Adding integers without number line 2 digit

Integers Recap Zero Negative integers Positive integers The numbers –1, –2, –3, … (to the left of zero) are called negative integers The numbers 1, 2, 3,… (to the right of zero) as positive integers. The new set of numbers …, -3, -2, -1, 0, 1, 2, 3,… are called Integers. ‘–’ symbol in front of a number is read as 'negative' or 'minus'. For example, –5 is read as negative 5 or minus 5. A number without a sign is considered as a positive number. For example, 5 is considered as +5.

+ ( + ) = + + ( - ) = - - ( - ) = + - ( + ) = - Rules of Addition and subtraction Rule 1 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 – + ( - ) = - - ( + ) = -

Worked Examples (Using Addition and subtraction rule) -7 + 3 Numbers have different sign Using Rule 2 – Subtract the numbers and copy bigger number sign 7- 3 = 4 Bigger number sign is “ – “ Answer : -4 -7- 3 Numbers have same sign Using Rule 1- Add the numbers and copy bigger number sign 7 + 3 = 10 Bigger number sign is “ – “ Answer : -10 7 - 3 Here we can write it as +7 - 3 Numbers have different sign Using Rule 2 – Subtract the numbers and copy bigger number sign 7- 3 = 4 Bigger number sign is “ + “ Answer : +4 +7 +3 Numbers have same sign Using Rule 1- Add the numbers and copy bigger number sign 7 + 3 = 10 Bigger number sign is “ + “ Answer : +10

+ ( + 7 ) + ( - 7 ) - ( + 7 ) - ( - 7 ) +(+)=+ +(-)=- -(+)=- -(-)=+ Worked Examples (Using Multiplication rule) + ( + 7 ) + ( - 7 ) - ( + 7 ) - ( - 7 ) +(+)=+ +(-)=- -(+)=- -(-)=+ Answer + 7 Answer -7 Answer - 7 Answer + 7

Answer: -33 + 87 = +54 Example 1: Add - 33 + 87 Solution: Step 1: Check the signs before each integer. Integers should have one sign in front. Let us take 33, it is having single sign (-) in front. Now take 87 ,it is having one sign (+) in front. Step 2: As per Addition rule 2, if the numbers have different sign, subtract the numbers and copy bigger number sign 87 – 33 = 54 & Bigger number sign is “ + “ Answer: -33 + 87 = +54

Answer: (-27) + (-36) = - 63 By rule, + ( - ) = - Example 2: Add (- 27) + (- 36) Solution: Step 1: Check the signs before each integer. Integers should have one sign in front. Let us take 27, it is having single sign (-) in front. Now take 36 ,it is having two signs (+ & -) in front. Step 2: By using Multiplication rule, we make it as single sign Therefore + (-36) = - 36 Step 3: Therefore, (- 27) + (- 36) = -27 - 36 Step 4: As per Addition rule 1, if the numbers have same sign, add the numbers and copy bigger number sign 27 + 36 = 63 & Bigger number sign is “ – “ By rule, + ( - ) = - Answer: (-27) + (-36) = - 63

Answer: 43 + (-43) = 0 By rule, + ( - ) = - Example 3: Add 43 + (- 43) Solution: Step 1: Check the signs before each integer. Integers should have one sign in front. Let us take 43, it is having single sign (+) in front. Now take second 43 ,it is having two signs (+ & -) in front. Step 2: By using Multiplication rule, we make it as single sign Therefore + (-43) = - 43 Step 3: Therefore, 43 + (- 43) = +43 - 43 Step 4: As per Addition rule 2, if the numbers have different sign, subtract the numbers and copy bigger number sign 43 - 43 = 0 & ”0” does not have any sign By rule, + ( - ) = - Answer: 43 + (-43) = 0

Try these 1. Add -44 + (- 56) 2. Add 55 + (- 60) 3. Add – 50 + 50