Question

Troy has a 5/6 in nail that he must hammer into a board. Each strike of the hammer moves the nail 1/12 in into the board. How many strikes of the hammer must he make to drive the nail completely into the board?

Answer 1

The nail is 5/6 inches long and each strike of the hammer moves it 1/12 inches into the board.

To determine how many strikes are needed to drive the nail completely into the board you have to divide the size of the nail by the length it moves into the board each strike:

`(5)/(6)/(1)/(12)`

To divide fractions, you have to multiply the dividend (first fraction) by the reciprocal of the divisor (second fraction)

To determine the reciprocal you have to turn the fraction upside down:

`(1)/(12)\to(12)/(1)`

Next, multiply both fractions:

`(5)/(6)\cdot(12)/(1)=(5\cdot12)/(6\cdot1)=(60)/(6)=10`

To drive the nail completely into the board, Troy has to strike the hammer 10 times.