Line segments

There are three line segments on the line: the length of MN = 3 1/2, the length of NO= 2 3/4, and the length of OP=1 2/3. Find the length of line segment MP.
Write your answer as a mixed number.

Correct answer:

d =  7 ¹¹⁄₁₂ = 95/12

Step-by-step explanation:

$$\begin{gathered} a=3\frac{1}{2}=3+\frac{1}{2}=\frac{3\cdot 2+1}{2}=\frac{6+1}{2}=\frac{7}{2}=3\frac{1}{2}=3.5 \\ b=2\frac{3}{4}=2+\frac{3}{4}=\frac{2\cdot 4+3}{4}=\frac{8+3}{4}=\frac{11}{4}=2\frac{3}{4}=2.75 \\ c=1\frac{2}{3}=1+\frac{2}{3}=\frac{1\cdot 3+2}{3}=\frac{3+2}{3}=\frac{5}{3}=1\frac{2}{3}\doteq 1.6667 \\ d=|MP|=|MN|+|NO|+|OP| \\ d=a+b+c=\frac{7}{2}+\frac{11}{4}+\frac{5}{3}=\frac{42}{12}+\frac{33}{12}+\frac{20}{12}=\frac{42+33+20}{12}=\frac{95}{12}=7\frac{11}{12}=7.9167 \end{gathered}$$

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