The People’s Share

GED Math

Signed Numbers Practice

The number line and absolute value; naming the case; adding with the same and different signs; every kind of subtraction; three or more numbers; multiplying and dividing. 202 problems, with the answer key at the end.

← Math · Family 2 · Signed Numbers

Practice for family 2. Signed Numbers explains everything on this sheet from the beginning, and Quizzes 20 to 22 go further. This sheet is for doing it until it is accurate and quick. 202 problems in six parts, each section starting with its plainest version.

Part One

The number line and absolute value

On the number line, the number farther to the right is larger. The absolute value of a number is its distance from zero: the number without its sign.

1.Which is larger?

ExampleWhich is larger: −8 or −3? −3 is farther to the right.

Circle or write the larger number.

  1. 1.Which is larger: 8 or −3?
  2. 2.Which is larger: −9 or −8?
  3. 3.Which is larger: 7 or −14?
  4. 4.Which is larger: −1 or −13?
  5. 5.Which is larger: 18 or −3?
  6. 6.Which is larger: −19 or −18?
  7. 7.Which is larger: −9 or −20?
  8. 8.Which is larger: −18 or −20?

2.Putting numbers in order

Example−5, 2, −1, 0 in order: −5, −1, 0, 2.

Write them from least to greatest.

  1. 9.Put in order, least to greatest: −1,  4,  −7,  −4,  0
  2. 10.Put in order, least to greatest: −3,  −1,  0,  11
  3. 11.Put in order, least to greatest: 10,  6,  −12,  5,  −1
  4. 12.Put in order, least to greatest: 6,  −8,  −14,  15,  2
  5. 13.Put in order, least to greatest: −4,  1,  4,  −6,  −15
  6. 14.Put in order, least to greatest: −6,  14,  −10,  −11,  −5

3.Absolute value and opposites

The opposite of a number is the same distance from zero on the other side.

Example|−6| = 6. The opposite of −6 is 6.

Answer each.

  1. 15.|3| =
  2. 16.The opposite of 4
  3. 17.|−3| =
  4. 18.|−13| =
  5. 19.|−14| =
  6. 20.The opposite of 25
  7. 21.|33| =
  8. 22.The opposite of −29
  9. 23.The opposite of 36
  10. 24.|−36| =

4.Farther from zero

Look at the numbers without their signs.

ExampleWhich is farther from zero: −9 or 4? Without signs, 9 and 4. −9 is farther.

Answer each.

  1. 25.Which is farther from zero: 11 or −7?
  2. 26.Which is farther from zero: 17 or −19?
  3. 27.Which is farther from zero: −24 or 18?
  4. 28.Which is farther from zero: −25 or 3?
  5. 29.Which is farther from zero: −25 or 16?
  6. 30.Which is farther from zero: 25 or −23?

Part Two

Naming the case

Before you work anything out, ask two questions. Am I adding or subtracting? Is the second number positive or negative? A number with no sign is positive: in 5 − 3, the 3 is a positive 3 being subtracted.

5.The four cases

The four cases are: add a positive, add a negative, subtract a positive, subtract a negative.

Example−7 − 2: subtracting, and the 2 is positive. Subtract a positive.

Name the case. Do not work out the answer.

  1. 31.Name the case:  −2 + 1
  2. 32.Name the case:  −3 + 1
  3. 33.Name the case:  1 − 3
  4. 34.Name the case:  −2 − 1
  5. 35.Name the case:  −3 + 8
  6. 36.Name the case:  9 − 4
  7. 37.Name the case:  −6 + 9
  8. 38.Name the case:  −6 + (−3)
  9. 39.Name the case:  −6 − 2
  10. 40.Name the case:  11 − 10
  11. 41.Name the case:  −12 + (−12)
  12. 42.Name the case:  −3 − (−11)

Part Three

Adding

Rule 1, same signs: add the absolute values and keep the sign. Rule 2, different signs, in two steps: first subtract (the smaller absolute value from the larger); then give the result the sign of the original larger absolute value.

6.The four cases with small numbers

Adding a positive or subtracting a negative goes up. Adding a negative or subtracting a positive goes down.

