A proportion is an equation that shows two ratios are equal. It is used to find unknown values by setting up two fractions and solving for the missing number. Proportions can help solve problems where quantities need to be scaled up or down while maintaining the same ratio.

To solve a proportion, you can use cross-multiplication. This means multiplying the numerator of one fraction by the denominator of the other, and setting the products equal to each other.

Examples:

Example 1: Finding an Unknown
If 3 pencils cost $6, how much do 5 pencils cost?
Set up the proportion:
3 pencils / $6 = 5 pencils / x
Cross-multiply:
3 × x = 6 × 5
Solve for x:
x = 30 / 3 = $10
So, 5 pencils cost $10.

Example 2: Recipe Adjustment
A recipe uses 2 cups of flour to make 8 cookies. How much flour is needed to make 12 cookies?
Set up the proportion:
2 cups / 8 cookies = x cups / 12 cookies
Cross-multiply:
8 × x = 2 × 12
Solve for x:
x = 24 / 8 = 3 cups
You need 3 cups of flour to make 12 cookies.

Solving proportions is a useful skill for comparing quantities and scaling them up or down while keeping their relationship consistent.

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