Question

# By the correct number, replace $\square$ in each of the following:${\text{(a) }}\dfrac{2}{7} = \dfrac{8}{\square } \\ {\text{(b) }}\dfrac{5}{8} = \dfrac{{10}}{\square } \\ {\text{(c) }}\dfrac{{45}}{{60}} = \dfrac{{15}}{\square } \\ {\text{(d) }}\dfrac{{18}}{{24}} = \dfrac{\square }{4} \\$

Hint- Here, we will be obtaining the values of the missing numbers by cross multiplication.
Here let us suppose the missing number be $x = {\text{ }}\square$. Now, we will cross multiply the equation and find the value of $x$.
${\text{(a)}}$ Let $\dfrac{2}{7} = \dfrac{8}{x}$
Now cross multiplying the above equation, we get
$\Rightarrow 2x = 8 \times 7 \Rightarrow 2x = 56 \Rightarrow x = 28$.
Therefore, the correct equation is $\dfrac{2}{7} = \dfrac{8}{{28}}$.
${\text{(b)}}$ Let $\dfrac{5}{8} = \dfrac{{10}}{x}$
Now cross multiplying the above equation, we get
$\Rightarrow 5x = 8 \times 10 \Rightarrow 5x = 80 \Rightarrow x = 16$.
Therefore, the correct equation is $\dfrac{5}{8} = \dfrac{{10}}{{16}}$.
${\text{(c)}}$ Let $\dfrac{{45}}{{60}} = \dfrac{{15}}{x}$
Now cross multiplying the above equation, we get
$\Rightarrow 45x = 60 \times 15 \Rightarrow x = \dfrac{{60 \times 15}}{{45}} \Rightarrow x = 20$
Therefore, the correct equation is $\dfrac{{45}}{{60}} = \dfrac{{15}}{{20}}$.
${\text{(d)}}$ Let $\dfrac{{18}}{{24}} = \dfrac{x}{4}$
Now cross multiplying the above equation, we get
$\Rightarrow 4 \times 18 = 24x \Rightarrow x = \dfrac{{4 \times 18}}{{24}} \Rightarrow x = 3$
Therefore, the correct equation is$\dfrac{{18}}{{24}} = \dfrac{3}{4}$.

Note- These types of problems are solved by simply cross multiplying the given equation with one unknown and then finally solving for that unknown.