Recognize the Operation

+ ( + ) = + + ( - ) = - - ( - ) = + - ( + ) = - 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 – + ( - ) = - - ( + ) = -

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

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

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

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

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, (+) ÷ (+) = + = - 308 + 80 = - 228 Simplify using addition rule 2 Answer: - 228

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