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 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 | : | $2.2$2.2 | ||||
× $\editable{}$ | × $10$10 | |||||
$\editable{}$ | : | $\editable{}$ |
$1$1 foot is approximately $0.3$0.3 meters.
State this as a ratio of feet to meters, in simplest form.
How many meters would a $seven$seven foot garden be?