Question

simplify: 4 2/5 ÷ 6 2/7 × 7 2/9​

Answer 1

★ How to do :-

Here, we are given with three fractions in which we are asked to find the answer for that by dividing two of them and multiplying the other. Here, we use a special concept that can be applicable to all the fractions, rational numbers and also integers. This concept is named as a BODMAS rule in which division, multiplication, addition and also the subtraction occurs. This rule says that, in the given question first we should divide the fractions and then we should multiply the other number with obtained fraction. So, let's solve!!

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➤ Solution :-

${\tt \leadsto 4 \dfrac{2}{5} \div 6 \dfrac{2}{7} \times 7 \dfrac{2}{9}}$

Convert all the three mixed fractions to improper fractions.

${\tt \leadsto \dfrac{22}{5} \div \dfrac{44}{7} \times \dfrac{65}{9}}$

According to the rule, first we should divide the numbers.

${\tt \leadsto \bigg( \dfrac{22}{5} \div \dfrac{44}{7} \bigg) \times \dfrac{65}{9}}$

Take the reciprocal of second fraction and multiply both numbers in bracket.

${\tt \leadsto \bigg( \dfrac{22}{5} \times \dfrac{7}{44} \bigg) \times \dfrac{65}{9}}$

Now, multiply the numbers given in bracket.

${\tt \leadsto \bigg( \dfrac{22 \times 7}{5 \times 44} \bigg) \times \dfrac{65}{9}}$

Multiply the numerator and denominator given in the bracket.

${\tt \leadsto \dfrac{154}{220} \times \dfrac{65}{9}}$

Write the numbers in lowest form by cancellation method.

${\tt \leadsto \dfrac{154 \times \cancel{65}}{\cancel{220} \times 9} = \dfrac{154 \times 13}{44 \times 9}}$

Now, multiply the remaining numbers as they cannot be cancelled further.

${\tt \leadsto \cancel \dfrac{2002}{396} = \dfrac{91}{18}}$

Write the obtained answer in the form of mixed fraction.

${\tt \leadsto \dfrac{91}{18} = 5 \dfrac{1}{18}}$

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$\red{\underline{\boxed{\bf So, \: the \: answer \: when \: simplified \: is \: \: 5 \dfrac{1}{18}}}}$