---
title: "Ratios: cheat sheet"
subtitle: "Number Foundations"
---

# Ratios

> The words and methods from this unit, with an example of each.

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**ratio**: Compares quantities in a stated order. The first thing named is the first number.

$$\text{red} : \text{blue} = 2 : 3$$

_2 red blocks to 3 blue blocks_

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**part to part, part to whole**: Part to whole adds the parts: $2 + 3 = 5$. The part-to-whole ratio $2 : 5$ matches the fraction $\tfrac{2}{5}$.

$$2 : 3 \text{ (red to blue)} \qquad 2 : 5 \text{ (red to all)}$$

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**equivalent ratios**: Multiply or divide both terms by the same number. Adding the same number to both changes the ratio.

$$2 : 3 = 4 : 6 = 6 : 9$$

_Three copies of 2 : 3 make 6 : 9_

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**simplest form of a ratio**: Divide both terms by their highest common factor (here 6). No number above 1 divides both.

$$12 : 18 = 2 : 3$$

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**share in a ratio**: Add the parts, divide the total by the parts to find one part, then multiply. The shares add back to the total.

$$\$60 \text{ in } 2 : 3 \to \$60 \div 5 = \$12 \to \$24, \$36$$

_$60 in the ratio 2 : 3: five parts of $12, Ana $24 and Ben $36_

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