Operations with Integers

What are Integers?

Integers are whole numbers and their opposites: $..., -3, -2, -1, 0, 1, 2, 3, ...$

Positive integers: $1, 2, 3, ...$ Negative integers: $-1, -2, -3, ...$ Zero: Neither positive nor negative

Adding Integers

Same signs: Add the absolute values, keep the sign

• $5 + 3 = 8$
• $-5 + (-3) = -8$

Different signs: Subtract the absolute values, use the sign of the larger

• $5 + (-3) = 2$
• $-5 + 3 = -2$

Subtracting Integers

Key rule: Subtracting is the same as adding the opposite

$a - b = a + (-b)$

Examples:

• $7 - 3 = 7 + (-3) = 4$
• $7 - (-3) = 7 + 3 = 10$
• $-7 - 3 = -7 + (-3) = -10$

Multiplying Integers

Sign rules:

• Same signs → positive result
• Different signs → negative result

Examples:

• $5 \times 3 = 15$ (both positive)
• $-5 \times (-3) = 15$ (both negative)
• $5 \times (-3) = -15$ (different signs)
• $-5 \times 3 = -15$ (different signs)

Dividing Integers

Same sign rules as multiplication:

• Same signs → positive result
• Different signs → negative result

Examples:

• $12 \div 3 = 4$
• $-12 \div (-3) = 4$
• $12 \div (-3) = -4$
• $-12 \div 3 = -4$