Question

# Find the fraction equivalent of $\frac{35}{42}$, having: (i) numerator 15 (ii) denominator 18 (iii) denominator 30 (iv) numerator 30

Open in App
Solution

## $\mathrm{Firstly},\mathrm{we}\mathrm{will}\mathrm{reduce}\frac{35}{42}\mathrm{into}\mathrm{the}\mathrm{lowest}\mathrm{term}.\phantom{\rule{0ex}{0ex}}\mathrm{Now},\mathrm{we}\mathrm{will}\mathrm{divide}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}\mathrm{the}\mathrm{HCFs}\mathrm{of}35&42.\phantom{\rule{0ex}{0ex}}⇒\frac{35÷7}{42÷7}=\frac{5}{6}\phantom{\rule{0ex}{0ex}}$ $\left(\mathrm{i}\right)\frac{5}{6}=\frac{15}{\mathrm{Denominator}}\phantom{\rule{0ex}{0ex}}\mathrm{We}\mathrm{will}\mathrm{consider}\mathrm{the}\mathrm{numerators}.\phantom{\rule{0ex}{0ex}}\mathrm{As}5×3=15,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}3.\phantom{\rule{0ex}{0ex}}⇒\frac{5×3}{6×3}=\frac{15}{18}$ $\left(\mathrm{ii}\right)\frac{5}{6}=\frac{\mathrm{Numerator}}{18}\phantom{\rule{0ex}{0ex}}\mathrm{We}\mathrm{will}\mathrm{consider}\mathrm{the}\mathrm{denominators}.\phantom{\rule{0ex}{0ex}}\mathrm{As}6×3=18,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}3.\phantom{\rule{0ex}{0ex}}⇒\frac{5×3}{6×3}=\frac{15}{18}$ $\left(iii\right)\frac{5}{6}=\frac{\mathrm{numerator}}{30}\phantom{\rule{0ex}{0ex}}Wewillconsider\mathrm{the}\mathrm{denominators},\phantom{\rule{0ex}{0ex}}\mathrm{Since},6×5=30,\mathrm{therefore}\mathrm{multiplying}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}5\phantom{\rule{0ex}{0ex}}⇒\frac{5×5}{6×5}=\frac{25}{30}$ $\left(\mathrm{iv}\right)\frac{5}{6}=\frac{30}{\mathrm{Denominator}}\phantom{\rule{0ex}{0ex}}\mathrm{We}\mathrm{will}\mathrm{consider}\mathrm{the}\mathrm{numerators}.\phantom{\rule{0ex}{0ex}}\mathrm{As}5×6=30,\mathrm{we}\mathrm{will}\mathrm{multiply}\mathrm{both}\mathrm{the}\mathrm{numerator}&\mathrm{denominator}\mathrm{by}6.\phantom{\rule{0ex}{0ex}}⇒\frac{5×6}{6×6}=\frac{30}{36}$

Suggest Corrections
1
Related Videos
Equivalent Fraction
MATHEMATICS
Watch in App
Explore more