Example4 − (−5) = 9: subtract a negative, so go up 5.

Work out each. Name the case to yourself first.

  1. 43.1 + 2 =
  2. 44.1 + (−3) =
  3. 45.4 − 4 =
  4. 46.9 + 6 =
  5. 47.4 + (−7) =
  6. 48.6 + (−7) =
  7. 49.8 + (−1) =
  8. 50.9 − 4 =
  9. 51.9 − 2 =
  10. 52.9 − 5 =
  11. 53.3 − (−6) =
  12. 54.2 − (−9) =

7.Same signs (Rule 1)

Example−8 + (−5): both negative. 8 + 5 = 13, keep the sign: −13.

Add.

  1. 55.−11 + (−1) =
  2. 56.−2 + (−17) =
  3. 57.−11 + (−17) =
  4. 58.−15 + (−19) =
  5. 59.28 + 21 =
  6. 60.28 + 4 =
  7. 61.−4 + (−22) =
  8. 62.−26 + (−20) =
  9. 63.−13 + (−26) =
  10. 64.−5 + (−26) =
  11. 65.−25 + (−28) =
  12. 66.−29 + (−28) =

8.Different signs, the positive farther from zero

Example11 + (−4): first subtract, 11 − 4 = 7; then the sign of the original larger absolute value, 11, which is positive. The answer is 7.

Add.

  1. 67.−4 + 8 =
  2. 68.−15 + 24 =
  3. 69.26 + (−25) =
  4. 70.−5 + 28 =
  5. 71.−7 + 29 =
  6. 72.30 + (−11) =
  7. 73.−29 + 33 =
  8. 74.−19 + 34 =
  9. 75.−12 + 35 =
  10. 76.39 + (−9) =

9.Different signs, the negative farther from zero

These are where most mistakes are made. Do both steps: after you subtract, go back to the original problem for the sign.

Example4 + (−11): first subtract, 11 − 4 = 7; then the sign of the original larger absolute value, −11, which is negative. The answer is −7.

Add.

  1. 77.3 + (−19) =
  2. 78.−24 + 7 =
  3. 79.20 + (−28) =
  4. 80.−28 + 11 =
  5. 81.−33 + 29 =
  6. 82.30 + (−35) =
  7. 83.−35 + 13 =
  8. 84.32 + (−35) =
  9. 85.−36 + 23 =
  10. 86.−40 + 22 =

10.Adding, all kinds

A number and its opposite add to zero.

Add.

  1. 87.−4 + 2 =
  2. 88.12 + (−9) =
  3. 89.−11 + 15 =
  4. 90.13 + (−18) =
  5. 91.18 + (−18) =
  6. 92.−16 + (−15) =
  7. 93.−17 + (−14) =
  8. 94.22 + (−22) =
  9. 95.−24 + 1 =
  10. 96.−23 + (−19) =
  11. 97.−27 + 13 =
  12. 98.−1 + (−24) =

Part Four

Subtracting

Rule 3: subtracting a number gives the same answer as adding its opposite. Rewrite the subtraction as an addition, then use Rule 1 or Rule 2. (Keep the first number, change − to +, change the sign of the second number.)

11.Subtracting a positive

The number goes down. When the second number is larger, the answer is below zero.

Example4 − 9 = 4 + (−9) = −5.

Work out each.

  1. 99.3 − 10 =
  2. 100.9 − 14 =
  3. 101.−1 − 10 =
  4. 102.9 − 17 =
  5. 103.19 − 1 =
  6. 104.20 − 6 =
  7. 105.−16 − 9 =
  8. 106.14 − 20 =
  9. 107.23 − 11 =
  10. 108.12 − 24 =
  11. 109.25 − 24 =
  12. 110.−22 − 21 =

12.Subtracting a negative

The number goes up.

Example−9 − (−4) = −9 + 4 = −5.

Work out each.

  1. 111.13 − (−5) =
  2. 112.−3 − (−11) =
  3. 113.−2 − (−14) =
  4. 114.20 − (−12) =
  5. 115.21 − (−15) =
  6. 116.−13 − (−17) =
  7. 117.24 − (−16) =
  8. 118.−20 − (−14) =
  9. 119.24 − (−12) =
  10. 120.−21 − (−2) =
  11. 121.−23 − (−13) =
  12. 122.−25 − (−19) =

13.Rewrite, then work it out

Example−2 − (−8) becomes −2 + 8 = 6.

