QuickCalculators adds, subtracts, multiplies, and divides integers with explicit sign rules so positive and negative whole numbers stay consistent on a number line. Enter two integers and an operation, then read the signed result with the rule that produced it.
Integers include zero and the positives and negatives without fractional parts. Sign mistakes dominate early errors, so each section states the rule before the numeric example.
Add and subtract integers
Adding and subtracting integers means combining directed distances on a number line. QuickCalculators applies same-sign and different-sign rules for addition and treats subtraction as adding the opposite so one framework covers both operations. Same signs keep the shared sign and add the absolute values.
Different signs subtract the absolute values and keep the sign of the larger absolute value. Subtraction never invents a separate "minus table"; it rewrites as addition of the opposite.
Apply the sign rules for addition
When both integers share a sign, add their absolute values and keep that sign. When signs differ, subtract the smaller absolute value from the larger and keep the sign of the larger absolute value. QuickCalculators labels which case applied so the rule is checkable.
Example: −7 + (−3) keeps the negative sign and adds 7 and 3 to get −10. Example: −7 + 3 subtracts 3 from 7 and keeps the negative of the larger absolute value, giving −4.
Subtract integers by adding the opposite
Subtracting an integer is the same as adding its opposite. Rewrite a − b as a + (−b), then use the addition rules. QuickCalculators shows that rewrite so a double negative does not become a mystery. Example: 5 − (−2) becomes 5 + 2 = 7.
Example: −4 − 6 becomes −4 + (−6) = −10. The phrase "minus a negative" means add the positive opposite of that negative.
Multiply and divide integers
Multiplying or dividing two integers yields a positive product or quotient when the signs match and a negative result when the signs differ. Zero times any integer is zero. QuickCalculators applies those sign rules after computing the absolute-value product or quotient.
Example: (−3)×(−4) = 12 and (−3)×4 = −12. Division follows the same sign pattern: (−12)÷3 = −4 and (−12)÷(−3) = 4. Division by zero is blocked.
Add −7 and −3 on a number line
The fixture adds −7 and −3 on QuickCalculators.
- Note that both addends are negative, so keep the negative sign.
- Add absolute values: 7 + 3 = 10.
- Attach the shared sign to obtain −10.
On a number line, start at −7 and move three units further left to land on −10. The same-sign addition rule matches that leftward move.
Avoid this common misconception
A common error is treating "two negatives make a positive" as a rule for addition. That slogan applies to multiplication and division of two negatives, not to adding two negatives. Adding −7 and −3 yields −10, not +10. QuickCalculators keeps addition and multiplication sign rules in separate sections so the slogan does not leak.
Frequently asked questions
How do you add integers with different signs?
To add integers with different signs, subtract the absolute values and keep the sign of the larger absolute value. Example: −7 + 3 = −4.
How do you subtract a negative integer?
To subtract a negative integer, add its opposite. Example: 5 − (−2) = 5 + 2 = 7.
What is −7 plus −3?
Negative seven plus negative three equals −10. Both signs match, so add 7 and 3 and keep the negative sign.
What are the sign rules for multiplying integers?
Matching signs give a positive product. Different signs give a negative product. Zero times any integer is zero.
Is zero an integer?
Zero is an integer. It is neither positive nor negative and sits at the origin of the number line used for these operations.
Why rewrite subtraction as adding the opposite?
Rewriting subtraction as adding the opposite lets one addition rule set cover both operations and clarifies cases such as minus a negative.
Summary
QuickCalculators applies integer sign rules for the four operations and treats subtraction as adding the opposite. Same-sign addition keeps the shared sign; different-sign addition follows the larger absolute value. Multiplication and division turn positive when signs match and negative when they differ. The fixture −7 + (−3) equals −10. Do not apply the "two negatives" product slogan to addition.