Question

For the following numbers write the ratio of first number to second number in the reduced form.

(i) 21, 48 (ii) 36, 90 (iii) 65, 117 (iv) 138, 161 (v) 114, 133

Answer 1

(i)
21 : 48 = $\frac{21}{48}=\frac{21÷3}{48÷3}=\frac{7}{16}$ = 7 : 16 (HCF of 21 and 48 = 3)

Thus, the reduced form of 21 : 48 is 7 : 16.

(ii)
36 : 90 = $\frac{36}{90}=\frac{36÷18}{90÷18}=\frac{2}{5}$ = 2 : 5 (HCF of 36 and 90 = 18)

Thus, the reduced form of 36 : 90 is 2 : 5.

(iii)
65 : 117 = $\frac{65}{117}=\frac{65÷13}{113÷13}=\frac{5}{9}$ = 5 : 9 (HCF of 65 and 113 = 13)

Thus, the reduced form of 65 : 117 is 5 : 9.

(iv)
138 : 161 = $\frac{138}{161}=\frac{138÷23}{161÷23}=\frac{6}{7}$ = 6 : 7 (HCF of 138 and 161 = 23)

Thus, the reduced form of 138 : 161 is 6 : 7.

(v)
114 : 133 = $\frac{114}{133}=\frac{114÷19}{133÷19}=\frac{6}{7}$ = 6 : 7 (HCF of 114 and 133 = 19)

Thus, the reduced form of 114 : 133 is 6 : 7.