Basic Math

Add, Subtract, Multiply, and Divide Integers

This guide will help you master the basics of adding, subtracting, multiplying, and dividing integers, with plenty of examples to make sure you grasp each concept.
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1. Adding Integers

Adding integers is similar to adding whole numbers, but you must consider the sign (positive or negative) of each number.

Rules for Adding Integers:

  • Same Signs: Add their absolute values (ignore the sign), and keep the common sign.
  • Different Signs: Subtract the smaller absolute value from the larger absolute value, and take the sign of the number with the larger absolute value.
Example 1: 5+3=8

(Both numbers are positive.)

Example2: -5+(-3)=-8

(Both numbers are negative, add their absolute values and keep the negative sign.)

Example3: -5+3=-2

(Numbers have different signs, subtract the smaller absolute value from the larger one, and keep the sign of the number with the larger absolute value.)

2. Subtracting Integers

To subtract integers, add the opposite of the number being subtracted.

Rule for Subtracting Integers:

  • Convert the subtraction operation into an addition operation by adding the additive inverse (opposite) of the number to be subtracted.
Example1: 7-3=7+(-3)=4
Example2: -7-3=-7+(-3)=-10
Example3: -7-(-3)=-7+3=-4

3. Multiplying Integers

Multiplying integers involves considering the signs of the numbers as well as their values.

Rules for Multiplying Integers:

  • Same Signs: The product is positive.
  • Different Signs: The product is negative.
Example1: 4×3=12
Example2: -4×3=-12
Example3: -4×(-3)=12

4. Dividing Integers

Dividing integers follows the same sign rules as multiplying integers.

Rules for Dividing Integers:

  • Same Signs: The quotient is positive.
  • Different Signs: The quotient is negative.
Example1: 12÷3=4
Example2: -12÷3=-4
Example3: -12÷(-3)=4

Practice Problems

Try these problems to test your understanding:

Problem1: -8+5

Problem2: 10-(-4)

Problem3: -6×7

Problem4: 24÷-6

Problem5: 3+(-9)

Problem6: -12+15

Problem7: 5×(-8)

Problem8: -35÷5

Problem9: 18-(-22)

Problem10: -4×11

Practice Problems with Solution

Try these problems to test your understanding:

Problem11: -9+14 =5

Problem12: 6-17 =-11

Problem13: -3×4 =-12

Problem14: 18÷-3 =-6

Problem15: -10+(-5) =-15

Problem16: 11+-6 =5

Problem17: 7×-2 =-14

Problem18: -28÷7 =-4

Problem19: 20-(-8) =28

Problem20: -5×9 =-45
Problem21: 15+9 =24

Problem22: -14+-7 =-21

Problem23: 12-(-3) =15

Problem24: -18×-2 =36

Problem25: 36÷-6 =-6

Problem26: 27+-9 =18

Problem27: -22×2 =-44

Problem28: 49÷-7 =-7

Problem29: 20-(-5) =25

Problem30: -10×4 =-40

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