Discover Mathematics P5: Term 1, Unit 6, Lessons 1–4
GoalUse the order of operations to work out an expression with several operations, with whole numbers and decimals.
New words
numerical expression · numbers and operation signs together, such as 8 + 6 × 3order of operations · the agreed order in which we work out an expressionevaluate · to work out the value of an expression
Explanation
An expression with more than one operation has only one correct value, so everybody must work in the same order. First do multiplication and division. Second do addition and subtraction. When operations of the same level meet, work from left to right. So 8 + 6 × 3 is 8 + 18 = 26, not 14 × 3 = 42. And 36 ÷ 4 × 3 is 9 × 3 = 27, because we go from left to right. The same order works with decimals. A good habit is to rewrite the expression after every step and underline the part you just worked out.
Level
Operations
When
1
× ÷
first, left to right
2
+ −
second, left to right
Worked examples
Step
Work
Result
1
6 × 3
18
2
8 + 18
26
Work out 8 + 6 × 3. Multiply first: 6 × 3 = 18. Then add: 8 + 18 = 26.
Step
Work
Result
1
12 ÷ 4
3
2
40 − 3
37
3
37 + 2
39
Work out 40 − 12 ÷ 4 + 2. Divide first: 12 ÷ 4 = 3. Then subtract and add from the left: 40 − 3 = 37, and 37 + 2 = 39.
Step
Work
Result
1
2.5 × 4
10
2
0.6 ÷ 2
0.3
3
10 + 0.3
10.3
Work out 2.5 × 4 + 0.6 ÷ 2. Both multiplication and division come first: 2.5 × 4 = 10 and 0.6 ÷ 2 = 0.3. Then 10 + 0.3 = 10.3.
Class activity
Race to the right value. Write ten short expressions on cards (for example 5 + 2 × 3, 18 − 6 ÷ 2, 4 × 5 − 3, 2 + 9 ÷ 3). The child turns a card, works out the value on paper, and the grown-up checks with a calculator that follows the order of operations. Count how many are right without help.
Practice
1
Work out 5 + 4 × 6.
4 × 6 = 24 and 5 + 24 = 29.
2
Work out 48 ÷ 6 × 2.
Left to right: 48 ÷ 6 = 8, then 8 × 2 = 16.
3
Work out 20 − 3.5 × 2.
3.5 × 2 = 7 and 20 − 7 = 13.
4
Work out 7.2 ÷ 2 + 1.5 × 4.
7.2 ÷ 2 = 3.6 and 1.5 × 4 = 6. Then 3.6 + 6 = 9.6.
5
Nour says 18 − 6 + 4 = 8 because 6 + 4 = 10. What is the right value?
Subtract and add from the left: 18 − 6 = 12, and 12 + 4 = 16.
