Question

Marissa buys a licorice candy rope to share with some friends. The rope is 30 and two-thirds inches long. She begins to cut the rope into pieces that are 3 and one-third inches long.

If she continues until the entire rope is cut into pieces, how many 3 and one-third inch pieces will she have?

Answer 1

9 pieces of 3 and one-third inches long

Explanation:

We are given that the length of the candy rope is
`\tex \displaystyle {30(2)/(3)} \tex` inches

Each piece is
`3(1)/(3)` inches long

Total number of pieces =
`\tex \displaystyle {30(2)/(3)} \tex / 3(1)/(3)`

Whenever working with mixed fractions, convert them to improper fractions. This makes these numbers easier to work with

The rule for converting a mixed fraction of the form
`a (b)/(c)` to an improper fraction is

`a(b)/(c)=(a* \:c+b)/(c)`

`30(2)/(3)=(30* 3+2)/(3) = (92)/(3)`

`3(1)/(3)=(3* 3+1)/(3) = (10)/(3)`

We get

`30(2)/(3)/ \:3(1)/(3)\\\\= (92)/(3)/ \:3(1)/(3)\\\\\mathrm{Apply\:the\:dfraction\:rule}:\:(a)/(b)/ (c)/(d)=(a)/(b)* (d)/(c)\\\\= (92)/(3)* (3)/(10)\\\\= (92)/(10)\\\\= 9(2)/(10)\\\\= 9(1)/(5)`
Ignoring the fraction of a piece she will have 9 pieces of 3 and one-third inches long