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))##