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Question

Find the missing number in the box:
$$\dfrac{16}{36}=\dfrac{\square}{63} =\dfrac{36}{\square}=\dfrac{\square}{117}$$

Solution
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$$\textbf{Step 1: Find the missing number in the first two ratios}$$
Ratios that are equal are called equivalent ratios and are said to be in proportion.
Let the missing number be x
$$\frac{16}{36}=\frac{x}{63}$$
By cross multiplying, we get
$$36 \times x=16 \times 63$$
$$x=\frac{16 \times 63}{36}=28$$
$$\textbf{Step 2: Find the missing number in the third ratio.}$$
$$\frac{16}{36}=\frac{28}{63}=\frac{36}{}=\frac{}{117}$$
Consider second and third ratios
Let the missing number be $$y$$
$$\frac{28}{63}=\frac{36}{y}$$
By cross multiplying, we get
$$\begin{gathered}28 \times y=63 \times 36 \\y=\frac{63 \times 36}{28}=81\end{gathered}$$
$$\textbf{Step 3: Find the missing number in the last ratio.}$$
From the last step,
$$\frac{16}{36}=\frac{28}{63}=\frac{36}{81}=\frac{}{117}$$
Consider last two ratios.
Let the missing number be z
$$\frac{36}{81}=\frac{z}{117}$$
By cross multiplying, we get
$$\begin{aligned}81 \times z &=36 \times 117 \\z &=\frac{36 \times 117}{81}=52\end{aligned}$$
$$\therefore \textbf{Missing numbers in the given ratio are 28, 81 and 52}$$

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