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# Ratios and Proportions

A ratio is a way to compare two quantities using division.

Ratios are often written as fractions.

For example:

â€¢ If a class of 24 students contains 11 women and 13 men, then the ratio of women to men is 11 to 13, which we can write as .

â€¢ If 10 pounds of watermelon costs \$3, then the ratio of cost to weight is .

A proportion is an equation that sets one ratio equal to another ratio.

Definition â€” Proportion

A proportion is an equation that can be written in the form Here b 0 and d 0.

Hereâ€™s a problem we can solve with a proportion.

If an 18-pound melon costs \$3.60, what is the cost of a 26-pound melon?

 If we assume that the ratio of cost to weight is the same for all melons, then we can write this proportion.  We let x represent the cost (in dollars) of the big melon and we substitute the given values.  To solve this equation for x, we can multiply both sides by 26.  We simplify. 5.2 = x

The cost of the big melon is \$5.20.