Write the addition, then the answer.

  1. 123.Rewrite as an addition, then work it out:  4 − 2
  2. 124.Rewrite as an addition, then work it out:  5 − 5
  3. 125.Rewrite as an addition, then work it out:  4 − (−8)
  4. 126.Rewrite as an addition, then work it out:  −5 − (−1)
  5. 127.Rewrite as an addition, then work it out:  −7 − (−2)
  6. 128.Rewrite as an addition, then work it out:  −12 − 4
  7. 129.Rewrite as an addition, then work it out:  −10 − (−8)
  8. 130.Rewrite as an addition, then work it out:  −11 − (−4)

14.Subtracting, all kinds

Work out each.

  1. 131.17 − 15 =
  2. 132.18 − 5 =
  3. 133.−13 − 16 =
  4. 134.19 − (−13) =
  5. 135.26 − 9 =
  6. 136.14 − (−25) =
  7. 137.29 − 30 =
  8. 138.36 − 8 =
  9. 139.2 − (−32) =
  10. 140.38 − 29 =
  11. 141.35 − (−9) =
  12. 142.−30 − 36 =

Part Five

Three or more numbers

Rewrite every subtraction as adding the opposite. Then add all the positives, add all the negatives, and combine the two totals. Cross out zero pairs first.

15.Strings of numbers

Example−4 + 9 − 12 + 3: positives 9 + 3 = 12; negatives −4 + (−12) = −16; 12 + (−16) = −4.

Work out each.

  1. 143.2 + 3 − 1 =
  2. 144.12 + 15 + 12 =
  3. 145.7 − 2 − (−4) =
  4. 146.−12 − 9 + 7 =
  5. 147.10 + (−1) + (−3) + (−3) =
  6. 148.−3 − (−1) − (−2) =
  7. 149.10 + (−9) + 15 + (−13) =
  8. 150.9 − (−14) − 3 =
  9. 151.−14 − (−7) − 1 =
  10. 152.−8 − (−15) − 8 =
  11. 153.−15 − (−2) − 14 − 7 =
  12. 154.−10 − (−8) − (−3) − (−1) =

16.Signed numbers in the world

Money in, rising, and gains are positive. Money out, falling, and losses are negative.

Answer each.

  1. 155.At 6 a.m. the temperature was −12°F. By noon it had risen 19 degrees. What was the temperature at noon?
  2. 156.A checking account shows a balance of −$35. A paycheck of $210 is deposited. What is the balance now?
  3. 157.An elevator starts on the 3rd floor, goes down 5 floors, then up 2 floors. The street is floor 0. Which floor is it on?
  4. 158.A football team gains 8 yards, loses 12 yards, then loses 3 yards. What is the total change in yards?
  5. 159.A diver is at −18 meters. She rises 7 meters, then goes down 11 meters. Where is she now?
  6. 160.The high temperature was 9°F and the low was −14°F. How many degrees apart are they?
  7. 161.A stock price changed by −$3, then +$5, then −$4, then +$1 over four days. What was the total change?
  8. 162.You owe a friend $40, shown as −40. The friend forgives $15 of it. Write the subtraction and find what you owe now.
  9. 163.The lows over four nights were −8°, −3°, 2° and −11°. What is the total of the four lows, and what is their mean (the total divided by 4)?
  10. 164.A submarine at −250 meters rises 90 meters, then dives 140 meters. How deep is it now?

Part Six

Multiplying and dividing

Same signs: the answer is positive. Different signs: the answer is negative. For more than two numbers, count the negatives: an even number gives a positive, an odd number a negative.

17.Multiplying

Example(−6) × (−7) = 42. (−6) × 7 = −42.

Multiply.

