Question

Beven has a collection of 72 music CDs. One-sixth of the CDs are dance music 1/4 are hip hop, and 3/8 are reggae. The rest of the CDs are rock music. What fraction of her CDs are rock music?

Answer 1

`5/24` of her CDs are rock music

Explanation:

In math, “of” can mean “multiply” the fraction or percent by the whole.

`1/6` “of” the total are dance music, so (`1/6`)(`72`) = 12 dance music cds.

`1/4` “of” the cds are hip hop, so (`1/4`)(72)=18 hip hop cds.

`3/8` “of” the cds are reggae, so (`3/8`)(72)= 27 are reggae cds.

The total cds now is 12+18+27= 57 cds.

The rest are rock music, and there is a total of 72 cds, so 72 - 57 = 15 rock cds.

The question asks “what fraction of the cds are rock music”. 15 cds are rock, out of 72 total cds, so `15/72` are rock music. You can reduce the fraction:

`15/72` = `(3*5)/(3*24)`

The `3/3` cancels and you are left with `5/24`
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Check:
`12/72` = `1/6` dance cds

`18/72` = `1/4` hip hop cds

`27/ 72` = `3/8` reggae cds

`15 / 72` = `5/24` rock cds
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`1/6` + `1/4` + `3/8` + `5/24` —-> (find common denominators)

`(1(4))/(6(4))` + `(1(6))/(4(6))` + `(3(3))/(8(3))` + `5/24`

`4/24` + `6/24` + `9/24` + `5/24` = `24/24` = 1

All fractions of the total should add to one whole ✅

Answer 2

`5/24`

Explanation:

The way that I'm going to solve this problem is a little bit different, but I feel that it's the simplest way to find the correct answer.

We know that Beven's `1` collection is equal to:
`"collection" = "dance" + "hip hop" + "reggae" + "rock"`

Beven has only one collection, so we'll say that `"collection"` is 1. We've been given some of the other values, so we can put those in:
`1 = 1/6 + 1/4 + 3/8 + r`

We need to give all of the fractions the same denominator so that we can add them together. I'll go ahead and change `1` to have the same denominator too:

`1/6 rarr 4/color(orange)24`

`1/4 rarr 6/color(orange)24`

`3/8 rarr 9/color(orange)24`

`1/1 rarr 24/color(orange)24`

Put these fractions back into the problem and add:

`24/24 = 4/24 + 6/24 + 9/24 + r`

`24/24 = 19/24 + r`

`5/24 = r`

So `5/24` of Beven's collection is `"rock music"`