SIGN IN VERSION Proportions!

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Proportions are set up between fractions that are equal ratios. If they are equal and you are missing one of the numbers, you can solve for the missing one.

For instance if x/6=8/12, then you can solve by multiplying both sides by 6 to get

x=48/12, then multiply both sides by 12 to get

12x=48 then divide both sides by 12 to get

x=4

Our result is correct, 4/6 is equal to 8/12 and they both can be reduced to 2/3 or as a decimal 0.66666

This process may seem a little weird but let's look at a harder example where the process makes more sense

For instance if 5/x=15/6, then you can solve by multiplying both sides by 6 to get

30/x=15, then multiply both sides by x to get

30=15x then divide both sides by 15 to get

2=x

Our result is correct, 5/2 is equal to 15/6 and they both can be reduced to 5/2 or as a decimal 2.5

This makes sense but most teachers simply tell students to cross-multiply. When cross-multiplying our last two examples look like this.

if x/6=8/12, then you can solve by multiplying both sides by 6 and both sides by 12 to get

12x = 48, then divide both sides by 12 to get

x=4

if 5/x=15/6, then you can solve by multiplying both sides by 6 and by x to get

30=15x then divide both sides by 15 to get

2=x

"Cross-multiplying" is a short-cut for clearing out the fractions in one step rather than 2.