Mathematics Year 7: Numerical expressions with integers, and problems
Mathematics, Year 7 (Portugal): Write, simplify and calculate expressions with parentheses and minus signs, choose an efficient path and solve problems.
Writing, simplifying and telling the story
In an expression, “−” can play two roles: inside −3 it is part of the number (its sign), and between two numbers it is the operation of subtracting. Parentheses keep them apart: 7 + (−3) is simplified to 7 − 3 = 4, and 7 − (−3) = 7 + 3 = 10. You can also read an expression as a story: −2 + 9 − 4 can be a morning at −2 °C when the temperature rises 9 degrees and then falls 4, ending at 3 °C.
Choosing the most efficient path
An expression with many terms has several paths to the same value. In −12 + 5 + 8 + 4 − 9: left to right gives −7, 1, 5, −4. Grouping: (5 + 8 + 4) + (−12 − 9) = 17 + (−21) = −4. Pairing: (−12 + 8) + (4 − 9) + 5 = −4 + (−5) + 5 = −4. All give −4. The most efficient depends on the numbers: joining those that cancel or make round numbers saves work. You can even predict the sign first: the negatives (−21) outweigh the positives (17).
A lift in a car park
A lift is at level −3 of a car park. It goes up 8 levels, down 5, up 2 and down 6. Where does it stop? Expression: −3 + 8 − 5 + 2 − 6. My reasoning: the ups add to 8 + 2 = 10, the downs add to 5 + 6 = 11, so overall it went down 1 more than it went up: 10 − 11 = −1. Then −3 + (−1) = −4. Check left to right: −3 + 8 = 5; 5 − 5 = 0; 0 + 2 = 2; 2 − 6 = −4. It stops at level −4.
Parentheses are not decoration
The reasonable mistake is to drop the parentheses because they “do nothing”. With a minus in front, they do a lot: 4 − (3 + 7) = 4 − 10 = −6, but 4 − 3 + 7 = 1 + 7 = 8. They are not equal. To take the parentheses off you would have to write 4 − 3 − 7 = −6. Safe rule: calculate what is inside the parentheses first, then the rest.
Statements, games and temperatures
Integer expressions appear whenever you record a sequence of gains and losses: the movements on a payment card, the points of a game where you can lose points, the temperature changes through the day. Writing the right expression and choosing a path lets you check the result two ways, and explain to someone how you thought it through.
Test what you learned
Which situation matches the expression −2 + 9 − 4?
- a) At −2 °C, the temperature rises 9 degrees and then falls 4
- b) At −2 °C, the temperature falls 9 degrees and then rises 4
- c) At 2 °C, the temperature rises 9 degrees and then falls 4
Correct answer: a) At −2 °C, the temperature rises 9 degrees and then falls 4 — Yes: −2 is the start, + 9 is a rise and − 4 is a fall. It ends at 3 °C.
A lift is at level −3 of a car park. It goes up 8 levels, down 5, up 2 and down 6. At which level does it stop?
- a) 2
- b) 4
- c) −4
- d) 18
Correct answer: c) −4 — Yes: −3 + 8 − 5 + 2 − 6 = −4. Up 10 in total, down 11: one level lower than the start.
What is the value of 4 − (3 + 7)?
- a) 8
- b) −6
- c) 6
- d) 14
Correct answer: b) −6 — Yes: parentheses first, 3 + 7 = 10, then 4 − 10 = −6.
Keep exploring
Other languages
Loading MyLeoNes™…