Tennessee 6 - 2020 Edition

3.07 Converting units

Lesson

We can apply our understanding of ratios and proportional relationships to convert units.

**Evaluate:** The ratio of miles to kilometers is $1:1.6$1:1.6. Use this fact to find out how many kilometers are equal to $5$5 miles.

**Think**: The given ratio of $1:1.6$1:1.6 means that $1$1 mile is equal to $1.6$1.6 kilometers. Set up a ratio problem, identifying by what factor each part of the ratio needs to be multiplied to give $5$5 miles.

**Do**:

miles | to | kilometers |

$1$1 | $:$: | $1.6$1.6 |

to get $5$5 miles, we need $5$5 lots of the part representing miles in the ratio | so we also need to multiply the number of kilometers by $5$5 | |

$1\times5$1×5 | $:$: | $1.6\times5$1.6×5 |

$5$5 | $:$: | $8$8 |

So $5$5 miles is equivalent to $8$8 kilometers.

$1$1 gallon is around $3.8$3.8 liters.

**a) **State this as a ratio of liters to gallons, in the form $a:b$`a`:`b`. Give your answer in simplest form.

**Think**: We want a ratio that compares the number of liters to the numer of gallons.

**Do**: Liters:Gallons = $3.8:1$3.8:1

Simplest form is without fractions or decimals:

$3.8$3.8 | $:$: | $1$1 | multiply both parts by $10$10 to remove the decimal |

$38$38 | $:$: | $10$10 | divide both parts by common factor of $2$2 |

$19$19 | $:$: | $5$5 | this is in simplest form |

This means that $19$19 liters is equivalent to $5$5 gallons.

**b)** How many liters would a $15$15 gallon vat hold?

**Think**: Use the conversion ratio.

**Do**:

Liters | to | Gallons | |

$19$19 | $:$: | $5$5 | for $15$15 gallons we need to multiply the $5$5 "gallons" parts by $3$3. |

$19\times3$19×3 | $:$: | $5\times3$5×3 | so we need to multiply both parts of the ratio by $3$3 |

$57$57 | $:$: | $15$15 |

So $15$15 Gallons is equivalent to $57$57 Liters.

The ratio of kilograms to ounces is $1:2.2$1:2.2. Use this fact to complete the workings below for finding out how many ounces are equal to $10$10 kilograms.

$1$1 **:**$2.2$2.2 × $\editable{}$ × $10$10 $\editable{}$ **:**$\editable{}$

$1$1 foot is equal to around $0.3$0.3 meters.

State this as a ratio of feet to meters, in the form $a:b$

`a`:`b`. Write your answer in simplest form.How many meters would a $100$100 foot garden be?

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g. By reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.