At a meeting, #7/10# of the attendees were female. Of the females, #4/5# wore jeans. What fraction of the attendees were females wearing jeans?

2 Answers
MathFact-orials.blogspot.com
Dec 24, 2016

#7/10 xx 4/5 = 28/50 = 14/25#

Explanation:

Let's first work this out using a concrete example, and then I'll show the direct way to do it.

Let's say we have a meeting where 100 people attend. We are told that #7/10# are female. So that means there were 70 females:

#100xx7/10=70#

Of those 70 females, #4/5# wore jeans. And so we have:

#70 xx 4/5 = 56# jeans-wearing females.

We can figure this example out more directly by writing it this way:

#100 xx 7/10 xx 4/5 = 56#

And we can figure out the ratio of jeans-wearing females for any size of meeting by simply multiplying the two fractions together - and we can express it as a fraction or a decimal/percentage:

#7/10 xx 4/5 = 28/50 = 56/100 = 0.56 = 56%#

#7/10 xx 4/5 = 28/50 = 14/25#

Tony B
Dec 30, 2016

#14/25#

Explanation:

Let the #color(blue)("'group looking at'")# be that proportion which is female

#color(white)(.)#

#4/5xxcolor(blue)("group looking at")# ....................Expression(1)

But the #color(blue)("group looking at"=7/10)# of the whole

#color(brown)("Substitute "color(blue)(7/10)" for "color(blue)("group looking at")" in Expression(1)")#

#color(brown)(4/5color(blue)(xx"group looking at")" " ->" " 4/5color(blue)(xx7/10))color(green)( = 28/50)#

#" "color(green)((28-:2)/(50-:2) = 14/25)#

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