Discover Mathematics P4: Term 1, Unit 8, Lessons 1–4
GoalKnow which operation to do first and evaluate expressions with two operations.
New words
expression · numbers and operation signs written together, such as 5 + 3 × 4order of operations · the rules that say what to calculate firstevaluate · to find the value of an expression
Explanation
If we read 5 + 3 × 4 from left to right we get 8 × 4 = 32, but the right answer is 17. Mathematicians agreed on an order so that everybody gets the same answer. First do anything in parentheses. Then multiply and divide, from left to right. Last add and subtract, from left to right. In 5 + 3 × 4 the multiplication comes first: 3 × 4 = 12, then 5 + 12 = 17. In 30 − 12 ÷ 3 the division comes first: 12 ÷ 3 = 4, then 30 − 4 = 26. When two operations are of the same level, go from left to right: 24 ÷ 4 × 3 = 6 × 3 = 18, and 18 − 5 + 2 = 13 + 2 = 15. Check: multiplication is repeated addition, so 5 + 3 × 4 means 5 plus three groups of 4.
Order
What to do
1
Parentheses ( )
2
Multiply and divide, left to right
3
Add and subtract, left to right
Worked examples
Step
Work
1
3 × 4 = 12
2
5 + 12 = 17
Find 5 + 3 × 4. Multiply first: 3 × 4 = 12. Then add: 5 + 12 = 17. It is not 32.
Same level goes left to right. 24 ÷ 4 × 3: divide first because it comes first: 24 ÷ 4 = 6, then 6 × 3 = 18. And 18 − 5 + 2: 18 − 5 = 13, then 13 + 2 = 15. The answer is 15, not 11.
Class activity
Calculator test. Press 5 + 3 × 4 = on a calculator or a phone. Does it show 17? Try 30 − 12 ÷ 3 as well. Then work them out by hand and compare.
Practice
1
Find 8 + 6 × 2.
6 × 2 = 12, then 8 + 12 = 20.
2
Find 36 ÷ 4 + 5.
36 ÷ 4 = 9, then 9 + 5 = 14.
3
Find 50 − 4 × 6.
4 × 6 = 24, then 50 − 24 = 26.
4
Find 9 × 3 − 7.
9 × 3 = 27, then 27 − 7 = 20.
5
Hana says 7 + 3 × 5 = 50. What did she do wrong? What is the correct value?
She added first (7 + 3 = 10, 10 × 5 = 50). Multiply first: 3 × 5 = 15, then 7 + 15 = 22.
