Question

example: an electrician has a piece of wire that is 4 and 3/8 centimetres long. she cuts the wire into pieces that are 1 and 1/2 centimetres long. how many pieces does she have?

Explanation:

Step1: Convert mixed - numbers to improper fractions

The length of the original wire is $4\frac{3}{8}$ centimetres. Convert it to an improper fraction: $4\frac{3}{8}=\frac{4\times8 + 3}{8}=\frac{32+3}{8}=\frac{35}{8}$ centimetres. The length of each piece is $1\frac{2}{3}$ centimetres. Convert it to an improper fraction: $1\frac{2}{3}=\frac{1\times3+2}{3}=\frac{3 + 2}{3}=\frac{5}{3}$ centimetres.

Step2: Divide the total length by the length of each piece

To find the number of pieces, we divide the total length of the wire by the length of each piece. So we calculate $\frac{35}{8}\div\frac{5}{3}$. According to the rule of dividing fractions $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$, we have $\frac{35}{8}\times\frac{3}{5}=\frac{35\times3}{8\times5}=\frac{105}{40}=\frac{21}{8}=2\frac{5}{8}$. Since we are talking about the number of whole - length pieces, we take the whole number part, which is 2.

Answer:

2