Question

To convert from ft² to yd², you should

(a) multiply by 3.

(b) multiply by 1/3.

(c) multiply by 9.

(d) multiply by 1/9.

(e) multiply by 6.

(f) multiply by 1/6.

Short answer

The correct option is (d).

Step-by-step solution

Step 1. Relation between yd and ft

The conversion of a unit is a process in which the unit of the measurement of a quantity changes from one prospect to another. There is a set factor by which the particular quantity needs to be multiplied or divided for every conversion.

You know that the relation between ft and yd is

$\begin{array}{c}1 \mathrm{yd}=3 \mathrm{ft}\\ 1 \mathrm{ft}=\frac{1}{3} \mathrm{yd}\end{array}$

Step 2. Conversion of ft2 to yd2

Now,

$\begin{array}{c}{\left(1 \mathrm{ft}\right)}^2={\left(\frac{1}{3} \mathrm{yd}\right)}^2\\ 1 {\mathrm{ft}}^2=\frac{1}{9} {\mathrm{yd}}^2\\ {\mathrm{ft}}^2=\frac{1}{9}\times {\mathrm{yd}}^2\end{array}$

Hence, to convert ft² to yd², the quantity must be multiplied by $\frac{1}{9}$.