Question

From a 12 foot roll of rubber hose, a person cuts lengths of 2 3/8 feet, 2 1/2 feet, and 3 1/4 feet. How much hose is left on the roll?

Answer 1

Sum the lengths that the person cuts:

To sum mixed numbers:

`2(3)/(8)ft+2(1)/(2)ft+3(1)/(4)ft=`

1. Add the whole numbers:

`2ft+2ft+3ft=7ft`

2. Add fractions

`\begin{gathered} (3)/(8)ft+(1)/(2)ft+(1)/(4)ft \\ \\ \text{Write all as fractions with denominator 8:} \\ \\ (3)/(8)ft+(4)/(8)ft+(2)/(8)ft=(3ft+4ft+2ft)/(8)=(9)/(8)ft \\ \\ \\ \end{gathered}`

Then, the person cuts 7 9/8 ft, substract it from the initial 12 ft roll of rubber hose:

`\begin{gathered} \text{Write the mixed number as a fraction:} \\ 7(9)/(8)ft=7ft+(9)/(8)ft=(56ft+9ft)/(8)=(65)/(8)ft \\ \\ \text{Substract the fraction above from 12ft}\colon \\ \\ 12ft-(65)/(8)ft=(96ft-65ft)/(8)=(31)/(8)ft \\ \\ \text{Write the result as a mixed number:} \\ \\ (31)/(8)ft=(24)/(8)ft+(7)/(8)ft=3(7)/(8)ft \end{gathered}`

Then, 3 7/8 ft of hose are left on the roll