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Proportion, as I told you before, states that two ratios are the same.

So, the statement $\frac{7}{4}=\frac{28}{16}$ because the ratios are the same when simplify.

A simpler way of determining if two ratios are proportional is to use cross-multiplication. This is because two ratios are proportional if their cross-products are the same.


$$7 \times 16 = 28 \times 4$$


Because their cross-products are the same, the two ratios are the same

But, what if we replace 7 with x so that it becomes: 


Since we know that cross product of a proportion is the same.

$$x \times 14= 28  \times 4$$



Using this fact, let's solve few examples

Example 1

Solve for x in $\frac{145}{232}=\frac{10}{2y}$


By cross multiplication

$$145 \times 2y=232 \times 10$$




Example 2

Solve $\frac{8}{10z}=\frac{0.4}{1.4}$


By cross multiplication

$$8 \times 1.4= 10z \times 0.4$$



Example 3

Solve for x in $\frac{5x}{150}=\frac{\frac{2}{3}}{5}$


First, we evaluate the right-hand side



$$5x ×15=150 × 2$$



Example 4

Solve for x in $\frac{32}{100}=\frac{40}{4y}$


By cross multiplication




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