Add, subtract, multiply and divide integers

Key notes :

Adding Integers

  • Rules:
    • Same Signs: Add the absolute values and keep the sign.
  • Different Signs: Subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.
  • Number Line:
    • To add integers on a number line, start at the first number and move to the right for positive integers and to the left for negative integers.

Subtracting Integers

  • Rules:
    • Subtracting an Integer: To subtract an integer, add its opposite.
  • Number Line:
    • To subtract integers on a number line, start at the first number and move to the left for positive subtractions and to the right for negative subtractions.

Multiplying Integers

  • Rules:
    • Same Signs: The product of two integers with the same sign is positive.
  • Different Signs: The product of two integers with different signs is negative.
  • Examples:

Dividing Integers

  • Rules:
    • Same Signs: The quotient of two integers with the same sign is positive.
  • Different Signs: The quotient of two integers with different signs is negative.
  • Examples:

Tips for Students

  • Consistent Practice:
    • Regular practice with varied problems helps reinforce the rules and concepts.
  • Use of Number Lines:
    • Number lines are particularly helpful for visualizing addition and subtraction of integers.
  • Understanding Signs:
    • Focus on the rules regarding the signs of integers to avoid common mistakes.

Classroom Activities

  1. Interactive Number Line:
    • Create a large number line on the classroom floor. Have students physically walk the number line to add or subtract integers.
  2. Integer Card Games:
    • Use cards with positive and negative integers. Students draw cards and practice addition, subtraction, multiplication, and division.
  3. Worksheets:
    • Provide worksheets with mixed integer operations to solve, ensuring varied practice.
  4. Group Activities:
    • Have students work in groups to solve integer problems, fostering collaboration and discussion.

Learn with an example

When you add a positive number and a negative number:

  • If the positive number has a bigger magnitude, the result is positive.
  • If the negative number has a bigger magnitude, the result is negative.

Ex:

When you add a positive number, 4,854,093, and a negative number, -650,163, the result has the same sign as the number with the larger magnitude.

The magnitude of 4,854,093 is 4,854,093.

The magnitude of -650,163 is 650,163.

Since 4,854,093 has a larger magnitude and 4,854,093 is positive, the result is positive.

You can check your answer by doing the maths.

4,854,093 + -650,163 = 4,203,930

As you can see, the result is positive.

When you add negative numbers, the result is negative.

Ex:

When you add two negative numbers, like -17 and -46,337, the result is negative.

You can check your answer by doing the maths.

-17 + -46,337 = -46,354

As you can see, the result is negative.

Instead of subtracting a number, you can add its opposite.

When you add a positive number and a negative number:

  • If the positive number has a bigger magnitude, the result is positive.
  • If the negative number has a bigger magnitude, the result is negative.

Ex:

Since you are subtracting a negative number, add a positive number instead:

-291 − –9 = -291 + 9

Now you have a negative number, -291, and a positive number, 9. The result has the same sign as the number with the larger magnitude.

The magnitude of -291 is 291.

The magnitude of 9 is 9.

Since -291 has a larger magnitude and -291 is negative, the result is negative.

You can check your answer by doing the maths.

-291 − -9 = -282

As you can see, the result is negative

When 2 integers have the same sign, the product is positive:

  • positive × positive = positive
  • negative × negative = positive

When 2 integers have different signs, the product is negative:

  • positive × negative = negative
  • negative × positive = negative

Ex:

875 is positive. -95 is negative. Use the rule:

positive × negative = negative

So, 875 × -95 is negative.

Now check your answer by doing the maths.

875 × -95 = -83,125

Yes, the answer is negative.

When 2 integers have the same sign, the quotient is positive:

  • positive ÷ positive = positive
  • negative ÷ negative = positive

When 2 integers have different signs, the quotient is negative:

  • positive ÷ negative = negative
  • negative ÷ positive = negative

EX:

3,264 is positive. -48 is negative. Use the rule:

positive ÷ negative = negative

So, 3,264 ÷ -48 is negative.

Now check your answer by doing the maths.

3,264 ÷ -48 = -68

Yes, the answer is negative.

Is -120 ÷ -30 positive or negative?

  • positive
  • negative

-120 is negative. -30 is negative. Use the rule:

negative ÷ negative = positive

So, -120 ÷ -30 is positive.

Now check your answer by doing the maths.

-120 ÷ -30 = 4

Yes, the answer is positive.

Let’s Practice!