We need to find the length of fabric that Rebecca needs to complete her quilt.
The length of fabric that Rebecca needs is [tex]3\dfrac{3}{4}[/tex].
The total length of fabric required is [tex]10\dfrac{1}{2}\ \text{yards}[/tex]
One piece of fabric is [tex]2\dfrac{1}{2}\ \text{yards}[/tex] long.
Another piece of fabric is [tex]4\dfrac{1}{4}\ \text{yards}[/tex] long.
Let [tex]x[/tex] be the missing length.
[tex]2\dfrac{1}{2}+4\dfrac{1}{4}+x=10\dfrac{1}{2}\\\Rightarrow 2+\dfrac{1}{2}+4+\dfrac{1}{4}+x=10+\dfrac{1}{2}\\\Rightarrow \dfrac{24+2+1}{4}+x=10+\dfrac{1}{2}\\\Rightarrow x=\dfrac{21}{2}-\dfrac{24+2+1}{4}\\\Rightarrow x=\dfrac{42-(24+2+1)}{4}\\\Rightarrow x=\dfrac{15}{4}[/tex]
Converting to mixed fractions
When 15 is divided by 4 the remainder is 3 and quotient is 3, so the length of fabric that Rebecca needs is [tex]3\dfrac{3}{4}[/tex].
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