Question

A picture framer has a thin board 10 1/2 feet long. The framer notices that 2 3/8 feet of the board is scratched and cannot be used. The rest of the board will be used to make small picture frames. Each picture frame needs 1 2/3 feet of the board. At most, how many complete picture frames can be made?

Answer 1

1. Find how many of the board can be used for picture frames:

$10\dfrac{1}{2}-2\dfrac{3}{8}=\dfrac{21}{2}-\dfrac{19}{8}=\dfrac{21\cdot 4-19}{8}=\dfrac{65}{8}\ ft.$

2. Each picture frame needs $1\dfrac{2}{3}=\dfrac{5}{3}$ feet of the board, then the farmer can complete

$\dfrac{65}{8}:\dfrac{5}{3}=\dfrac{65}{8}\cdot \dfrac{3}{5}=\dfrac{39}{8}=4\dfrac{7}{8}$

picture frames.

Answer: at most he can complete 4 picture frames.