Question

Find the mean proportion between $\frac{1}{4}$ and $\frac{1}{9}$

• A. $\frac{1}{6}$
• B. $\frac{1}{36}$
• C. 6
• D. 0.36

Answer 1

The correct option is A

$\frac{1}{6}$

Let $b$ be the mean proportion between $\frac{1}{4}$ and $\frac{1}{9}$

Then $\frac{1}{4}$ :$b$ :: $b$ : $\frac{1}{9}$

$b^2=\frac{1}{9}\times \frac{1}{4}$

$b^2=\frac{1}{36}$

$b=\sqrt{\frac{1}{36}}$

$b=\frac{1}{6}$

Hence the mean proportion between $\frac{1}{4}$ and $\frac{1}{9}$ is $\frac{1}{6}$