Foundations
Integer operations
ALEKS · foundation repairTEAS math
Signed arithmetic is one question: are the signs the same or different?
What this covers
- Adding with matching signs: add the sizes and keep the shared sign.
- Adding with opposite signs: subtract the smaller size from the larger and keep the sign of the larger.
- Subtracting is adding the opposite, so a - b becomes a + (-b).
- Multiplying or dividing: an even count of negatives is positive, an odd count is negative.
Worked example
Worked example
Simplify -7 - (-3) + (-4).
- −7+3+(−4)Subtracting -3 is the same as adding 3.
- −4+(−4)-7 + 3 has opposite signs, so 7 - 3 = 4 and the larger size was negative.
- −8Matching signs now, so add the sizes and keep the negative.
Another worked example
Compute −4 − (−7).
- −4−(−7)=−4+7Subtracting −7 adds its opposite, +7.
- −4+7=3Move seven units right from −4, crossing zero.
A common mistake
A mistake Lemma catches
From −7−(−3)+(−4)
−7−3+(−4)−7+3+(−4)
“You wrote -(-3) as -3, but subtracting a negative is adding: the two minus signs cancel, so -(-3) is +3.”
Try one
Sample problem
Evaluate exactly.
(5)(−6)Practice integers free
No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.
Where this fits
After this