457.2 cm

##color(brown)(“Using ratios. Note that a ratio when written this way is not the same”)####color(brown)(“thing as a fraction. It is comparing the count of the top number to the”)## ##color(brown)(“count of the bottom number.”)##

##color(green)(“In a fraction the bottom number is used as an indicator of size, not a count”)##

Using the conversion of 1 inch is approximately ##2.54## cm

Write this as: ##(2.54″ cm”)/(1″ inch”)##

‘………………………………………………………………………………………………..

1 foot has 12 inches so to see how many centimetres there are in 1 foot we need to change the 1 inch in ##2.54/1## into 12 inches. So we need 12 lots of ##2.54/1##.

What we do to the bottom we do to the top

Multiply by 1 but in the form of ##1=12/12##

##2.54/1xx1″ “->” “(2.54xx12)/(1xx12)” “=” “30.48/12##

##color(brown)(“So 30.48 is the number of centimetres in 12 inches (1 foot)”)##

‘…………………………………………………………………………………………………….

But we need 15 feet so we need 15 lots of ##30.48/12##

Multiply by 1 but in the form of ##1=15/15##

##30.48/12xx1″ “->” “30.48/12xx15/15” “=” “(457.2″ cm”)/(180″ inches”)##

where 180 inches is the same length as 15 feet

##color(brown)(“So 457.2 is the number of centimetres in 180 inches (15 feet)”)##