  1. 165.(−1) × (−2) =
  2. 166.(−3) × 9 =
  3. 167.9 × (−6) =
  4. 168.(−10) × 3 =
  5. 169.8 × (−10) =
  6. 170.(−10) × 9 =
  7. 171.(−11) × 9 =
  8. 172.3 × (−11) =
  9. 173.10 × (−12) =
  10. 174.(−12) × 7 =

18.Dividing

Example−48 ÷ 6 = −8. −48 ÷ (−6) = 8.

Divide.

  1. 175.−1 ÷ (−1) =
  2. 176.6 ÷ (−6) =
  3. 177.−15 ÷ (−5) =
  4. 178.24 ÷ (−4) =
  5. 179.−21 ÷ (−7) =
  6. 180.−36 ÷ 4 =
  7. 181.−56 ÷ (−8) =
  8. 182.63 ÷ (−7) =
  9. 183.−70 ÷ (−7) =
  10. 184.−77 ÷ (−7) =

19.Three or four numbers

Example(−2) × (−3) × (−5): three negatives, odd, so −30.

Multiply.

  1. 185.2 × 3 × 4 =
  2. 186.1 × (−3) × 1 =
  3. 187.2 × 6 × 1 × (−2) =
  4. 188.4 × 1 × (−3) × (−2) =
  5. 189.(−5) × 4 × (−3) =
  6. 190.(−4) × (−5) × (−6) =

20.Review: all four operations

Check first whether you are adding, subtracting, multiplying or dividing. The sign rules for adding are not the same as the rules for multiplying.

Work out each.

  1. 191.9 × 3 =
  2. 192.3 + 14 =
  3. 193.(−1) × 10 =
  4. 194.(−10) × 11 =
  5. 195.(−9) × (−6) =
  6. 196.−5 + (−9) =
  7. 197.12 × (−13) =
  8. 198.15 − 5 =
  9. 199.20 ÷ 4 =
  10. 200.−2 − (−10) =
  11. 201.−3 − (−14) =
  12. 202.−210 ÷ 15 =

Answer Key

For subtraction, the key shows the rewritten addition, so that you can see where a wrong answer went off.

1.Which is larger? (1–8)

  1. 1.8
  2. 2.−8
  3. 3.7
  4. 4.−1
  5. 5.18
  6. 6.−18
  7. 7.−9
  8. 8.−18

2.Putting numbers in order (9–14)

  1. 9.−7,  −4,  −1,  0,  4
  2. 10.−3,  −1,  0,  11
  3. 11.−12,  −1,  5,  6,  10
  4. 12.−14,  −8,  2,  6,  15
  5. 13.−15,  −6,  −4,  1,  4
  6. 14.−11,  −10,  −6,  −5,  14

3.Absolute value and opposites (15–24)

  1. 15.3
  2. 16.−4
  3. 17.3
  4. 18.13
  5. 19.14
  6. 20.−25
  7. 21.33
  8. 22.29
  9. 23.−36
  10. 24.36

4.Farther from zero (25–30)

  1. 25.11
  2. 26.−19
  3. 27.−24
  4. 28.−25
  5. 29.−25
  6. 30.25

5.The four cases (31–42)

  1. 31.add a positive
  2. 32.add a positive
  3. 33.subtract a positive
  4. 34.subtract a positive
  5. 35.add a positive
  6. 36.subtract a positive
  7. 37.add a positive
  8. 38.add a negative
  9. 39.subtract a positive
  10. 40.subtract a positive
  11. 41.add a negative
  12. 42.subtract a negative

6.The four cases with small numbers (43–54)

  1. 43.3  (add a positive)
  2. 44.−2  (add a negative)
  3. 45.0  (subtract a positive)
  4. 46.15  (add a positive)
  5. 47.−3  (add a negative)
  6. 48.−1  (add a negative)
  7. 49.7  (add a negative)
  8. 50.5  (subtract a positive)
  9. 51.7  (subtract a positive)
  10. 52.4  (subtract a positive)
  11. 53.9  (subtract a negative)
  12. 54.11  (subtract a negative)

7.Same signs (Rule 1) (55–66)

  1. 55.−12
  2. 56.−19
  3. 57.−28
  4. 58.−34
  5. 59.49
  6. 60.32
  7. 61.−26
  8. 62.−46
  9. 63.−39
  10. 64.−31
  11. 65.−53
  12. 66.−57

