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What Is the Integers?(With Examples)

Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. The set of integers is written as {..., -3, -2, -1, 0, 1, 2, 3, ...} and extends infinitely in both directions.

Grades 6-7Key Stage 3 (Year 7-9)Årskurs 6-7Klasse 5-6

📖Definition

📐Formula

ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}

The symbol ℤ (from German "Zahlen" meaning numbers) represents the set of all integers. Positive integers are greater than zero, negative integers are less than zero, and zero is neither positive nor negative.

📝Step-by-Step Guide

Adding Integers

Same signs: Add absolute values, keep the sign. Different signs: Subtract absolute values, use the sign of the larger absolute value.

(-5) + (-3) = -8; (-5) + 3 = -2

Subtracting Integers

Change subtraction to addition of the opposite (add the additive inverse).

a - b = a + (-b); 5 - (-3) = 5 + 3 = 8

Multiplying Integers

Same signs give positive result. Different signs give negative result.

(-3) × (-4) = 12; (-3) × 4 = -12

Dividing Integers

Same rules as multiplication: same signs = positive, different signs = negative.

(-12) ÷ (-4) = 3; (-12) ÷ 4 = -3

⚠️Common Mistakes to Avoid

Confusing the rules for adding and multiplying integers
Forgetting that subtracting a negative becomes addition
Including fractions or decimals as integers
Making sign errors when working with multiple operations
Thinking zero is a positive number

✏️Practice Problems

Easy

Calculate (-7) + 4

Answer: -3

Medium

Calculate (-6) × (-8)

Answer: 48

Hard

Calculate (-24) ÷ 6 + (-3) × (-2)

Answer: 2

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Negative Numbers Absolute Value Number Line Order of Operations

Curriculum Alignment

CommonCore (6.NS.C.5)KS3KMK

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