Ratios and Rates

NZ Level 6 (NZC) Level 1 (NCEA)

Decimal Ratios

Lesson

Expressing ratios as decimals is a similar process to converting fractions to decimals. It can be useful to convert ratios to fractions when conceptualising these ratios.

**Question**: Express $35:100$35:100 as a single decimal.

**Think:** $35:100$35:100 is the same as $\frac{35}{100}$35100 and since the second number in the ratio (which becomes the denominator) is already a multiple of $10$10, we do not need to change any of our numbers around.

**Do:**

$35:100$35:100 | $=$= | $\frac{35}{100}$35100 | turn the ratio into a fraction |

$=$= | $0.35$0.35 | change the fraction into a decimal |

Let's look at a question where we don't have a multiply of $10$10 as the denominator.

**Question**: Express $23:4$23:4 as a single decimal.

**Think:** There are a few different ways to approach this question. My first step is going to be to change this ratio into a mixed number. Then I'll change it to a decimal.

**Do:**

$23:4$23:4 | $=$= | $\frac{23}{4}$234 | convert the ratio to a fraction |

$=$= | $5\frac{3}{4}$534 | convert to mixed number | |

$=$= | $5.75$5.75 | convert to decimal |

If you need a refresher on how to change fractions to decimals, click here.

Express $31.8:3180$31.8:3180 as a single decimal.

We've already looked at finding unknown whole values in ratios in Keeping it in Proportion. The same process applies whether we have whole numbers or decimal values.

**Question**: Find $b$`b` if $b:40=12$`b`:40=12

**Think:** This ratio means that $\frac{b}{40}=12$`b`40=12 , so to get b by itself, we need to multiply both sides by $40$40.

**Do:**

$b:40$b:40 |
$=$= | $12$12 | |

$\frac{b}{40}$b40 |
$=$= | $12$12 | change ratio into a fraction |

$b$b |
$=$= | $12\times40$12×40 | multiply both sides by $40$40 |

$b$b |
$=$= | $480$480 | evaluate |

Find $a$`a` if $a:17=4.83$`a`:17=4.83

The same rule applies if there is more than one decimal.

Find $a$`a` if $a:7.7=54.98$`a`:7.7=54.98

Apply direct and inverse relationships with linear proportions

Apply numeric reasoning in solving problems