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Welcome to our Math lesson on Working with Negative Numbers, this is the seventh lesson of our suite of math lessons covering the topic of Order of Operations and PEMDAS Rule, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Working with Negative Numbers
Before explaining how to solve expressions involving negative numbers, we must explain the sign rules for each operation.
1. Addition
For addition, we have the following rules:
- positive + positive = positive
For example, (+8) + (+11) = (+19)
- negative + negative = negative
For example, (-6) + (-4) = (-10)
- positive + negative = their difference with the sign of the number that is farther from origin
For example, (+9) + (-2) = + (9 - 2) = (+7),
(+5) + (-8) = - (8 - 5) = (-3), etc.
2. Subtraction
Subtraction. In this case, since subtraction is the inverse operation of addition, we turn the subtraction into addition and at the same time, we change the sign of the second number for compensation. Then, we apply the same rules as in addition. For example,
(-8) - (+7)
= (-8) + (-7)
= (-15)
(+8) - (+11)
= (+8) + (-11)
= - (11 - 8)
= (-3)
etc.
3. Multiplication
Multiplication. There are two basic rules in multiplication:
- The product of two factors of the same sign is positive
- The product of two factors of opposite signs is negative
For example,
(-3) × (-2) = (+6); (+4) × (+3) = (+12); (-8) × (+3) = (-24), etc.
4. Division
Since division is the inverse operation of multiplication, the same rules used for multiplication are applied. For example,
For example,
(-12) ÷ (-4) = (+3); (+20) ÷ (+10) = (+2); (-24) ÷ (+3) = (-8), etc.
Example 8
Calculate the value of the expression
(-12) ÷ (-4) + (+3) × (-7) - (-17) =
Solution 8
We follow the same rules regarding the order of operations as in all arithmetic expressions without brackets (here brackets are used only to highlight the sign of numbers). Hence, first we do the division and multiplication (simultaneously), then the rest of operations. We have
(-12) ÷ (-4) + (+3) × (-7) - (-17)
= (+3) + (-21) - (-17)
= (-17) - (-17)
= (-17) + (+17)
= 0
Remark! It is not necessary to write the symbol (+) before positive numbers as it is implied. Hence, in most cases we don't write the plus before positive numbers.
More Order of Operations and PEMDAS Rule Lessons and Learning Resources
Arithmetic Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 1.4 | Order of Operations and PEMDAS Rule | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 1.4.1 | Order of Operation in Arithmetic Expressions Containing Only Addition and Subtraction | | |
| 1.4.2 | Order of Operation in Arithmetic Expressions Containing Only Multiplications and Division | | |
| 1.4.3 | Expressions Containing Additions, Subtractions, Multiplications and Divisions | | |
| 1.4.4 | Expressions Containing Exponents | | |
| 1.4.5 | Expressions Containing Brackets. PEMDAS Rule | | |
| 1.4.6 | Types of Parenthesis and Their Order of Priority | | |
| 1.4.7 | Working with Negative Numbers | | |
| 1.4.8 | Powers of Negative Numbers | | |
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