SME
Grade 6 Math · The Number System
Integers and rational numbers
Use this for “What is the opposite of −4, and what is its absolute value?”
Diagram
−4 is 4 from 0.
Its opposite is 4.
This is an example. Type your own values to start a new problem.
−(
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Formulas
−(−4) = 4
The number with its sign changed = its opposite
|−4| = 4
Distance of the number from 0 = its absolute value
Assumptions
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Numbers left of 0 are negative; numbers right of 0 are positive.
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The opposite of the opposite is the number: −(−4) = 4.
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Absolute value is the distance from 0, so it is never negative.
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Numbers from −100 to 100, in quarters.
Step-by-step
WE KNOW
Number: −4
FIND
its opposite, its absolute value
Step 1 · Find its opposite
−(−4) = ?
The number with its sign changed = its opposite
The opposite is the same distance from 0, on the other side of 0.
Its opposite = 4
Step 2 · Find its absolute value
|−4| = ?
Distance of the number from 0 = its absolute value
Absolute value is the distance from 0: the number without its sign.
Its absolute value = 4
Check
Put the numbers back in. Both sides should match.
−(−4) = 4 ✓
|−4| = 4 ✓
Topic check
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Use this for “A drop of 8 degrees is −8”: everyday positive and negative amounts.