Ratio and Proportion:

Ratio: 

A comparison of two quantities by division is called a ratio.

A ratio can be written in different forms like a : b or a/b and is commonly read as, a is to b.

Proportion:

Equality of two ratios is called proportion.

A proportion is written as a : b : : c : d, and is read as a is to b as c is to d. Here, a/b = c/d where b & d are not equal to 0.

There are two types of proportions.

• Direct Proportion
• Inverse Proportion

Direct Proportion:

Direct proportion describes the direct relationship between two quantities. If one quantity increases, the other quantity also increases and vice-versa.

Inverse Proportion:

Inverse proportion describes the relationship between two quantities in which if one quantity increases, the other quantity decreases and vice-versa.

Practice Problems:

1. Write the below ratios in its simplest form.

     a)    3:9            b)    5 : 125            c)  2 : 16

2. The scale on the map is 1: 10000.What actual distance does a length

    of 5 cm on the map represent ?

3. In a school there are 850 pupils and 40 teachers. Write the ratio of 

    teachers to pupils.

4. If 15 liters of petrol cost BD 2.1. Find the cost of 50 liters of petrol.

5. If  3 copies of a book cost $ 27. Calculate the cost of 10 books.

6. Ali and Zahra are given BD 50. They decided to divide the money in

    the ratio 2:3. How much dose each receive ?

7. A train normally complete a 270 km journey in 4.5 hours. How much

   faster would it have to travel to complete the journey in 4 hours ?

 Problems on percentages:

Practice problems on percentages.

1. What is 81 percent of 70 ?

2. What is 95 percent of 50 ?

3. What percent of 72 is  35 ?

4. 92 is 70 percent of what ?

5. $22 is 12 percent of what number ?

6. If the price of a mobile phone changes from 110 to 

   145. Calculate the percent change ?

7. A test has 20 questions. If peter gets 60% correct, 

   how many questions did peter miss?

8. In a school, 20% of the teachers teach basic math. If 

    there are 25 basic math teachers, how many teachers

   are there in the school?

9. 22 students in a class took an algebra test. If 15 

    students passed the test, what percent do not pass?

10. In a class 60% of the students are girls. If the total 

   number of students is 30, what is the number of boys?

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 Evaluation of numerical expressions using calculator:

1. Practice Problems:

2. Practice Problems involving fractions.