Question

Determine whether the following numbers are in proportion or not$:$

$4\frac{1}{2},7\frac{1}{3},54,88$

Answer 1

Step $1:$ To check whether the given numbers are in proportion or not

As we know that any four numbers $a,b,c$ and $d$ are saif to be in proportion if and only if

$\frac{a}{b}=\frac{c}{d}$

Step $2:$ Given four numbers are $4\frac{1}{2},7\frac{1}{3},54,88$

$\frac{9}{2},\frac{22}{3},54,88$

Find the ratio of first and second number

$=\frac{{\displaystyle \frac{9}{2}}}{{\displaystyle \frac{22}{3}}}$

$=\frac{9}{2}\times \frac{3}{22}$

$=\frac{27}{44}$

Step $3:$Now find the ratio of third and fourth number

$=\frac{54}{88}$

$=\frac{{\displaystyle \frac{54}{2}}}{{\displaystyle \frac{88}{2}}},$divide the numerator and denominator by $2$

$=\frac{27}{44}$

therefore the ratio of first term to second term is equal to the ratio of third term to fourth term

$\frac{{\displaystyle \frac{9}{2}}}{{\displaystyle \frac{22}{3}}}$$=\frac{54}{88}$

Hence, the given four numbers $4\frac{1}{2},7\frac{1}{3},54,88$ are in proportion.