Question

Reduce each of the following fractions to its lowest term (simplest form):
(i) $\frac{40}{75}$
(ii)$\frac{42}{28}$
(iii)$\frac{12}{52}$
(iv) $\frac{40}{72}$
(v) $\frac{80}{24}$
(vi) $\frac{84}{56}$

Answer 1

(i) Given$\frac{40}{75}$
Factors of $40$ are $1,2,4,5,8,10,20$ and $40$.
Factors of 75 are $1,3,5,15$ and $75$.
Common factors of $40$ and $75$ are $1$ and $5$.
HCF $=5$
Divide both the numerator & denominator by 5.
$\Rightarrow \frac{40÷5}{75÷5}=\frac{8}{15}$
(ii) Given $\frac{42}{28}$
Factors of $42$ are$1,2,3,6,7,14,21,42$
Factors of $28$ are$1,2,4,7,14,28$
Common factors of $42$ & $28$ are $1,2,7,14$
HCF=14
Divide both the numerator & denominator by 14.
$\therefore \frac{42÷14}{28÷14}=\frac{3}{2}$
(iii) Given $\frac{12}{52}$
Factors of $12$ are $1,2,3,4,6$ and $12$.
Factors of $52$ are $1,2,4,13,26$ and $52$.
Common factors of $12$ & $52$ are$1,2,$ and $4$.
HCF$=4$
Divide both the numerator & denominator by $4$.
$\therefore \frac{12÷4}{52÷4}=\frac{3}{13}$
(iv) Given $\frac{40}{72}$
Factors of $40$ are $1,2,4,5,8,10,20,40$
Factors of $72$ are $1,2,3,4,6,8,9,12,18,24,36,72$
Common factors of $40$ & $72$ are $1,2,4,8$
HCF$=8$
Divide both the numerator & denominator by 8
$\therefore \frac{40÷8}{72÷8}=\frac{5}{9}$
(v) Given $\frac{80}{24}$
Factors of $80$ are $1,2,4,5,8,10,16,20,40$ and $80$.
Factors of $24$ are $1,2,3,4,6,8,12$ and $24$.
Common factors of $80$ & $24$ are $1,2,4$ and $8$.
HCF$=8$
Divide both the numerator & denominator by $8$.
$\therefore \frac{80÷8}{24÷8}=\frac{10}{3}$
(vi) Given $\frac{84}{56}$
Factors of $84$ are $1,2,3,4,6,7,12,14,21,28,42$ and $84$.
Factors of $56$ are $1,2,4,7,8,14,28$ and $56$.
Common factors of $84$ & $56$ are $1,2,4,7,14$ and $28$.
HCF$=28$
Divide both the numerator & denominator by $28$.
$\therefore \frac{84÷28}{56÷28}=\frac{3}{2}$