Question

a carpenter wants to cut a board 16 1/2 ft in length into 1 7/8 feet pieces how many pieces can be cut from the board

Answer 1

A) 8

B) 1/5 ft

1) We need to divide 16 1/2 by 1 7/8, but firstly let's turn those into improper fractions to make it easy our calculations:

`\begin{gathered} 16(1)/(2)=(2*16+1)/(2)=(33)/(2) \\ 1(7)/(8)=(8*1+7)/(8)=(15)/(8) \end{gathered}`

Notice that we kept the denominator, and multiplied by the whole number and then added it to the numerator to get into an improper fraction

2) Now let's proceed with that dividing 33/2 by 15/8:

`(33)/(2)\colon(15)/(8)=(33)/(2)*(8)/(15)=(264)/(30)=(44)/(5)`

3) Hence, there is going to be 44/5 or 8.8 pieces or we can rewrite into a Mixed Number dividing 44 by 5, and placing the remainder as the new numerator and the divisor as the new bottom number:

Part B) Let's assume the whole number 8 and 4/5 as the leftover. Cutting them into 4 pieces:

`(4)/(5)\colon4=(4)/(5)*(1)/(4)=(4)/(20)=(1)/(5)`

So the answers are:

A) 8 pieces

B) 1/5 ft