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3.07 Converting units


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

Worked examples

Question 1

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.


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.


Question 2

$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.


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. 


Practice questions

Question 3

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

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

Question 4

$1$1 foot is approximately $0.3$0.3 meters.

  1. State this as a ratio of feet to meters, in simplest form.

  2. How many meters would a $seven$seven foot garden be?





Use ratio reasoning with equivalent whole-number ratios to solve real-world and mathematical problems by:• Creating and using a table to compare ratios.• Finding missing values in the tables. • Using a unit ratio. • Converting and manipulating measurements using given ratios. • Plotting the pairs of values on the coordinate plane.

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