Question

A school had 180 boys and 240 girls attending

(a) What is the ratio of boys to girls?
(b) What is the ratio of girls to boys?
(c) What is the ratio of students to boys?
(d) What is the ratio of girls to students?

Answer 1

(a) 3:4

(b) 4:3

(c) 7:3

(d) 4:7

Explanation:

(a) 3:4

180:240 = 3:4 (after simplification)

(b) 4:3

240:180 = 4:3 (after simplification)

(c) 7:3

Total number of students = 240 + 180 = 420

420:180 = 7:3 (after simplification)

(d) 4:7

Total number of students = 240 + 180 = 420

240: 420 = 4:7 (after simplification)

Answer 2

a) 3 : 4

b) 4 : 3

c) 7 : 3

d) 4 : 7

Explanation:

(just a side note: you can write ratios in fraction form as well!)

To find the ratio between boys to girls, we would write it like this:

180/240 or 180 : 240 or 180 to 240

Although that is right, that isn't simplified.

Thus, we need to find a common factor that both the numerator and denominator share!

180 and 240 are both divisible by 60!

180 ÷ 60 = 3

240 ÷ 60 = 4

Therefore, you would get a simplified ratio of 3 : 4! For every 3 boys. there are 4 girls!

For part b, you simply switch the 4 and 3 around so you get 4 : 3. For every 4 girls, there are 3 boys.

Now part c involves the total amount of students...

Basically, add the number of boys and the number of girls together, and you would get 420.

420 : 120 shows the amount of students there are to boys...but it is not in its simplest form!!

Like we did before, we have to find a common factor between the two...which is 60!

420 ÷ 60 = 7

120 ÷ 60 = 3

Thus, there are 7 students for every 3 boys (7 : 3)

Finally, part d! Simply the ratio:

420 : 240

Divide both by 60 and...

You get 4 :7! For every 4 girls, there are 7 students

Hope this helps! Let me know if you have any other questions :D