Question

Question 5

Fill the following blanks:

$\frac{15}{18}=\frac{\square }{6}=\frac{10}{\square }=\frac{\square }{30}$

Are these equivalent ratios?

Answer 1

Two ratios are called equivalent ratios when their simplest forms (or standard forms) are equal.

By cross multiplying each of the equations, the missing values can be found out.

15 x 6 = 18 x $\square$

On solving, first square = $\frac{15\times 6}{18}$ = 5

Similarly, we can fill rest of the squares as given below.
$\frac{5}{6}=\frac{10}{\square }5\times \square =10\times 6Secondsquare\square =\frac{10\times 6}{5}=12Similarly\frac{10}{12}=\frac{\square }{30}ThirdSquare\square =\frac{10\times 30}{12}=25$

$\frac{15}{18}=\frac{\begin{array}{c}5\end{array}}{6}=\frac{10}{\begin{array}{c}12\end{array}}=\frac{\begin{array}{c}25\end{array}}{30}$

Yes, these are equivalent ratios as the standard form of all the above ratios are 5:6.