Curtains and bed cover

Grandma bought 16 3/4 meters of cloth. She uses 8 1/2 meters for curtains and 7 1/2 meters for bed covers. How many meters of clothing were not used?

Correct answer:

x =  3/4 m

Step-by-step explanation:

$$\begin{gathered} a=16\frac{3}{4}=16+\frac{3}{4}=\frac{16\cdot 4+3}{4}=\frac{64+3}{4}=\frac{67}{4}=16.75\text{m} \\ b=8\frac{1}{2}=8+\frac{1}{2}=\frac{8\cdot 2+1}{2}=\frac{16+1}{2}=\frac{17}{2}=8.5\text{m} \\ c=7\frac{1}{2}=7+\frac{1}{2}=\frac{7\cdot 2+1}{2}=\frac{14+1}{2}=\frac{15}{2}=7.5\text{m} \\ u=b+c=\frac{17}{2}+\frac{15}{2}=\frac{17+15}{2}=\frac{32}{2}=16\text{m} \\ x=a-u=\frac{67}{4}-16=\frac{67}{4}-\frac{16\cdot 4}{4}=\frac{67}{4}-\frac{64}{4}=\frac{67-64}{4}=\frac{3}{4}=\frac{3}{4}\text{m}=0.75\text{m} \end{gathered}$$

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