# 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?

Mar 30, 2018

$\frac{5}{24}$ of her CDs are rock music

#### Explanation:

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

$\frac{1}{6}$ “of” the total are dance music, so ($\frac{1}{6}$)($72$) = 12 dance music cds.

$\frac{1}{4}$ “of” the cds are hip hop, so ($\frac{1}{4}$)(72)=18 hip hop cds.

$\frac{3}{8}$ “of” the cds are reggae, so ($\frac{3}{8}$)(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 $\frac{15}{72}$ are rock music. You can reduce the fraction:

$\frac{15}{72}$ = $\frac{3 \cdot 5}{3 \cdot 24}$

The $\frac{3}{3}$ cancels and you are left with $\frac{5}{24}$
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Check:
$\frac{12}{72}$ = $\frac{1}{6}$ dance cds

$\frac{18}{72}$ = $\frac{1}{4}$ hip hop cds

$\frac{27}{72}$ = $\frac{3}{8}$ reggae cds

$\frac{15}{72}$ = $\frac{5}{24}$ rock cds
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$\frac{1}{6}$ + $\frac{1}{4}$ + $\frac{3}{8}$ + $\frac{5}{24}$ —-> (find common denominators)

$\frac{1 \left(4\right)}{6 \left(4\right)}$ + $\frac{1 \left(6\right)}{4 \left(6\right)}$ + $\frac{3 \left(3\right)}{8 \left(3\right)}$ + $\frac{5}{24}$

$\frac{4}{24}$ + $\frac{6}{24}$ + $\frac{9}{24}$ + $\frac{5}{24}$ = $\frac{24}{24}$ = 1

All fractions of the total should add to one whole ✅

Mar 30, 2018

$\frac{5}{24}$

#### 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:
$\text{collection" = "dance" + "hip hop" + "reggae" + "rock}$

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

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:

$\frac{1}{6} \rightarrow \frac{4}{\textcolor{\mathmr{and} a n \ge}{24}}$

$\frac{1}{4} \rightarrow \frac{6}{\textcolor{\mathmr{and} a n \ge}{24}}$

$\frac{3}{8} \rightarrow \frac{9}{\textcolor{\mathmr{and} a n \ge}{24}}$

$\frac{1}{1} \rightarrow \frac{24}{\textcolor{\mathmr{and} a n \ge}{24}}$

Put these fractions back into the problem and add:

$\frac{24}{24} = \frac{4}{24} + \frac{6}{24} + \frac{9}{24} + r$

$\frac{24}{24} = \frac{19}{24} + r$

$\frac{5}{24} = r$

So $\frac{5}{24}$ of Beven's collection is $\text{rock music}$