multiplying fractions and whole numbers Archives

Multiplying Fractions by Whole Numbers:

When any fractions either proper or improper are multiplied with a whole number, the numerators are multiplied with whole number and the denominator will remains the same.
In generalise form, fraction $\cfrac{a}{b}$ and whole number ‘c’

$\cfrac{a}{b}$ of c = $\cfrac { a \times c }{ b }$

Example

Find:

$\cfrac{3}{12}$ of 6

Explanation

In this question ‘of’ means to multiply

When any fractions either proper or improper are multiplied with a whole number, the numerators are multiplied with whole number and the denominator will remains the same.

So, $\cfrac{3}{12}$ of 6

= $\cfrac{6}{1} \times \cfrac{3}{12}$

= $\cfrac{18}{12}$

HCF of 18 and 12 is 6

Since, both numerator and denominator are divide by their HCF i.e,

$\cfrac{18 \div 6 }{12 \div 6 }$ = $\cfrac{3}{2}$

So, the answer is $\cfrac{3}{2}$

Multiplying Fractions by Fractions:

When any fractions either proper or improper are multiplied, the numerators are multiplied with each other and the denominators are multiplied with each other.
Product of Fractions = $\cfrac { Product\quad of\quad their\quad Numerators }{ Product\quad of\quad their\quad Denominators }$
In generalise form, for any two fractions $\cfrac{a}{b}$ and $\cfrac{c}{d}$

$\cfrac{a}{b} \times \cfrac{c}{d}$ = $\cfrac { a\times c }{b\times d}$

Example

Find the product of $\cfrac{3}{5} \times \cfrac{3}{4}$

Explanation

Product of Fractions = $\cfrac { Product\quad of\quad their\quad Numerators }{ Product\quad of\quad their\quad Denominators }$

$\cfrac{3}{5} \times \cfrac{3}{4}$ = $\cfrac { 3\times 3 }{5\times 4}$ = $\cfrac{9}{20}$

Hence, product of $\cfrac{3}{5} \times \cfrac{3}{4}$ = $\cfrac{9}{20}$

Multiplying Mixed Fractions with Fractions

When a mixed fraction is multiplied by a proper or improper fraction, convert mixed fraction into improper fraction and then multiply them.

Example

Find $3 \cfrac{3}{7} \times \cfrac{1}{2}$

Explanation

In order to multiply a Mixed Fraction with a Improper/ Proper Fraction, we first convert mixed Fraction into Improper Fraction , and then multiply it with the Improper/Proper Fraction

$3\cfrac { 3 }{ 7 }$