Class 5 Exam  >  Class 5 Notes  >  Mathematics for Class 5  >  Chapter Notes: Ratio and Proportion

Ratio and Proportion Chapter Notes | Mathematics for Class 5 PDF Download

In this chapter we will be learning about two different things that is ratio and proportion , both of which are applicable in our day to day life.

Ratio and Proportion Chapter Notes | Mathematics for Class 5

Ratios

What are Ratios?

  • A Ratio is a way to compare two or more quantities. 
  • It shows how much of one thing there is compared to another.
  • Ratios help us understand relationships between different items or groups.

How to Write Ratios

1. Colon Form:

  • A ratio can be written using a colon ' : '
  • For example, if there are 4 cats and 2 dogs, 
    the ratio of cats to dogs is written as 4:2.

2. Fraction Form:

  • The same ratio can also be expressed as a fraction. 
  • So, 4:2 can be written as 4/2, which simplifies to 2/1.

Example 1: If there are 35 boys and 25 girls in a class, then what is the ratio of
1. Number of boys to total students
2. Number of girls to total students.

Sol: 
In the ratio, we want the total number of students.
Total number of students = Number of boys + Number of girls
35 + 25 = 60

1. Ratio of number of boys to total number of students
Ratio and Proportion Chapter Notes | Mathematics for Class 5

2. The ratio of the number of girls to the total number of students
Ratio and Proportion Chapter Notes | Mathematics for Class 5

EduRev Tip:
  • The units must be the same to compare two quantities.
  • If we have to compare two quantities with different units then we need to convert them in the same unit. then only they can be compared using ratio.

Example 2: What is the ratio of the height of Raman and Radha if the height of Raman is 175 cm and Radha is 1.35 m?

Sol: In this case we will first convert the heights into  same unit (cm)  and then will proceed.

  • The unit of the height of Raman and Radha is not same so convert them in the same unit.
  • Height of Radha is 1.35 m = 1.35 × 100 cm = 135 cm
  • The ratio of the height of Raman and Radha
  • Ratio and Proportion Chapter Notes | Mathematics for Class 5

Question for Chapter Notes: Ratio and Proportion
Try yourself:
What is the ratio of apples to oranges if there are 20 apples and 10 oranges?
View Solution

Equivalent Ratios

  • If we multiply or divide both the numerator and denominator by the same number then we get the equivalent ratio. 
  • There could be so many equivalent ratios of the same ratio.
  • In the case of equivalent ratios only their value changes but they represent the same portion of the quantity.

Example: Find two equivalent ratios of 2/4.


Sol:

Ratio and Proportion Chapter Notes | Mathematics for Class 5

  • To get the equivalent ratio we multiply both the numerator and denominator with 2.
  • Ratio and Proportion Chapter Notes | Mathematics for Class 5
  • To get another equivalent ratio we divide both the numerator and denominator with 2.
  • Ratio and Proportion Chapter Notes | Mathematics for Class 5
  • From the above figure, we can see that in all the equivalent ratios only the number of equal parts is changing but all the ratios are representing the half part of the circle only.

Lowest Form of the Ratio

  • If there is no common factor of numerator and denominator except one then it is the lowest form of the ratio.
  • Example: 3/8 , 2/7 etc. 

Example 1: Find the lowest form of the ratio 25: 100.

Sol: Firstly write the ratio into fractional form i.e  25/100

  • The common factor of 25 and 100 is 25, so divide both the numerator and denominator with 25.
  • Ratio and Proportion Chapter Notes | Mathematics for Class 5
  • Hence the lowest ratio of 25: 100 is 1: 4.

Proportions

What are Proportions?

  • A proportion is an equation that states that two ratios are equal.
  • It shows how two quantities relate to each other.

How to write Proportions?

  • A proportion can be written as:
  • Ratio and Proportion Chapter Notes | Mathematics for Class 5
  • We write it as a: b : : c: d or a: b = c: d and reads as “a is to b as c is to d”.
  • If the two ratios are not equal then these are not in proportion.

Example 1: If a man runs at a speed of 20 km in 2 hours then with the same speed would he be able to cross 40 km in 4 hours?

Sol: We can use simple comparison to solve this question 

  • Here the ratio of the distances given is 20/40 = 1/2 = 1: 2
  • And the ratio of the time taken by them is also 2/4 = 1/2 = 1: 2
  • Hence the four numbers are in proportion.
  • We can write them in proportion as 20: 40 : : 2: 4
  • And reads as “20 is to 40 as 2 is to 4”.

