Proportion Examples

Are the ratios 15:24 and 65:104 proportional?

Ugh, these numbers are U.G.L.Y. They ain't got no alibi. So let's reduce both to their simplest terms. Though it isn't necessary, rewriting them as fractions first may help.

The ratio 15:24 in fraction form is . The GCF of 15 and 24 is 3. Divide numerator and denominator by the GCF to reduce it.

The ratio 65 to 104 in fraction form is . The GCF of 65 and 104 is 13. Divide the numerator and denominator by the GCF to reduce that one, too.

Since they both reduce to the same fraction,  and  are equivalent, meaning the ratios are proportional. They're both equal to .

Identify three sets of proportional ratios among 16 squares: 1 blue, 2 green, 3 yellow, 4 orange, and 6 red.

Proportional ratios are equivalent ratios. One set of equivalent ratios are all equivalent to . They are blue:green (1:2), green:orange (2:4), and yellow:red (3:6).

Another set of equivalent ratios is green:yellow (2:3) and orange:red (4:6).

A third set of equivalent ratios is blue:yellow (1:3) and green:red (2:6).

What value of y will make this statement a proportion?

We can solve this with cross-multiplication.

3 × 42 = 7y
126 = 7y
18 = y

So sticking a numerator of 18 on that right-hand ratio will turn this into a proportion.

What value of x will make this statement a proportion?

Use cross-multiplication.
4 × 9 = xx
36 = x²
6 = x

Double-check that the ratios are actually proportional: ⁴⁄₆ is indeed equivalent to ⁶⁄₉, so we're good.