{5}\)

= 8 x 3

= 24

**1. Similarly \(\frac{11}{7} \times 4\)**

= \(\frac{11}{7} \times 4\)

= \(\frac{11 \times 4}{7}\)

= 44/7

= \(4 \frac{2}{7}\)

\(\frac{11}{7} \times 4\) = \(4 \frac{2}{7}\)

**2. Similarly \(\frac{15}{4} \times 9\)**

= \(\frac{15}{4} \times 9\)

= \(\frac{15 \times 9}{4}\)

= 135/2

= \(33 \frac{3}{4}\)

\(\frac{15}{4} \times 9\) = \(33 \frac{3}{4}\)

**3. Similarly \(\frac{24}{8} \times 14\)**

= \(\frac{24}{8} \times 14\)

= \(\frac{21 \times 14}{8}\)

= 147/4

= \(36 \frac{3}{4}\)

\(\frac{24}{8} \times 14\) = \(36 \frac{3}{4}\)

**3. Multiplication of a mixed fraction or a complex fraction by a whole number :**

- To multiply a mixed fraction or a complex fraction by a whole number, first, we have to convert the given fraction to the improper fraction and then according to the rule of 5.1.B.
- The multiplication is to be completed.

**1. For Example \(5 \frac{1}{3} \times 7\)**

= \(5 \frac{1}{3} \times 7\)

= \(\frac{16}{3} \times 7\)

= \(\frac{16 \times 7}{3}\)

= 112/3

= \(37 \frac{1}{3}\)

\(5 \frac{1}{3} \times 7\) = \(37 \frac{1}{3}\)

**2. For Example \(7 \frac{1}{2} \times 12\)**

= \(7 \frac{1}{2} \times 12\)

= \(\frac{15}{2} \times 12\)

= \(\frac{15 \times 12}{2}\)

= 15 x 6

= 90

\(7 \frac{1}{2} \times 12\) = 90

**3. For Example \(\frac{\frac{3}{4}}{\frac{5}{7}} \times 14\)**

= \(\frac{\frac{3}{4}}{\frac{5}{7}} \times 14\)

= \(\left(\frac{3}{4} \times \frac{7}{5}\right) \times 14\)

= \(\frac{21}{20} \times 14\)

= \(\frac{21 \times 14}{20}\)

= \(\frac{21 \times 7}{10}\)

= 147/10

= \(14 \frac{7}{10}\)

\(\frac{\frac{3}{4}}{\frac{5}{7}} \times 14\) = \(14 \frac{7}{10}\)