1. Recognize the Operation

2. + ( + ) = + + ( - ) = - - ( - ) = + - ( + ) = - Rules of Addition
Two numbers have same sign
Add the numbers
Copy bigger number sign
Rule 2
Two numbers have different sign
Subtract the numbers
Copy bigger number sign
Rules of multiplication
Converting 2 symbols into 1
Rule 1
Multiply same sign  Answer is +
+ ( + ) = +
- ( - ) = +
Rule 2
Multiply different sign Answer is –
+ ( - ) = -
- ( + ) = -

3. Solving Equations Using Multiplication or Division
Rule 3: If a variable has been multiplied by a nonzero number, divide both sides by that number. Rule 4: If a variable has been divided by a number, multiply both sides by that number.
Terminologies X ÷
Multiply
Divide
Product
Quotient

4. Example 1: The product of two numbers is - 60. If one number is 10,
find the other number
Solution:
Given:
The product of two numbers = - 60
One of the number = 10
To find: Other number.
Let Number1(N1) and Number2(N2) be two numbers &
Product is – 60           N1 x N2 = - 60
Let N1 be the known number and N2 be unknown
N1 X N2 = 60
10 X N2 = -60 6
Rule 3: 10 has been multiplied by b, so divide both sides by number 10
N2 = -6
So, the other number is - 6

5. Example 2: By what number should -135 be divided to obtain 15
Solution:
Given:
- 135 ÷ = 15
To find: The number which divides -135
Let x be the number
∴ -135 should be divided by x to get 15
Rule 4: -135 has been divided by x, so multiply both sides by x -9
Rule 3: 15 has been multiplied by x, so divide both sides by number 15
-9 = x
Ans: x = - 9

6. Ans: x = 52 Example 3: What should be divided by - 4 to obtain - 13
Solution:
Given:
---- ÷ (-4) = - 13
To find: Number that is divided by (-4)
Let ‘x’ be a number
x is divided by -4 to get -13
Rule 4: - 4 has been divided by a x, so multiply both sides by - 4
x =-13 x -4
x= +52
By rule, (-) x (-) = +
Ans: x = 52

7. Example 4 : Add the product of 22 and - 14 to the quotient of 240 by 3
Solution:
Product of 22 and -14
Add
Quotient of 240 by 3 +
= - 308 + 80
By multiplication rule, (+) x (-) = -
By division rule,
(+) ÷ (+) = + = =
Simplify using addition rule 2
Answer: - 228

8. Try these
1. The product of two numbers is 78. If one number is -6, find the other number
2. By what number should -200 be divided to obtain 8
3. What should be divided by 8 to get 8
4. Add the product of 22 and -14 to the quotient of 240 by 3