Question

Richard is given one of four pieces of equal-sized fabric. After using some of his fabric for a project, he has 5/6 of a square yard left. If the total amount of fabric from the four original pieces was 11/23 square yards, about how much fabric did Richard use for his project?

Answer 1

Richard used
`2(1)/(12)\ yd ^2` of fabric for his project.

Explanation:

Given:

Total amount of fabric =
`11\frac23\ yd^2`

Now To convert a mixed fraction to an improper fraction, Multiply the whole number part by the fraction's denominator, Add that to the numerator,Then write the result on top of the denominator.

`11\frac23\ yd^2` can be Rewritten as
`(35)/(3)\ yd^2`

Number of pieces fabric was cut = 4

Richard is given one of four pieces of equal-sized fabric.

Amount of fabric Richard was given =
`\frac14 * (35)/(3)=(35)/(12)\ yd^2`

Amount of fabric left with Richard =
`\frac56 \ yd^2`

We need to find the amount of fabric Richards used for his project.

Solution:

Now we can say that;

amount of fabric Richards used for his project is equal to Amount of fabric Richard was given minus Amount of fabric left with Richard.

framing in equation form we get;

amount of fabric Richards used for his project =
`(35)/(12)-\frac56`

Now we will make the denominator common using LCM we get;

amount of fabric Richards used for his project =
`(35)/(12)-(5*2)/(6*2) = (35)/(12)-(10)/(12)`

Now Denominator is same so we will solve the numerator.

amount of fabric Richards used for his project =
`(35-10)/(12)= (25)/(12)\ yds^2`

`(25)/(12)\ yds^2` can be rewritten as
`2(1)/(12)\ yd ^2`

Hence Richard used
`2(1)/(12)\ yd ^2` of fabric for his project.