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Ratios: cheat sheet

Number Foundations · The words and methods from the lessons, with an example of each.

ratio

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

red:blue=2:3\text{red} : \text{blue} = 2 : 3
2 red blocks to 3 blue blocks
2 red blocks to 3 blue blocks

simplest form of a ratio

Divide both terms by their highest common factor (here 6). No number above 1 divides both.

12:18=2:312 : 18 = 2 : 3

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 in 2:3→$60÷5=$12→$24,$36\$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
$60 in the ratio 2 : 3: five parts of $12, Ana $24 and Ben $36

part to part, part to whole

Part to whole adds the parts: 2+3=52 + 3 = 5. The part-to-whole ratio 2:52 : 5 matches the fraction 25\tfrac{2}{5}.

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

equivalent ratios

Multiply or divide both terms by the same number. Adding the same number to both changes the ratio.

2:3=4:6=6:92 : 3 = 4 : 6 = 6 : 9
Three copies of 2 : 3 make 6 : 9
Three copies of 2 : 3 make 6 : 9