Ratios in Algebra – GCSE Maths
Introduction
- Ratios are number of one thing compared to another thing.
(how much one quantity is present with respect to other)
Simplification:
- (Common Factor : 3) If we multiply or divide the ratio’s numbers the ratios still remains the same
- From this simplification using common factor we can say that there are 5 Apples for each 4 Mangoes.
Ratios Representation
- Ratios in Algebra are used to solve problem finding unknown quantities and understanding variables.
Types of Ratios:
- Part to Part: Compares two or more parts of whole
- Part to Whole: Compares parts to whole
Divide in the Ratios
We can divide a quantity in some ratio by following these steps:
- Step#1: Add the number present in the ratio
- Step#2: Divide the quantity by the sum
- Step#3: Multiply each ratio part by value of one part
Key Point: When one of the parts in the ratio is 1 it is called Unit Ratio.
Solved Example
Solved ExampleProblem: Divide 120 in 2:3
Solution:
Step #1: Add the number present in the ratio:
2 + 3 = 5
Step #2: Divide the quantity by the sum:
This gives us value of one part.
Step #3: Multiply each ratio part by value of one part:
The quantity is divided into two parts 48, 72 in the ratio 2 : 3 .
Final Answer: 48, 72
Solved Example
Problem: 200 divide it in the Ratio : 4 : 6
Solution:
Step #1: Addition:
4 + 6 = 10
Step #2: Division:
Step #3: Multiplication:
The quantity 200 is divided into two parts 80, 120 in the ratio 4 : 6
Final Answer: 80, 120
Solved Example
Problem: 1080 divide it in the Ratio: 4 : 8
Solution:
Step #1: Addition:
4 + 8 = 12
Step #2: Division:
Step #3: Multiplication:
The quantity 1080 is divided into two parts 360, 720 in the ratio 4 : 8
Final Answer: 360, 720
Solved Example
Problem: 900 Divide it in the Ratio: 1 : 3 : 5
Solution:
Step #1: Addition:
1 + 3 + 5 = 9
Step #2: Division:
Step #3: Multiplication:
The quantity 900 is divided into three parts 100, 200, 300 in the ratio 1 : 3 : 5
Final Answer: 100, 200, 300
Solved Example: Reasoning Problems
Problem: Suppose you and your friend have 51 toffees and you want to share it with him in 1 : 2 . Then how will you divide the quantity?
Solution: The quantity is 51 and we need to divide it in 1 : 2
Step #1: Adding the parts:
1 + 2 = 3
Step #2: Finding value of one part:
Step #3: Finding value of each part of the ratio:
Now, 51 toffees are divided into 17, 34 in the ratio 1 : 2
Final Answer: 17, 34
Solved Example:
Problem: Suppose there are 540 crayons to be divide into the ratio 4 : 5 for distribution between two children. How will you divide the crayons that the ratio is satisfies with the parts.
Solution: The quantity is 540 and we need to divide it in 4 : 5
Step #1: Adding the parts:
4 + 5 = 9
Step #2: Finding value of one part:
Step #3: Finding value of each part of the ratio:
Now, 540 crayons are divided into 240, 300 in the ratio 4 : 5
Final Answer: 240, 300
Solved Example:
Problem: Suppose there are 12 classes in a school. each class contains 40 students and the ratio of girls to the boys is 4 : 5, then find how many girls and boys are there in the school?
Solution: The quantity is 12 x 40 = 480 and the ratio of girls to the boys is 5 : 7
Step #1: Addition:
5 + 7 = 9
Step #2: Division:
Step #3: Finding value of each part of the ratio:
Now, 480 crayons are divided into 200, 280 in the ratio 5 : 7
Final Answer: 200, 280
Solved Example:
Problem: If James and Jason divided the money they got in the ratio 6 : 8 and James got £150 then how much Jason got ? and what was the total amount?
Solution:
Step #1: Find the value of one part:
Step #2: Thus, one part values 25 and using it we can find the value of second part:
Step #3: Now we know how much money James and Jason got, So the total amount was:
Verification add the parts and divide with total amount
Final Answer: 25
Table of Content