Question

lily bought 13 yards to sew 3 shirts for her family. the first shirt requires 2 4/6 yards. the second shirt uses 3 1/3 yards. finally the last shirt needs 4.5 yards. after making the three shirts how many yards does she have left?

Answer 1

Add the three quantities to figure out the total amount of used yards. Then, substract that total from the original 13 yards to calculate how many yards does she have left.

Write each fraction as an improper fraction:

`\begin{gathered} 2(4)/(6)=2+(4)/(6) \\ =(2\cdot6)/(6)+(4)/(6) \\ =(12)/(6)+(4)/(6) \\ =(12+4)/(6) \\ =(16)/(6) \\ =(16/2)/(6/2) \\ =(8)/(3) \end{gathered}`

Similarly:

`\begin{gathered} 3(1)/(3)=3+(1)/(3) \\ =(10)/(3) \end{gathered}`
`\begin{gathered} 4.5=4+0.5 \\ =4+(1)/(2) \\ =(9)/(2) \end{gathered}`

Add the three fractions:

`\begin{gathered} 2(4)/(6)+3(1)/(3)+4.5=(8)/(3)+(10)/(3)+(9)/(2) \\ =(8+10)/(3)+(9)/(2) \\ =(18)/(3)+(9)/(2) \\ =(18/3)/(3/3)+(9)/(2) \\ =(6)/(1)+(9)/(2) \\ =(6\cdot2)/(2)+(9)/(2) \\ =(12)/(2)+(9)/(2) \\ =(21)/(2) \end{gathered}`

The total amount of yards used to make shirts was 21/2. Substract 21/2 from 13:

`\begin{gathered} 13-(21)/(2)=(13\cdot2)/(2)-(21)/(2) \\ =(26)/(2)-(21)/(2) \\ =(26-21)/(2) \\ =(5)/(2) \end{gathered}`

Rewrite 5/2 as a mixed fraction:

`\begin{gathered} (5)/(2)=(4+1)/(2) \\ =(4)/(2)+(1)/(2) \\ =2+(1)/(2) \\ =2(1)/(2) \end{gathered}`

Therefore, 2 1/2 yards are left after making the three shirts.