HARTLAND MIDDLE SCHOOL
Operations with Signed Numbers (positive and negative numbers)
Lesson Sheet
Adding and Subtracting
When adding or subtracting signed numbers, think about winning or losing money:
• a positive number means winning.
• a negative number OR subtracting a positive number means losing.
Examples:
-3 + 8 = 5 (lost $3, won $8; outcome: won $5)
-4 + (–7) = -11 (lost $4, lost $7 more; outcome: lost $11)
5 + (-9) = -4 (won $5, lost $9; outcome: lost $4)
3 – 8 = -5 (won $3, lost $8; outcome: lost $5)
-2 – 7 = -9 (lost $2; lost $7 more; outcome: lost $9)
A special case is subtracting a negative number. When there are two “minus” signs in a row (with no number in between), change them both to a “plus” sign.
Examples:
5 – (-7) becomes 5 + 7 = 12 -4 – (-2) becomes -4 + 2 = -2
8 – –2 becomes 8 + 2 = 10 -5 – –9 becomes -5 + 9 = 4
Multiplying and Dividing
This is the easy part! Use the same rule for multiplying and for dividing:
• if the two numbers have the same sign (both positive or both negative), the answer is positive.
• if the two numbers have different signs (one positive and one negative), the answer is negative.
Remember that when a number is touching parentheses, it means to multiply.
For example, 4(7) means to multiply 4x7.
Examples:
-3(-7) = 21 (positive answer, since both numbers are negative)
-5(8) = -40 (negative answer, since the numbers have different signs)
6(-7) = -42 (again negative answer, since the numbers have different signs)
-24 ÷ (-6) = 4 (positive answer, since both numbers are negative)
-15 ÷ 3 = -5 (negative answer, since the numbers have different signs)
Problems with mixed operations
When doing adding or subtracting, think about winning/losing money!
When doing multiplying or dividing, think about same sign / different sign!
Example: 4(-7) + 12
First do 4(-7) = -28 (multiplication: different signs means negative answer)
Then do -28 + 12 = -16 (lost $28, won $12; outcome: lost $16)
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