subtracting integers without number line 3 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: - 110 - (- 168) = + 58 By rule, - ( - ) = + Example 1: Subtract - 110 - ( - 168 ) Solution: Step 1: Check the signs before each integer. Integers should have one sign in front. Let us take 110, it is having single sign (-) in front. Now take 168 ,it is having two signs (- & -) in front. Step 2: By using Multiplication rule, we make it as single sign Therefore - (- 168) = + 168 Step 3: Therefore, -110 - (-168) = -110 + 168 Step 4: As per Addition rule 2, if the numbers have different sign, subtract the numbers and copy bigger number sign 168 - 110 = 58 & Bigger number sign is “+“ By rule, - ( - ) = + Answer: - 110 - (- 168) = + 58
Answer: 250 - (- 349) = + 599 By rule, - ( - ) = + Example 2: Subtract 250 - ( - 349) Solution: Step 1: Check the signs before each integer. Integers should have one sign in front. Let us take 250, it is having single sign (+) in front. Now take 349 ,it is having two signs (- & -) in front. Step 2: By using Multiplication rule, we make it as single sign Therefore - (- 349) = + 349 Step 3: Therefore, 250 - (-349) = +250 + 349 Step 4: As per Addition rule 1, if the numbers have same sign, add the numbers and copy bigger number sign 250 + 349 = 599 & Bigger number sign is “+“ By rule, - ( - ) = + Answer: 250 - (- 349) = + 599
275 + 100 = 375 & Bigger number sign is “-“ Example 3 : Subtract (- 275) - (100) Solution: Step 1: Check the signs before each integer. Integers should have one sign in front. Let us take 275, it is having single sign (-) in front. Now take 100 ,it is having single sign (-) in front. Step 2: As per Addition rule 1, if the numbers have same sign, add the numbers and copy bigger number sign 275 + 100 = 375 & Bigger number sign is “-“ Answer: - 275- (100) = - 375
Try these 1. Subtract - 321 - (- 222) 2. Subtract 233 - (- 345)