Start with a reference point
Zero gives a reference point. An elevation of −8 m is 8 m below sea level; +8 m is 8 m above it. A negative sign describes which side of the reference point a value lies on.
Understand integers
Make sense of negative numbers before reaching for a rule.
Understand it
Make the idea make sense.
Compare positions, not just digits
On a horizontal number line, the number farther right is greater. −2 > −7 because −2 is farther right. Both numbers are less than zero.
Distance and value are different
−9 is less than −4, but |−9| is greater than |−4|. Distance from zero is never negative. Opposites have equal absolute values and add to zero.
An integer is a value, not a way of writing it
−5, 0 and 12 are integers. 2.5 is not. The decimal 3.0 represents the integer 3, and 6 ÷ 2 has the integer value 3. A decimal point or fraction notation alone does not tell you the value.
Words worth knowing
- Integer
- A number with a whole-number value: … −2, −1, 0, 1, 2, …
- Opposite
- A number the same distance from zero on the other side. Zero is its own opposite.
- Absolute value
- The distance from a number to zero, written with vertical bars: |−7| = 7.
Make the connection
One position. Three ways to describe it.
Move the point and compare the signed value, its opposite and its distance from zero.
−10010−4
Value−4
Opposite4
Absolute value4
Khan Academy
Pause before the next calculation. Predict the sign and explain the model, then compare the reasoning.
See the thinking
One step at a time.
Predict each next step, then reveal the explanation.
Order −6, 3, −1, 0 from least to greatest
- Picture the values on a number line.
- The farthest-left value is −6, followed by −1, then 0, then 3.
- Least to greatest: −6 < −1 < 0 < 3.
|−8| and the opposite of −8
- Absolute value asks for distance from zero: |−8| = 8.
- The opposite asks for the matching number across zero: the opposite of −8 is 8.
- These happen to be the same here. For +8, absolute value is still 8 but its opposite is −8.
Try together
A little support. Your thinking.
Which is greater: −4 or −9?
Nicely reasoned. Try a fresh question below, or revisit any step.
Your turn
Practice with purpose.
New questions, useful feedback and hints that build on your thinking.
Question 1 of 8Build confidence
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Progress stays on this device.Hints help you learn. First-try answers and supported answers are recorded separately.
Connections
In the real world
All Class Notes →Temperature, sea level and bank balances all use a reference point. Always name what zero means.