Discover Mathematics P4: Term 1, Unit 8, Lessons 1–4
GoalUse parentheses to change the order and write expressions for everyday stories.
New words
parentheses · ( ) show which part to calculate firstgrouping · putting numbers together in parenthesesnumber sentence · an equation that tells a story with numbers
Explanation
Parentheses can change the order. In 6 + 4 × 5 we multiply first and get 6 + 20 = 26. In (6 + 4) × 5 we add first because of the parentheses: 10 × 5 = 50. The same numbers give two different answers, so parentheses matter. In stories we use parentheses when one amount is made first and then used again. Four friends each pay 12 LE for a ticket and 3 LE for a drink. One friend pays 12 + 3 = 15 LE, so all pay 4 × (12 + 3) = 4 × 15 = 60 LE. Without the parentheses, 4 × 12 + 3 = 51 would be a different story. When you write an expression for a story, ask: which amount is calculated first?
Worked examples
Expression
First
Then
Value
(6 + 4) × 5
6 + 4 = 10
10 × 5
50
6 + 4 × 5
4 × 5 = 20
6 + 20
26
Compare (6 + 4) × 5 and 6 + 4 × 5. In the first, parentheses make us add first: 10 × 5 = 50. In the second, multiplication comes first: 4 × 5 = 20, then 6 + 20 = 26.
Marwan buys 3 notebooks at 8 LE each and one pen for 5 LE. The expression is 3 × 8 + 5. Multiply first: 24, then add: 24 + 5 = 29 LE. No parentheses are needed because the multiplication already comes first.
Find (9 − 4) × 6 and 40 ÷ (2 + 3). The first: 9 − 4 = 5, then 5 × 6 = 30. The second: 2 + 3 = 5, then 40 ÷ 5 = 8.
Class activity
Write a story. Pick the expression 3 × (5 + 2). Together invent a market or school story for it, then work out the answer (21). Change it to 3 × 5 + 2 and see how the story changes.
Practice
1
Find (12 + 8) ÷ 4.
12 + 8 = 20, then 20 ÷ 4 = 5.
2
Find 7 × (10 − 6).
10 − 6 = 4, then 7 × 4 = 28.
3
Put parentheses in 3 + 5 × 4 so that its value is 32.
(3 + 5) × 4 = 8 × 4 = 32.
4
At the cinema 2 adults pay 15 LE each and 3 children pay 8 LE each. Write one expression and find the total.
2 × 15 + 3 × 8 = 30 + 24 = 54 LE.
5
Karim says 30 − 10 ÷ 5 = 4. What did he do? What is the correct value?
He subtracted first: 30 − 10 = 20, then 20 ÷ 5 = 4. Divide first: 10 ÷ 5 = 2, then 30 − 2 = 28.
