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# 6th Grade - Ratios and Proportions

## Ratios

• A comparison of two numbers by division is called a Ratio.
• A ratio can be expressed in three different ways: .
• A ratio $\frac{a}{b}$ is read as "a ratio of a to b".
• A ratio is a fraction that can be simplified.
• Two ratios are called equal ratios or equivalent ratios if are equal.
• $\frac{2}{5}$ and $\frac{4}{10}$are equal ratios as $\frac{4}{10}=\frac{2}{5}×\frac{2}{2}$ (numerator and denominator are multiplied by the same number).
• A table of equivalent ratios is called a ratio table.
•  2 4 6 8 10 5 10 15 20 25
• All ratios in the ratio table are equivalent.

## Proportion

• Two ratios are said to be in proportion if their cross-product are equal.
•   are in proportion if .

## Solved Examples

1. Find the ratio of 7 to 10.

The ratio of 7 to 10 is $\frac{7}{10}$

2. Find the ratio of 16 oranges to 21 apples.

The ratio of 16 to 21 is $\frac{16}{21}$

3. Complete the following ratio table:

 Number of Lemons 5 10 ? Glasses of Lemonade 10 ? 30

To keep the ratio table equal, the top and the bottom numbers should be multiplied by the same number.

 Number of Lemons 5 10 ($5×2$) 15 ($5×3$) Glasses of Lemonade 10 20 ($10×2$) 30 ($10×3$)

4. Do the following ratios form a proportion: ?

The cross-product should be the same for the ratios to form a proportion. Since , the ratios are not in proportion.

5. 6 pastries cost $5. What should 18 pastries cost? Put the provided information as a proportion: $\frac{6}{5}=\frac{18}{?}$. Since 6 is multiplied by 3 to get 18, 5 must be multiplied by 3. The answer is$15.

## Cheat Sheet

• The quantity that comes first in the ratio statement becomes the numerator in the ratio fraction.
• A proportion consists of 4 terms. It is a comparison of two ratios.
• If the numerator and denominator of a ratio are multiplied by the same number, the resulting ratio is equivalent to the first one.
• Their cross-product should be the same for the ratios to be in proportion.

## Blunder Area

• In the case of word problems, pay attention to which value goes as a numerator and which one goes as a denominator.
• Not all ratios are in proportion.