Highway

A stretch of highway 12 1/4 kilometers long has speed limit signs every 7/8 of a kilometer. How many speed limit signs are on this stretch of highway?

Correct answer:

n =  14

Step-by-step explanation:

$$\begin{gathered} s=12\frac{1}{4}=12+\frac{1}{4}=\frac{12\cdot 4+1}{4}=\frac{48+1}{4}=\frac{49}{4}=12\frac{1}{4}=12.25\text{km} \\ a=7/8=\frac{7}{8}=0.875\text{km} \\ {n}_1=s/a=\frac{49}{4}/\frac{7}{8}=\frac{49}{4}:\frac{7}{8}=\frac{49}{4}\cdot \frac{8}{7}=\frac{49\cdot 8}{4\cdot 7}=\frac{392}{28}=14 \\ n=\lfloor n_1\rfloor =\lfloor 14\rfloor =14 \end{gathered}$$

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