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Welcome to our Math lesson on Expressions Containing Additions, Subtractions, Multiplications and Divisions, this is the third 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.
Expressions Containing Additions, Subtractions, Multiplications and Divisions
Multiplications and divisions are of the same order of priority with each other but of a higher order of priority than additions and subtractions. Therefore, if an arithmetic expression contains all four basic operations, we start the calculation by completing the multiplications and divisions first, regardless of their position in the expression. Then, after completing multiplications and divisions, we continue with the rest (additions and subtractions) from left to right.
Example 3
Calculate the value of the following expressions
- 13 - 6 ÷ 2 + 7 × 8 - 9 =
- 21 + 4 × 5 - 12 ÷ 6 - 9 × 7
Solution 3
- Since the expression in question contains all four operations, we calculate the multiplications and divisions first. We can do the division and multiplication at the same time, as they are not consecutive operations. Then, after completing divisions and multiplications, we continue with the rest of operations (addition and subtraction) from working from left to right. Thus, we have
13 - 6 ÷ 2 + 7 × 8 - 9
= 13 - 3 + 56 - 9
= 10 + 56 - 9
= 66 - 9
= 57
- We follow the same procedure as in (a), that is first we calculate the multiplications and divisions (again, here we can do them simultaneously as they are not consecutive operations), then we deal with additions and subtractions. We have
21 + 4 × 5 - 12 ÷ 6 - 9 × 7
= 21 + 20 - 2 - 63
= 41 - 2 - 63
= 39 - 63
= (- 24)
If operations of the same order of priority are consecutive in an expressions, we do them one by one, not simultaneously. Look at the example below:
Example 4
Calculate the value of the following expression
39 ÷ 3 × 4 - 208 ÷ 8 × 2 + 7 × 9 =
Solution 4
First, we start with terms where two consecutive operations of the same order of priority are present. This means we start with 39 ÷ 3 and 208 ÷ 8. We have
39 ÷ 3 × 4 - 208 ÷ 8 × 2 + 7 × 9
= 13 × 4 - 26 × 2 + 7 × 9
Now, the remaining multiplications are not consecutive. Hence, we can do them simultaneously before we continue with additions and subtractions. We have
13 × 4 - 26 × 2 + 7 × 9
= 52 - 52 + 63
= 0 + 63
= 63
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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