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Integers: cheat sheet

Number Foundations · The words and methods from the lessons, with an example of each.

integer

A whole number, zero, or a negative whole number.

…,  −3,  −2,  −1,  0,  1,  2,  3,  …\ldots,\; -3,\; -2,\; -1,\; 0,\; 1,\; 2,\; 3,\; \ldots

less than, greater than

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

−7<−23>−1-7 < -2 \qquad 3 > -1
−7 is further left than −2, so −7 < −2
−7 is further left than −2, so −7 < −2

subtracting

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

2−5=−32 - 5 = -3

subtracting a negative

Adding −3-3 would move left 3, so subtracting it moves right 3. It gives the same as adding 33.

5−(−3)=85 - (-3) = 8
Adding −3 would go left; subtracting it goes right 3, to 8
Adding −3 would go left; subtracting it goes right 3, to 8

dividing integers

The same sign rule as multiplying, because dividing undoes it: check 3×(−4)=−123 \times (-4) = -12.

−12÷3=−4-12 \div 3 = -4

negative number

A number below zero, to the left of 00 on a number line: five below zero.

−5-5

further from zero

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

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

adding a negative

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

4+(−6)=−24 + (-6) = -2
From 4, left 6, to −2
From 4, left 6, to −2

multiplying integers

Same signs give a positive, different signs a negative. On the line: aa jumps of bb; a negative number of jumps goes the opposite way.

−3×(−2)=63×(−2)=−6-3 \times (-2) = 6 \qquad 3 \times (-2) = -6
−3 jumps of −2 go the opposite way: to 6
−3 jumps of −2 go the opposite way: to 6