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Pre-Algebra

Operations with Integers

Lesson

Integers are the whole numbers and their negatives: …,−3,−2,−1,0,1,2,3,…\dots, -3, -2, -1, 0, 1, 2, 3, \dots. Working with them comes down to a few sign rules.

Adding and subtracting

  • Same signs: add the values, keep the sign. −4+(−3)=−7-4 + (-3) = -7
  • Different signs: subtract the smaller value from the larger, keep the sign of the larger. −7+3=−4-7 + 3 = -4
  • Subtracting a number is the same as adding its opposite: 5−(−2)=5+2=75 - (-2) = 5 + 2 = 7.

Multiplying and dividing

  • Same signs (positive × positive, or negative × negative) → positive result.
  • Different signs → negative result.

Worked example 1

−8+5-8 + 5

Different signs, so subtract: 8−5=38 - 5 = 3. The larger value (8) was negative, so the answer keeps the negative sign.

=−3= -3

Worked example 2

6−(−4)6 - (-4)

Subtracting a negative is adding its opposite:

=6+4=10= 6 + 4 = 10

Worked example 3

−3×−7-3 \times -7

Two negatives → positive: 3×7=213 \times 7 = 21.

=21= 21

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

−3+7-3 + 7

Problem 2

−8+5-8 + 5

Problem 3

4−94 - 9

Problem 4

−2×6-2 \times 6

Practice

Standard problems matching the lesson.

Problem 5

−5+3-5 + 3

Problem 6

−4+(−7)-4 + (-7)

Problem 7

8−128 - 12

Problem 8

−6−5-6 - 5

Problem 9

9−(−3)9 - (-3)

Problem 10

−2−(−8)-2 - (-8)

Problem 11

−3×4-3 \times 4

Problem 12

−6×−5-6 \times -5

Problem 13

20÷(−4)20 \div (-4)

Problem 14

−18÷(−3)-18 \div (-3)

Problem 15

−15+8−2-15 + 8 - 2

Problem 16

−2×−3×−4-2 \times -3 \times -4

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 17

−8+5−3-8 + 5 - 3

Problem 18

−4×3+2-4 \times 3 + 2

Problem 19

12÷(−4)+(−3)12 \div (-4) + (-3)

Problem 20

−5−(−3)+(−7)-5 - (-3) + (-7)

Problem 21

−2×(−4)+(−6)-2 \times (-4) + (-6)

Problem 22

15−3×(−2)15 - 3 \times (-2)