Explains positive and negative whole numbers using the number line, then sets out the rules for adding, subtracting, multiplying and dividing integers with worked examples. Finishes with an order of operations example and a self-check so students can confirm they have the sign rules right.
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Curriculum: Texas grade levels (TEKS). We show specific outcome codes only where they have been verified against the official curriculum document.
Completed: Integers Explained: Working with Negative Numbers
7th Grade students (typically ages 12–13) working on integers. It is pitched at level 2 · standard.
This is a study guide, so there is no separate answer sheet; the 'Check yourself' questions include answers.
About 20 minutes. Short, regular sessions work best: two or three a week beats one long one.
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Try 7th Grade Integers (Positive and Negative Numbers) Worksheet — Level 1.
Success TutoringWorksheets7th Grade · Mathematics · IntegersIntegers are the whole numbers and their opposites: … −3, −2, −1, 0, 1, 2, 3 … Negative numbers sit to the left of zero on the number line, so the further left a number is, the smaller it is. −5 is smaller than −2, even though 5 is bigger than 2. Think of temperatures: −5 °C is colder than −2 °C.
Ordering from smallest to largest: −5 < −2 < 0 < 3. The opposite of a number is the same distance from zero on the other side: the opposite of 4 is −4.
Work out −5 + (−3) and 6 − (−2)
Multiplying and dividing. Multiply or divide the numbers as usual, then decide the sign: same signs give a positive, different signs give a negative.
| Signs | Result | Example |
|---|---|---|
| positive × positive | positive | 4 × 6 = 24 |
| negative × negative | positive | −3 × −7 = 21 |
| positive × negative | negative | 5 × −4 = −20 |
| negative ÷ positive | negative | −18 ÷ 3 = −6 |
| negative ÷ negative | positive | −20 ÷ −4 = 5 |
Order of operations (PEMDAS). PEMDAS still applies with negative numbers: Parentheses, Exponents (powers), Multiplication and Division, then Addition and Subtraction. Be especially careful with the signs.
2 − 3 × (−4)
Answers: 1. 3 2. −13 3. 8 4. 40 5. −4 6. −13 (2 × (−5) = −10, then −3 + (−10) = −13)
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