Operations with Integers

Add, subtract, multiply, and divide positive and negative numbers

Operations with Integers

Adding Integers

Same Signs

Add and keep the sign:

$5 + 3 = 8$
$-5 + (-3) = -8$

Different Signs

Subtract and use the sign of the larger absolute value:

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

Subtracting Integers

Rule: Add the opposite! $a - b = a + (-b)$

Examples:

$5 - 8 = 5 + (-8) = -3$
$-3 - 7 = -3 + (-7) = -10$
$4 - (-6) = 4 + 6 = 10$

Multiplying Integers

Same signs → Positive

$5 \times 3 = 15$
$(-5) \times (-3) = 15$

Different signs → Negative

$5 \times (-3) = -15$
$(-5) \times 3 = -15$

Dividing Integers

Same rules as multiplication:

Same signs → Positive
Different signs → Negative

Examples:

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

📚 Practice Problems

1Problem 1easy

❓ Question:

Calculate: $-8 + 5$

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Solution:

Different signs - subtract and use sign of larger absolute value: $|-8| = 8, \quad |5| = 5$ $8 - 5 = 3$

Since -8 has the larger absolute value, the answer is negative.

Answer: $-3$

2Problem 2medium

❓ Question:

Calculate: $-6 \times (-4) + 8 \div (-2)$

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Solution:

Follow order of operations:

Step 1: Multiply and divide (left to right) $-6 \times (-4) = 24$ $8 \div (-2) = -4$

Step 2: Add $24 + (-4) = 20$

Answer: $20$

3Problem 3hard

❓ Question:

The temperature at 6 AM was $-12°$ F. It rose $3°$ per hour for 5 hours, then dropped $2°$ per hour for 3 hours. What was the final temperature?

💡 Show Solution

Solution:

Start: $-12°$

Rose $3°$ per hour for 5 hours: $5 \times 3 = 15°$ increase $-12 + 15 = 3°$

Dropped $2°$ per hour for 3 hours: $3 \times 2 = 6°$ decrease $3 - 6 = -3°$

Answer: $-3°$ F

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