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?

2 Answers
Mar 30, 2018

Answer:

#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#
—————————————————————————
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
———————————————————

#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 ✅

Mar 30, 2018

Answer:

#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"#