Extreme Terms and Middle Terms of Proportion

Ratio and Proportion Chapter Notes | Mathematics for Class 5

  • The first and the fourth term in the proportion are called extreme terms 
  • The second and third terms are called the Middle or the Mean Terms.
  • In this statement of proportion, the four terms which we have written in order are called the Respective Terms.

Example 1: Check whether the terms 30 , 99 ; 20 ,66 are in proportion or not.

Sol: Yes, the given terms are in proportion

  • To check the numbers are in proportion or not we have to equate the ratios.Ratio and Proportion Chapter Notes | Mathematics for Class 5
  • As both the ratios are equal so the four terms are in proportion.
  • 30: 99 :: 20: 66

Example 2: Find the ratio 30 cm to 4 m is proportional to 25 cm to 5 m or not?

Sol: No, the ratios are not in proportion.

  • As the unit is different so we have to convert them into the same unit.
  • 4 m = 4 × 100 cm = 400 cm
  • The ratio of 30 cm to 400 cm isRatio and Proportion Chapter Notes | Mathematics for Class 5
  • 5 m = 5 × 100 cm = 500 cm
  • Ratio of 25 cm to 500 cm isRatio and Proportion Chapter Notes | Mathematics for Class 5
  • Here the two ratios are not equal so these ratios are not in proportion.
  • 3: 40 ≠ 1: 20

Question for Chapter Notes: Ratio and Proportion
Try yourself:
What is the lowest form of the ratio 16: 24?
View Solution

Did You Know:

  • If you have to see if two ratios are equal, you can just cross-multiply. 
  • For example, If you have to check the ratios 2:3 and 4:6
  • Cross-multiply:
    • 2×6=122×6=12
    • 3×4=123×4=12
  • Since both products are equal, we say that 2:3 is proportional to 4:6

Unitary Method

  • If we find the value of one unit then calculate the value of the required number of units then Unitary method is used.

Example 1: If the cost of 3 books is 320 Rs. then what will be the cost of 6 books?

Ratio and Proportion Chapter Notes | Mathematics for Class 5

Sol: 

  • Cost of 3 books = Rs. 320
  • Cost of 1 book = 320/3 Rs.
  • Cost of 6 books = (320/3) × 6 = 640 Rs.
  • Hence, the cost of 6 books is Rs. 640.

Example 2: If the cost of 20 toys is Rs. 4000 then how many toys can be purchased for Rs. 6000?

Sol:

  • In Rs. 4000, the number of toys can be purchased = 20
  • In Rs. 1, the number of toys can be purchased = Rs. 20/4000
  • Therefore, in Rs. 6000, the number of toys can be purchased = (20/4000) × 6000 = 30
  • Hence, 30 toys can be purchased by Rs. 6000.

Question for Chapter Notes: Ratio and Proportion
Try yourself:
What is the cost of 8 pens if the cost of 4 pens is Rs. 120?
View Solution

The document Ratio and Proportion Chapter Notes | Mathematics for Class 5 is a part of the Class 5 Course Mathematics for Class 5.
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FAQs on Ratio and Proportion Chapter Notes - Mathematics for Class 5

1. What is a ratio and how is it represented?
Ans.A ratio is a way to compare two quantities by using division. It shows how many times one number contains another. Ratios are typically represented using a colon, such as 3:1, or as a fraction, like 3/1.
2. How do you simplify a ratio?
Ans.To simplify a ratio, you divide both parts of the ratio by their greatest common divisor (GCD). For example, to simplify the ratio 8:12, you would divide both 8 and 12 by 4, resulting in the simplified ratio of 2:3.
3. What is a proportion and how is it different from a ratio?
Ans.A proportion is an equation that states that two ratios are equal. For example, if we have the ratio 1:2 and the ratio 2:4, we can say that 1:2 = 2:4, making it a proportion. The key difference is that a ratio compares two quantities, while a proportion shows the equality of two ratios.
4. How can you solve a proportion?
Ans.To solve a proportion, you can use cross-multiplication. For example, if you have the proportion a/b = c/d, you can cross-multiply to get ad = bc. Then, you can solve for the unknown variable.
5. Can you give an example of a real-life situation where ratios and proportions are used?
Ans.Ratios and proportions are commonly used in recipes. For instance, if a recipe calls for 2 cups of flour to 3 cups of sugar, the ratio of flour to sugar is 2:3. If you want to make a larger batch, you can use proportions to maintain the same ratio, such as using 4 cups of flour with 6 cups of sugar.
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