Discover Mathematics P6: Term 1, Unit 2, Lessons 4–6
GoalCompare absolute values and tell apart “which number is less” from “which number is farther from 0”.
New words
compare · decide which is greater, less or equalsize of a change · how big a change is, ignoring whether it is up or downfarther from 0 · having the greater absolute value
Explanation
There are two different questions about two numbers. “Which number is greater?” looks at the position on the line: the one further right. “Which has the greater absolute value?” looks at the distance from 0, whichever side it is on. The temperatures −8 °C and −3 °C: −8 < −3, so −8 °C is colder, but |−8| = 8 is greater than |−3| = 3, because it is further below zero. We compare absolute values with the same symbols: |−8| > |−3|. Also watch the minus sign outside the bars: |−5| = 5 but −|−5| = −5.
★Remember
Less number = further left. Greater absolute value = further from 0. These can disagree!
Worked examples
−8
−3
Which is less?
−8
Absolute value
8
3
Farther from 0
−8
Compare −8 and −3 in two ways. As numbers −8 < −3. As distances |−8| = 8 and |−3| = 3, so |−8| > |−3|.
Day
Change (LE)
Absolute value
Monday
−50
50
Tuesday
30
30
Karim lost 50 LE on Monday (−50) and gained 30 LE on Tuesday (30). −50 < 30, so Monday's number is less. But |−50| = 50 is greater than |30| = 30: the loss was the bigger change in size.
Order −9, 4, −2 and 7 by absolute value, from least to greatest. The absolute values are 9, 4, 2 and 7. So the order is −2, 4, 7, −9.
Class activity
Two questions game. A grown-up writes two numbers, one or both negative, such as −6 and 4. The child answers two questions in a row: “Which number is greater?” and “Which number is farther from 0?” Notice when the answers are different. Try ten pairs and write down the pairs where the answers disagree.
Practice
1
Write <, > or = : |−6| ___ |5| and −6 ___ 5.
|−6| > |5| because 6 > 5, but −6 < 5.
2
Which is farther from 0: −4.5 or 3.9?
−4.5, because |−4.5| = 4.5 is greater than 3.9.
3
Order by absolute value, least to greatest: −1, 0.5, −2.5, 2.
The absolute values are 1, 0.5, 2.5, 2, so the order is 0.5, −1, 2, −2.5.
4
Rana’s account changes by −35 LE and Amal’s by +40 LE. Whose change is bigger in size, and whose number is less?
Amal’s change is bigger in size (40 > 35). Rana’s number is less (−35 < 40).
5
Find |−5| and −|−5|.
|−5| = 5, and −|−5| = −5 (the minus outside the bars stays).
