Question

Express the following percentages as ratios in the reduced form.

(i) 75 : 100

(ii) 44 : 100

(iii) 6.25%

(iv) 52 : 100

(v) 0.64%

Answer 1

(i)
75 : 100 = $\frac{75}{100}=\frac{75÷25}{100÷25}=\frac{3}{4}$ = 3 : 4 (HCF of 75 and 100 = 25)

(ii)
44 : 100 = $\frac{44}{100}=\frac{44÷4}{100÷4}=\frac{11}{25}$ = 11 : 25 (HCF of 44 and 100 = 4)

(iii)
6.25% = $\frac{6.25}{100}=\frac{625}{10000}=\frac{{\displaystyle 625÷625}}{{\displaystyle 10000÷625}}=\frac{1}{16}$ = 1 : 16 (HCF of 625 and 10000 = 625)

(iv)
52 : 100 = $\frac{52}{100}=\frac{52÷4}{100÷4}=\frac{13}{25}$ = 13 : 25 (HCF of 52 and 100 = 4)

(v)
0.64% = $\frac{0.64}{100}=\frac{64}{10000}=\frac{{\displaystyle 64÷16}}{{\displaystyle 10000÷16}}=\frac{4}{625}$ = 4 : 625 (HCF of 64 and 10000 = 16)