Solving Ratios

Intro

To solve some ratio problems, multiplication or division must be used to reduce or simplify the ratio terms. For example, at Acme Academy, there are 260 boys and 240 girls.

Sample Problem

What is the ratio of the number of boys to the number of girls? What is the ratio of the number of girls to the total number of students in the academy?

Solution

A) There are 260 boys and 240 girls. What is the ratio of the number of boys to the number of girls?

Answer:
Currently, the number of boys to girls is (260 : 240).

Both sides of the ratio can be divided by 10 .
260/240 (divide each by 10) = 26/24 or (26 : 24)

Both sides of the ratio can be divided again by 2.
26/24 (divide each by 2) = 13/12 or (13 : 12)

B) There are 260 boys and 240 girls. What is the ratio of the number of girls to the total number of students in the academy?

Answer:
First, we must find the total number of students.
260 girls + 240 boys = 500 total students

Now, we know our current ratio is (260 : 500).

Again, notice that both sides can be divided by 10.
260/500 (divide each by 10) = 26/50 or (26 : 50)

Both sides of the ratio can be divided again by 2.
26/50 (divide each by 2) = 13/25 or (13 : 25)



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