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

Answer:

Richard used $2\frac{1}{12}\ yd ^2$ of fabric for his project.

Step-by-step 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 $\frac{35}{3}\ yd^2$

Number of pieces fabric was cut = 4

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

Amount of fabric Richard was given = $\frac14 \times \frac{35}{3}=\frac{35}{12}\ yd^2$

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 = $\frac{35}{12}-\frac56$

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

amount of fabric Richards used for his project = $\frac{35}{12}-\frac{5\times2}{6\times2} = \frac{35}{12}-\frac{10}{12}$

Now Denominator is same so we will solve the numerator.

amount of fabric Richards used for his project  = $\frac{35-10}{12}= \frac{25}{12}\ yds^2$

$\frac{25}{12}\ yds^2$ can be rewritten as $2\frac{1}{12}\ yd ^2$

Hence Richard used $2\frac{1}{12}\ yd ^2$ of fabric for his project.