Question

Colin has a plank of wood that is 2 yards long. If he plans to cut this plank

into 67 yard pieces, how many pieces can he cut?

Answer 1

`2(1)/(3)`

Explanation:

So this question is essentially asking how many 6/7s can fit into 2/1. Or in other words, what is 2 divided by 6/7. This gives you the equation:
`(2)/(1)/(6)/(7)`. Whenever you're dividing by a fraction, you just keep the first fraction (don't change anything), change the operation (from division to multiplication) and "flip" the fraction so if you had the fraction a/b it's now b/a. This gives you the equation:
`(2)/(1)*(7)/(6)`. You can now just multiply the denominator and numerator. This gives you the fraction:
`(2*7)/(1*6)` which simplifies to
`(14)/(6)`. This can be further simplified by dividing both the numerator and denominator by 2. If you don't know why this keeps the original value think of it as multiplying the fraction by
`(0.5)/(0.5)` or
`((1)/(2))/((1)/(2))`. Which is technically multiplying the value by 1, so it should keep the original value, you're just simplifying the numerator and denominator. Simplifying it, gives you the fraction:
`(7)/(3)`. This can be a mixed fraction by splitting it up into two parts:
`(6)/(3)+(1)/(3)`. Which when added is the same thing, except the second side simplifies, and you get
`2(1)/(3)`

Answer 2

He can cut 2 1/3 pieces, so a is the correct answer.

Explanation:

`(6)/(7) x = 2`

`x = 2 / (6)/(7) = 2 * (7)/(6) = (7)/(3) = 2 (1)/(3)`