Signed Numbers: Quick Reference (Adding, Subtracting, Multiplying, Dividing)

Signed Numbers: Quick Reference

Adding Signed Numbers

• Determine the function: addition. Use SAS: Same signs Add, Same sign.

  • If the signs are the same (both positive or both negative), add magnitudes and keep the sign:

  • $(+a) + (+b) = +(a+b)$

  • $(-a) + (-b) = -(a+b)$

  • If the signs are different, take the difference of magnitudes and give the sign of the larger magnitude:

  • $(+a) + (-b) = \text{sign of larger}(a,b) \cdot |a-b|$

  • Example: $(+3) + (-9) = -6$, $(-7) + (+9) = +2$

• Note: When there’s no explicit sign in front of a number, it is treated as positive.

• Mnemonic: SAS = Same, Add, Same.

Subtracting Signed Numbers

• Use Keep Change Change (KCC): keep the first number, change the subtraction sign to addition, and change the sign of the second number.

  • Then apply the addition rules.

  • Examples:

  • $7 - (-9) = 7 + (+9) = +16$

  • $-7 - (+9) = -7 + (-9) = -16$

• Alternatively, you can apply the addition rules after transforming subtraction as above.

Multiplying and Dividing Signed Numbers

• Rule (same as each other for multiplication and division):

  • If the signs are the same, the result is positive.

  • If the signs are different, the result is negative.

• Do the operation on the magnitudes, then assign the correct sign.

• Examples:

  • $(-12) \times (-3) = +36$

  • $12 \times (-3) = -36$

  • $(-12) \div 4 = -3$

  • $(-12) \div (-3) = +4$

• Important: The sign rules for adding/subtracting do not apply to multiplying/dividing; use the single sign rule above.

Mnemonics and Quick Tips

• Adding:

  • If signs are the same: add magnitudes, keep sign (SAS).

  • If signs are different: take the difference, sign of larger magnitude.

• Subtracting:

  • Keep Change Change (KCC): keep first, switch subtraction to add, flip sign of second, then add.

• Multiply/Divide:

  • Same sign => positive; Different signs => negative.

• Practice with many problems to build fluency.

Practice Tools and Tips

• Practice: background advice to do many problems for mastery.

• PhotoMath: can read handwriting and show solving steps; useful for checking work.

  • Available as a free app on smartphones.

• REOC calculators: used for tests; can be checked out from the bookstore at no charge.

Quick Reference Examples

• Adding same signs: $(+12) + (+8) = +(20)$, $(-7) + (-9) = -(16)$

• Adding different signs (difference): $(+3) + (-9) = -6$, $(-7) + (+9) = +2$

• Subtracting: $7 - (-9) = 7 + 9 = 16$, $-7 - (+9) = -7 + (-9) = -16$

• Multiplying/Dividing: $(-12) \times (-3) = 36$, $12 \div (-3) = -4$