SME
Grade 6 Math · Problem type
Compare rational numbers
Use this to compare −8.5 and −8, or −6 and 4, on the number line, and their absolute values.
Diagram
From −7.5 to −7: 0.5 to the right.
This is an example. Type your own values to start a new problem.
x
y
First number’s absolute value
worked out (not typed)
Second number’s absolute value
worked out (not typed)
Distance apart
worked out (not typed)
Formulas
sign < between −7.5 and −7
The sign between the two numbers
|−7.5| = 7.5
|first number| = first number’s absolute value
|−7| = 7
|second number| = second number’s absolute value
From −7.5 to −7 is 0.5
Distance between the two numbers on the line = distance apart
Assumptions
•
On a number line, the number further right is greater: −7 > −7.5.
•
For negative numbers, the one closer to 0 is greater, though its absolute value is smaller.
•
Absolute value is the distance from 0; comparing distances is not comparing the numbers.
•
Numbers from −100 to 100.
Step-by-step
WE KNOW
First number: −7.5
Second number: −7
FIND
sign, first number’s absolute value, second number’s absolute value, distance apart
Step 1 · Find sign
−7.5 ? −7
The sign between the two numbers
The first is left of the second on the line: <.
c: <
Step 2 · Find first number’s absolute value
|−7.5| = ?
|first number| = first number’s absolute value
The first number’s distance from 0.
First number’s absolute value = 7.5
Step 3 · Find second number’s absolute value
|−7| = ?
|second number| = second number’s absolute value
The second number’s distance from 0.
Second number’s absolute value = 7
Step 4 · Find distance apart
From −7.5 to −7 is ?
Distance between the two numbers on the line = distance apart
Count the distance between the two points on the line.
−7.5 and −7 are on the same side of 0: subtract their distances from 0.
|−7.5| − |−7| = 7.5 − 7 = 0.5
Distance apart = 0.5 (−7.5 < −7; |−7.5| > |−7|)
Check
Put the numbers back in. Both sides should match.
−7.5 < −7 ✓
|−7.5| = 7.5 ✓
|−7| = 7 ✓
|−7.5| − |−7| = 7.5 − 7 = 0.5 ✓
Topic check
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Related lessons
Integers and rational numbers
Main lesson
How much warmer or colder?
Use this for the change from −5 °C up to 3 °C, or a drop from 8 °C to −2 °C.
Order rational numbers
Use this for “Order from least to greatest: −6, −2 1/2, 3/4, |−5|.”
Positive and negative numbers in context
Use this for “A drop of 8 degrees is −8”: everyday positive and negative amounts.