RATIO AND PERCENTAGE

HELLO, WELCOME TO A NEW TERM

A ratio is used to compare two quantities. It is usually represented with the symbol (:). A ratio just like fractions has two parts which are NUMERATOR and DENOMINATOR. Ratio can also be reduced to its lowest term.

EXAMPLE

Write the ratio of 16 to 28 in its lowest form.

Solution

16 to 28 = 16:28

= or 4:7

In a bus, there are 9 women and 15 men. Find the ratio to the simplest form of the number of:
Men to women
Women to men
People to men

Solution

Men to women = 15 : 9

= or 5:3

Women to men = 9 : 15

= or 3:5

People to men = 24 : 15

= or 8:5

Express 350m as a fraction of 1km in its lowest form.

Solution

350m to 1km = 350m to 1000m

= or 7: 20

John is 27 years old. His brother James is 15 years old. What is the ratio of John’s age to his brother age? In 6 years-time, what will be the ratio of James’ age to John?

Solution

John’s age to James’ age = John’s age : James’ age

= 27:15

= or 9: 5

In 6 years-time,

John’s age = 27 + 6 = 33

James’ age = 15 + 6 = 21

James’s age to John’s age = 21:33

= or 7:11

PROBLEMS ON RATIO

One of the most common use of ratio is in sharing. It plays an important role in everyday’s activity such as sharing money between or among people.

Example

Alex and Charles were instructed by their parents to share a pocket money of N600 in the ratio of 3:5. How much does each receive?

Solution

Total ratio = 3 + 5

= 8

Alex’s share =

= N225

Charles share = N600 – N225

= N375

The angles in a triangle are in the ratio 1:2:3. Find the largest angle.

Solution

The total angles in a triangle = 180⁰

Total ratios = 1 + 2 + 3

= 6

Largest ratio = 3

Largest angle =

= 90⁰

Emmanuel and Isaac shared some money in the ratio of 4: 5 respectively. If Emmanuel got N120, how much did Isaac get?

Solution

Emmanuel : Isaac

4 : 5

120 : x

Cross multiply.

Isaac share =

= 30 5

= N150

Total money shared = N120 + N150

= N270

Karisa and Hope saved some money in the ratio 6:4. If Hope saved N280, how much did Karisa save?

Solution

Karisa : Hope

6 : 4

X : 280

Karisa’s share =

= 70 6

= N420

Total money saved = N280 + N420

= N700

Percentage

Percentage means one hundredth. The word “per cent” actually mean “per hundred” in Latin. The symbol for percent is %. Therefore, 1% means 1/100 or one hundredth and 7% means 7/100 or seven hundredth. A percent can be expressed as a Decimal or a Fractions

A half pizza can be written as:

Percentage = 50%
As a decimal = 0.5
As a fraction = ½

PERCENTAGE OF QUANTITIES AND NUMBERS

Example:

Calculate 25% of 80.

Solution

25% of 80

= 20

If only 10 out of 200 apples are bad, what percent is that?

Solution

Total apples = 200

Bad apples = 10

Fraction of bad apples =

Percentage of bad apples =

= 5%

15% of 200 apples are bad. How many apples are bad?

Solution

Total apples = 200

Bad apples = 15% of 200

= 30 apples

30 apples are bad

PERCENTAGE PROBLEMS

EXAMPLES

25 people were absent in a class of 125 students. What is the percentage of those present?

Solution

Total students = 125

Number of students absent = 25

Number of student present = 125 – 25 = 100

Percentage of students present =

= 80%

2^nd method

Total students = 125

Number of students that are absent = 25

Percentage of students absent =

= 20%

Therefore, percentage of students present = 100 -20

= 80%

What percentage of 250 is 50?

Solution

This question is the same as finding what percentage of 250 the figure 50 is.

= 20%

Quiz

In a box, there are 20 balls. 6 are red, 10 are green and 4 are blue
What is the ratio of red to green balls?
What is the ratio of green to blue balls?
What is the ratio of blue to red balls?
What is the ratio of red balls to the total number of balls?
Mary finished her chores in 2hours 3omins. The following day, Martha finished hers in 1hour 30mins. Find the ratio of time taken Mary to Martha.
In a basket filled with oranges and mangoes, the ratio of mangoes to all the fruits is 9:13. If the basket contains 154 fruits:
How many are mangoes?
How many are oranges?
Ojo shared an amount of money between Paul and Peter in the ratio 3:5. If Peter received N100. Find:
How much Paul received
The total amount shared between them.
What percent of 270 is 90?
In a basket of 288 oranges, 36 are bad. What percent are good?