Example of Arithmetic Operations
Example 1. The sum of the two numbers is 100, and their difference is 60. Find the numbers.
Solution:
Let the two numbers be x and y
Now, according to the question
x + y = 100 . . . (i)
x β y = 60 . . . (ii)
From equation (i)
β x = 100 β y
Therefore, putting the value of x
β 100 β y β y = 60
β 100 β 2y = 60
β 2y = 40
β y = 20
Putting the value of y in equation (ii)
β x β y = 60
β x = 60 + 20
β x = 80
Therefore, the numbers are 80 and 20 respectively.
Example 2: Simplify 50 + 10(9) β 9
Solution:
50 + 10(9) β 9
β 50 + 90 β 9
β 140 β 9
β 131
Example 3: If the sum of two numbers x and a + 5 is 39. Find the value of x.
Solution:
According to the question,
x + (x + 5) = 39
β 2x + 5 = 39
Subtracting 5 on both sides,
2x + 5 β 5 = 39 β 5
β 2x = 34
x = 34/2 = 17
Therefore, the value of x is 17.
Example 4: The difference between the two numbers is given by finding the value of p.
Solution:
According to the equation,
p β 4 = 11
Adding 4 to the both sides,
p β 4 + 4 = 11 + 4
β p = 15
Therefore, the value of p is 15.
Example 5: Find the value of y in the given equation y β 9 = 3.
Solution:
According to the question,
y β 9 = 3
β y = 9 + 3
β y = 12
Therefore, the value of y is 12.
Example 6: Simplify: -1[(3 β 28) Γ· 5] β 2 Γ 24 Γ· 6
Solution:
-1[(3 β 28) Γ· 5] β 2 Γ 24 Γ· 6
β -1 Γ [(-25) Γ· 5] β 2 Γ 24 Γ· 6
β -1 Γ [-5] β 2 Γ 24 Γ· 6
β 5 β 2 Γ 24 Γ· 6
β 5 β 48 Γ· 6
β 5 β 8
β -3
Example 7: Solve 2x = 10
Solution:
According to question,
β 2 Γ x = 10
Dividing both sides with 2
2 Γ x/2 = 10/2
β x = 5
Therefore, the value of x is 5.
Example 8: Solve the given equation 5x/4 + 1/2 = 2x β 1/2
Solution:
5x/4 + 1/2 = 2x β 1/2
Multiplying both sides with 4
4(5x/4 + 1/2) = 4(2x β 1/2)
β 5x + 2 = 8x β 2
β -3x + 2 = -2
Subtracting both sides with 2
-3x + 2 β 2 = -2 β 2
β x = -4/-3
β x = 4/3
Therefore, the value of x is 4/3.
Example 9: Find the value of the unknown number 3/2y β 2/3 = 1/5y
Solution:
According to the question,
3/2y β 2/3 = 1/5y
Multiplying both sides with 30(LCM of 2, 3, and 5)
30(3/2y β 2/3) = 30(1/5y)
β 45y β 20 = 6y
Adding 20 on both sides,
45y β 20 + 20 = 6y + 20
β 45y = 6y + 20
β 39y = 20
β y = 20/39
Therefore, the value of y is 20/39.
Arithmetic Operations
Arithmetic Operations are the basic mathematical operations used for calculation. Arithmetic Operations are the backbone of Mathematics. There are four basic arithmetic operations, namely, Addition, Subtraction, Multiplication, and Division. These four basic arithmetic operations are very helpful in solving daily life calculations such as sharing biscuits among your friend and sibling, counting the total bill you have to pay at a shop, complex calculations such as problems of time and work, data interpretations, etc.
In this article, we will learn about basic arithmetic operations in detail.
Table of Content
- What is Arithmetic Operation?
- Basic Arithmetic Operations
- Addition Definition
- Subtraction Definition
- Multiplication Definition
- Division Definition