An electricfan

An electric fan has a piece of wire 4 3/8 centimeters long. If she divides the wire into parts that are 1 2/3 centimeters long, she has how many pieces?

Correct answer:

n =  3

Step-by-step explanation:

$$\begin{gathered} a=4\frac{3}{8}=\frac{35}{8}=4\frac{3}{8}=4.375\text{cm} \\ b=1\frac{2}{3}=1+\frac{2}{3}=\frac{1\cdot 3+2}{3}=\frac{3+2}{3}=\frac{5}{3}=1\frac{2}{3}\doteq 1.6667\text{cm} \\ {n}_1=a/b=\frac{35}{8}/\frac{5}{3}=\frac{35}{8}:\frac{5}{3}=\frac{35}{8}\cdot \frac{3}{5}=\frac{35\cdot 3}{8\cdot 5}=\frac{105}{40}=\frac{21}{8}=2\frac{5}{8}=2.625 \\ n=\lfloor n_1\rfloor +1=\lfloor 2.625\rfloor +1=3 \end{gathered}$$

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