Ratios and Imperial and Metric Units

Our ratio journey so far has taken us through the process of simplifying, using ideas similar to how we simplify fractions.  We have also explored a number of applications of ratios where we scaled the ratios up or down to answer questions in context.  We have also used tables of values in ratio tables to explore the proportional connection between two quantities.  

Another application of ratios can also be seen in converting units, imperial to metric and vice versa.

Examples

Question 1

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 groups 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: Litres: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 litres is equivalent to $5$5 gallons.

 

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

Think: Use the conversion ratio.

Do: 

Litres	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 Litres. 

 

Question 3

 

Question 4