A rope

From a rope of length 18 3/4 m, two smaller pieces of lengths 5 m and 7 1/2 m are cut out. Find the length of the remaining piece of rope.

Correct answer:

x =  6 ¹⁄₄ = 25/4

Step-by-step explanation:

$$\begin{gathered} a=18\frac{3}{4}=18+\frac{3}{4}=\frac{18\cdot 4+3}{4}=\frac{72+3}{4}=\frac{75}{4}=18\frac{3}{4}=18.75\text{m} \\ b=5\text{m} \\ c=7\frac{1}{2}=7+\frac{1}{2}=\frac{7\cdot 2+1}{2}=\frac{14+1}{2}=\frac{15}{2}=7\frac{1}{2}=7.5\text{m} \\ s=b+c=5+\frac{15}{2}=\frac{5\cdot 2}{2}+\frac{15}{2}=\frac{10}{2}+\frac{15}{2}=\frac{10+15}{2}=\frac{25}{2}=12.5\text{m} \\ x=a-s=\frac{75}{4}-\frac{25}{2}=\frac{75}{4}-\frac{50}{4}=\frac{75-50}{4}=\frac{25}{4}=6\frac{1}{4}=6.25 \end{gathered}$$

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