Sarah is making scarfs. She has #1 3/4# yards of fabric. She needs #2 1/2# yards of fabric to make all of the scarves she wants to make. How much more fabric does Sarah need?

1 Answer
Oct 11, 2017

See a solution process below:

Explanation:

First, convert each number of yards from mixed numbers to improper fractions:

Needs:

#2 1/2 = 2 + 1/2 = (2/2 xx 2) + 1/2 = 4/2 + 1/2 = (4 + 1)/2 = 5/2#

Has:

#1 3/4 = 1 + 3/4 = (4/4 xx 1) + 3/4 = 4/4 + 3/4 + (4 + 3)/4 = 7/4#

To find out how much more fabric Sarah needs we can subtract how much Sarah has from how much total fabric Sarah needs:

#5/2 - 7/4#

To add or subtract fractions the must be over a common denominator. We can multiply the fraction on the left by the appropriate form of #1# to put it over a common denominator without changing the value of the fraction:

#(2/2 xx 5/2) - 7/4 =>#

#(2 xx 5)/(2 xx 2) - 7/4 =>#

#10/4 - 7/4#

We can now subtract the numerators over the common denominator:

#(10 - 7)/4 => 3/4#

Sarah needs #3/4# more yards of fabric to complete the dress.