Jalan Ruas D7, Block D6 No.
2, Kota Baru Kemayoran, Jakarta Pusat 14410
Indonesia +62 21 6542654
Chapter 7: Ratio
Ratio: A ratio is a comparison of two quantities of the same unit. The ratio formula for two
𝒂
numbers, a and b is expressed as a : b or 𝒃.
Ratios are expressed using the symbol of the colon ( : ).
It is expressed in terms of times, i.e., the number of times the first value contains the
second.
For example, if there are 3 red flowers and 2 blue flowers, the ratio of red to blue flowers
is 3:2
A proportion: A proportion is an equation that equates two ratios.
When two or more ratios are equal, they are said to be in proportion. The concept of ratio
and proportion is based on fractions.
Proportion is an equation that says that two ratios are equivalent.
A proportion is written as x : y : : z : w, and is read as x is to y as z is to w.
𝑥 𝑧
Here, = 𝑤 where w & y are not equal to 0.
𝑦
There are two types of proportions.
Direct Proportion
Inverse Proportion
By: RAJENDER KONKA. B.Sc., M.Sc., B.Ed. Page 1 of 5
Jalan Ruas D7, Block D6 No.2, Kota Baru Kemayoran, Jakarta Pusat 14410
Indonesia +62 21 6542654
Direct Proportion: Direct proportion describes the direct relationship between two
quantities. If one quantity increases, the other quantity also increases and vice-versa.
Thus, a direct proportion is written as y ∝ x.
Inverse Proportion: Inverse proportion describes the relationship between two quantities
in which if one quantity increases, the other quantity decreases and vice-versa.
𝟏
Thus, an inverse proportion is written as 𝒚 ∝ 𝒙.
Equivalent Ratios: The ratios 1 : 6 and 20 : 120 and 5 : 30 are all equivalent ratios, but
1 : 6 is the simplest form.
Example 1 Write each of these ratios in its simplest form:
(a) 7 : 14 (b) 15 : 25
Solution (a) Divide both sides by 7, giving
7 14
∶ =1:2
7 7
(b) Divide both sides by 5, giving
15 25
∶ =3 :5
5 5
Example 1: Julie and Jack run a stall at a car boot sale and take a total of £90. They
share the money in the ratio 4 : 5. How much money does each receive?
Sol by 1st method: As the ratio is 4 : 5, first add these numbers together to see by
how many parts the £90 is to be divided.
4 + 5 = 9 , so 9 parts are needed. Now divide the total by 9.
90
= 10 , so each part is £10.
9
The 1 st share = 4 x 10 = 40
The 2 nd share = 5 x 10 = 50
Sol by 2 nd method:
4 + 5 = 9 , so 9 parts are needed.
4
The 1 st share = x 90 = 40
9
5
The 2 nd share = x 90 = 50
9
By: RAJENDER KONKA. B.Sc., M.Sc., B.Ed. Page 2 of 5
Jalan Ruas D7, Block D6 No.2, Kota Baru Kemayoran, Jakarta Pusat 14410
Indonesia +62 21 6542654
Example 2 : Rachel, Ben and Emma are given $ 52. They decide to divide the
money in the ratio of their ages, 10 : 9 : 7. How much does each receive?
Sol : 10+9+7 = 26
10
Rachel = × 52 = 20
26
9
Ben = × 52 = 18
26
7
Emma = × 52 = 14
26
Do this:
1) A business man distributes his properties among his three sons, in the ratio
4 : 3 : 2. The second son received an amount of $ 3 million, find the others
shares.
2) Sarah has some chocolates. 24 are white chocolate. 16 are milk chocolate. 8 are
dark chocolate. Write down the ratio of white chocolate to milk chocolate to dark
chocolate. Give your ratio in its simplest form
3) Chris and Molly win money in a competition. They share the money in the ratio 2 :
3 Molly receives $ 240. How much money does Chris receive?
4) A school has 240 students. The ratio girls : boys = 25 : 23.
i) Show that the number of boys is 115.
ii) One day, there are 15 girls absent and 15 boys absent. Find the ratio girls :
boys in school on this day. (Give your answer in its simplest form).
5) Alex has $20 and Bobbie has $25.
i. Alex and Bobbie each spend 1/5 of their money. Find the ratio of Alex’s :
Bobbie’s remaining money.
ii. Alex and Bobbie then each spend $4. Find the new ratio of Alex’s : Bobbie’s
remaining money.
6)
7)
8)
By: RAJENDER KONKA. B.Sc., M.Sc., B.Ed. Page 3 of 5
Jalan Ruas D7, Block D6 No.2, Kota Baru Kemayoran, Jakarta Pusat 14410
Indonesia +62 21 6542654
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By: RAJENDER KONKA. B.Sc., M.Sc., B.Ed. Page 4 of 5
Jalan Ruas D7, Block D6 No.2, Kota Baru Kemayoran, Jakarta Pusat 14410
Indonesia +62 21 6542654
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By: RAJENDER KONKA. B.Sc., M.Sc., B.Ed. Page 5 of 5
