Question

Rebecca needs $10\frac{1}{2}$ yards of fabric to make a quilt.

She has one piece of fabric that is $2\frac{1}{2}$ yards and another piece of fabric that is $4\frac{1}{4}$ yards.

How many more yards of fabric does Rebecca need to make a quilt.

Answer 1

Find the fabric yards does Rebecca need to make a quilt:

Given that, the total number of yards that is required $10\frac{1}{2}$.

One piece of fabric is $2\frac{1}{2}$ yards and another piece of fabric is $4\frac{1}{4}$.

Step 1. Calculate the yards that are required:

Consider $x$ as the yard that is required:

$\begin{array}{rcl}& & \Rightarrow \left(2\frac{1}{2}\right)+\left(4\frac{1}{4}\right)+x=\left(10\frac{1}{2}\right)\\ & & \Rightarrow \left(\frac{5}{2}\right)+\left(\frac{17}{4}\right)+x=\left(10\frac{1}{2}\right)\end{array}$

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$:
$\Rightarrow \frac{5}{2}·\frac{2}{2}+\frac{17}{4}+x=10\frac{1}{2}$
Write each expression with a common denominator of $4:$
$\Rightarrow \frac{5·2}{4}+\frac{17}{4}+x=10\frac{1}{2}$
Combine the numerators over the common denominator.
$\begin{array}{rcl}& \Rightarrow & \frac{5·2+17}{4}+x=10\frac{1}{2}\\ & \Rightarrow & \frac{27}{4}+x=10\frac{1}{2}\\ & \Rightarrow & \frac{27}{4}+x=\frac{21}{2}\end{array}$

Step 2. Move all the terms not containing $x$ to one side.

$\Rightarrow x=\frac{21}{2}-\frac{27}{4}$

To write ${\displaystyle \frac{21}{2}}$ as a fraction with a common denominator, multiply by${\displaystyle \frac{2}{2}}$.

$\begin{array}{rcl}& \Rightarrow & x=\frac{21}{2}\cdot \frac{2}{2}-\frac{27}{4}\\ & \Rightarrow & x=\frac{21.2}{4}-\frac{27}{4}\\ & \Rightarrow & x=\frac{42}{4}-\frac{27}{4}\\ & \Rightarrow & x=\frac{15}{4}\left[\frac{15}{4}=3+\frac{3}{4}\right]\\ & \Rightarrow & x=3\frac{3}{4}\end{array}$

Hence, Rebecca needs $\mathbf{3}\frac{\mathbf{3}}{\mathbf{4}}$ yards more to make a quilt.