---
title: "Integers: cheat sheet"
subtitle: "Number Foundations"
---

# Integers

> The words and methods from this unit, with an example of each.

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**integer**: A whole number, zero, or a negative whole number.

$$\ldots,\; -3,\; -2,\; -1,\; 0,\; 1,\; 2,\; 3,\; \ldots$$

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**negative number**: A number below zero, to the left of $0$ on a number line: five below zero.

$$-5$$

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**less than, greater than**: The wide end of the sign faces the greater number. Further left on the line is less.

$$-7 < -2 \qquad 3 > -1$$

_−7 is further left than −2, so −7 < −2_

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**further from zero**: The size of a number without its sign. Among negatives, the one further from zero is the lesser: $-10 < -1$.

$$-10 \text{ is further from zero than } {-1}$$

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**adding a negative**: Start at the first number. Adding a positive moves right; adding a negative moves left.

$$4 + (-6) = -2$$

_From 4, left 6, to −2_

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**subtracting**: Subtracting moves the opposite way to adding: subtracting a positive moves left, past zero if it has to.

$$2 - 5 = -3$$

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**subtracting a negative**: Adding $-3$ would move left 3, so subtracting it moves right 3. It gives the same as adding $3$.

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

_Adding −3 would go left; subtracting it goes right 3, to 8_

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**multiplying integers**: Same signs give a positive, different signs a negative. On the line: $a$ jumps of $b$; a negative number of jumps goes the opposite way.

$$-3 \times (-2) = 6 \qquad 3 \times (-2) = -6$$

_−3 jumps of −2 go the opposite way: to 6_

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**dividing integers**: The same sign rule as multiplying, because dividing undoes it: check $3 \times (-4) = -12$.

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

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