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3.07 Converting units

Lesson

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.

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.

 

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.

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. 

 

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?

 

 

Outcomes

6.RP.3

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.

6.RP.3d

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

6.RP.A.3.e

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 e. Solve problems that relate the mass of an object to its volume.

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