Ratio and Proportion

Rumman Ansari Software Engineer 2024-07-28 09:21:07 167 Share
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Ratio and Proportion Formulas

Ratio: A ratio is a relationship between two numbers indicating how many times the first number contains the second.

Proportion: A proportion states that two ratios are equal.

The ratio of $a$ to $b$ is written as:

a : b or \frac{a}{b}

If $a : b = c : d$ , then $a, b, c,$ and $d$ are in proportion. It can be written as:

\frac{a}{b} = \frac{c}{d}

If $\frac{a}{b} = \frac{c}{d}$ , then multiplying both sides by the same non-zero number gives the same ratio:

\frac{a \times k}{b \times k} = \frac{c \times k}{d \times k}

If $\frac{a}{b} = \frac{c}{d}$ , then inverting both sides gives:

\frac{b}{a} = \frac{d}{c}

If $a : b = c : d$ , then:

a \times d = b \times c

\p>If

\frac{a}{b} = \frac{c}{d}

, then:

\frac{a}{c} = \frac{b}{d}

If $\frac{a}{b} = \frac{c}{d}$ , then:

\frac{a + b}{b} = \frac{c + d}{d}

If $\frac{a}{b} = \frac{c}{d}$ , then:

\frac{a - b}{b} = \frac{c - d}{d}

If $\frac{a}{b} = \frac{c}{d}$ , then:

\frac{a + b}{a - b} = \frac{c + d}{c - d}

If the ratio of boys to girls in a class is 3:2, then for every 3 boys, there are 2 girls.

If 4 pens cost $20 and 6 pens cost $30, then the cost of pens is in proportion.

\frac{4}{20} = \frac{6}{30}

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