Algebraic Proportions Review

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What is an algebraic proportion?

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An algebraic proportion is an equation that states that two ratios are equal. It can be expressed in the form \( \frac{a}{b} = \frac{c}{d} \), where a, b, c, and d are numbers or algebraic expressions.

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How do you solve for a variable in a proportion?

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To solve for a variable in a proportion, cross-multiply the terms. For example, in \( \frac{a}{b} = \frac{c}{d} \), you can solve for a variable by calculating \( a \cdot d = b \cdot c \) and then isolating the variable.

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x = 10

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d = -1

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p = 13

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g = 20

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c = 26

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What is cross-multiplication in proportions?

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Cross-multiplication is a method used to solve proportions by multiplying the numerator of one ratio by the denominator of the other ratio. For example, in \( \frac{a}{b} = \frac{c}{d} \), it results in \( a \cdot d = b \cdot c \).

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What does it mean if two ratios are in proportion?

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If two ratios are in proportion, it means that the two fractions represent the same value or relationship, indicating that the cross-products are equal.

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What is the first step in solving a proportion?

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The first step in solving a proportion is to set the two ratios equal to each other and identify the variable you need to solve for.