ADD the numbers and KEEP the sign

• Positive + Positive = Positive

• Negative + Negative = Negative

Examples:

5 + 3 = 8 (both positive, add and keep +)

−7 + (−4) = −11 (both negative, add and keep −)

12 + 9 = 21

−15 + (−10) = −25

SUBTRACT the numbers and use the sign

of the number with the LARGER absolute value

• Find absolute values

• Subtract smaller from larger

• Use sign of larger absolute value

Examples:

8 + (−3) = 5 (|8| > |−3|, so answer is +)

−10 + 4 = −6 (|−10| > |4|, so answer is −)

−7 + 12 = 5 (|12| > |−7|, so answer is +)

15 + (−20) = −5 (|−20| > |15|, so answer is −)

To subtract integers: ADD THE OPPOSITE!

KEEP the first number the same

CHANGE subtraction (−) to addition (+)

CHANGE the sign of the second number

a − b = a + (−b)

Example 1: 7 − 3

Example 2: −5 − 8

Example 3: 6 − (−9)

Example 4: −10 − (−4)

SAME signs = POSITIVE result

• Positive × Positive = Positive

• Negative × Negative = Positive

DIFFERENT signs = NEGATIVE result

• Positive × Negative = Negative

• Negative × Positive = Negative

(+) × (+) = +

(−) × (−) = +

(+) × (−) = −

(−) × (+) = −

Memory Trick: "If the signs are the same, the answer is LAME (positive)!" 😊

SAME as multiplication!

SAME signs = POSITIVE result

• Positive ÷ Positive = Positive

• Negative ÷ Negative = Positive

DIFFERENT signs = NEGATIVE result

• Positive ÷ Negative = Negative

• Negative ÷ Positive = Negative

(+) ÷ (+) = +

(−) ÷ (−) = +

(+) ÷ (−) = −

(−) ÷ (+) = −

Remember: PEMDAS (Please Excuse My Dear Aunt Sally)

P - Parentheses

E - Exponents

M - Multiplication (left to right)

D - Division (left to right)

A - Addition (left to right)

S - Subtraction (left to right)

Problem: −5 + 3 × (−2) − 8 ÷ 4

Addition (+): total, sum, increase, gain, deposit, rise

Subtraction (−): difference, decrease, loss, withdrawal, fall, drop

Multiplication (×): times, product, of, multiple

Division (÷): quotient, split, per, average, each

Problem 1: The temperature was −5°C. It rose 8°C. What is the new temperature?

Problem 2: A submarine at −120 meters dives another 45 meters. What is its depth?

Problem 3: A stock drops $3 per day for 5 days. What is the total change?

✓ Addition same signs: Add and keep the sign

✓ Addition different signs: Subtract and use sign of larger

✓ Subtraction: Always use Keep-Change-Change

✓ Multiplication/Division: Same signs = positive, different = negative

✓ Two negatives multiply/divide = POSITIVE

✓ Subtracting a negative = ADDING a positive

✓ Use PEMDAS for order of operations

✓ Parentheses first, then exponents, then × ÷, finally + −

✓ Practice with number lines for visual understanding

✓ Check your work - does the answer make sense?

Addition Same Signs:

"Same sign means we're aligned - just ADD and the sign is assigned!"

Addition Different Signs:

"Different signs? Subtract and see - bigger absolute value's sign is the KEY!"

Subtraction (KCC):

"KEEP the first, CHANGE the sign, CHANGE the second - subtraction is fine!"

Multiplication & Division:

"Same signs make a POSITIVE treat, different signs make NEGATIVE we meet!"

Two Negatives Multiply:

"A negative times a negative is POSITIVE - it's definitive!"

PEMDAS:

"Please Excuse My Dear Aunt Sally - parentheses to subtraction, that's the rally!"