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Describe what makes a proportion. Give an example of a proportion.
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A proportion is an equation that states two ratios (or fractions) are equal. In symbols, a proportion looks like
a/b = c/d
with b and d not zero. A useful test is cross-multiplication: the proportion holds exactly when ad = bc. In the four terms a, b, c, d, the outer ones (a and d) are called the extremes and the inner ones (b and c) the means.
Example 1 (numbers):
3/5 = 6/10 because 3 × 10 = 30 and 5 × 6 = 30, so the cross-products are equal.
Example 2 (solve for an unknown):
x/4 = 3/8 → cross-multiply: 8x = 12 → x = 12/8 = 3/2 = 1.5.
a/b = c/d
with b and d not zero. A useful test is cross-multiplication: the proportion holds exactly when ad = bc. In the four terms a, b, c, d, the outer ones (a and d) are called the extremes and the inner ones (b and c) the means.
Example 1 (numbers):
3/5 = 6/10 because 3 × 10 = 30 and 5 × 6 = 30, so the cross-products are equal.
Example 2 (solve for an unknown):
x/4 = 3/8 → cross-multiply: 8x = 12 → x = 12/8 = 3/2 = 1.5.
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