8.Different signs, the positive farther from zero (67–76)

  1. 67.4
  2. 68.9
  3. 69.1
  4. 70.23
  5. 71.22
  6. 72.19
  7. 73.4
  8. 74.15
  9. 75.23
  10. 76.30

9.Different signs, the negative farther from zero (77–86)

  1. 77.−16
  2. 78.−17
  3. 79.−8
  4. 80.−17
  5. 81.−4
  6. 82.−5
  7. 83.−22
  8. 84.−3
  9. 85.−13
  10. 86.−18

10.Adding, all kinds (87–98)

  1. 87.−2
  2. 88.3
  3. 89.4
  4. 90.−5
  5. 91.0
  6. 92.−31
  7. 93.−31
  8. 94.0
  9. 95.−23
  10. 96.−42
  11. 97.−14
  12. 98.−25

11.Subtracting a positive (99–110)

  1. 99.3 + (−10) = −7
  2. 100.9 + (−14) = −5
  3. 101.−1 + (−10) = −11
  4. 102.9 + (−17) = −8
  5. 103.19 + (−1) = 18
  6. 104.20 + (−6) = 14
  7. 105.−16 + (−9) = −25
  8. 106.14 + (−20) = −6
  9. 107.23 + (−11) = 12
  10. 108.12 + (−24) = −12
  11. 109.25 + (−24) = 1
  12. 110.−22 + (−21) = −43

12.Subtracting a negative (111–122)

  1. 111.13 + 5 = 18
  2. 112.−3 + 11 = 8
  3. 113.−2 + 14 = 12
  4. 114.20 + 12 = 32
  5. 115.21 + 15 = 36
  6. 116.−13 + 17 = 4
  7. 117.24 + 16 = 40
  8. 118.−20 + 14 = −6
  9. 119.24 + 12 = 36
  10. 120.−21 + 2 = −19
  11. 121.−23 + 13 = −10
  12. 122.−25 + 19 = −6

13.Rewrite, then work it out (123–130)

  1. 123.4 + (−2) = 2
  2. 124.5 + (−5) = 0
  3. 125.4 + 8 = 12
  4. 126.−5 + 1 = −4
  5. 127.−7 + 2 = −5
  6. 128.−12 + (−4) = −16
  7. 129.−10 + 8 = −2
  8. 130.−11 + 4 = −7

14.Subtracting, all kinds (131–142)

  1. 131.2
  2. 132.13
  3. 133.−29
  4. 134.32
  5. 135.17
  6. 136.39
  7. 137.−1
  8. 138.28
  9. 139.34
  10. 140.9
  11. 141.44
  12. 142.−66

15.Strings of numbers (143–154)

  1. 143.4
  2. 144.39
  3. 145.9
  4. 146.−14
  5. 147.3
  6. 148.0
  7. 149.3
  8. 150.20
  9. 151.−8
  10. 152.−1
  11. 153.−34
  12. 154.2

16.Signed numbers in the world (155–164)

  1. 155.7°F
  2. 156.$175
  3. 157.Floor 0, the street level (3 − 5 + 2 = 0)
  4. 158.−7 yards, a loss of 7
  5. 159.−22 meters
  6. 160.23 degrees (9 − (−14) = 23)
  7. 161.−$1
  8. 162.−40 − (−15) = −25; you owe $25
  9. 163.Total −20°; mean −5°
  10. 164.−300 meters, 300 meters below the surface

17.Multiplying (165–174)

  1. 165.2
  2. 166.−27
  3. 167.−54
  4. 168.−30
  5. 169.−80
  6. 170.−90
  7. 171.−99
  8. 172.−33
  9. 173.−120
  10. 174.−84

18.Dividing (175–184)

  1. 175.1
  2. 176.−1
  3. 177.3
  4. 178.−6
  5. 179.3
  6. 180.−9
  7. 181.7
  8. 182.−9
  9. 183.10
  10. 184.11

19.Three or four numbers (185–190)

  1. 185.24
  2. 186.−3
  3. 187.−24
  4. 188.24
  5. 189.60
  6. 190.−120

20.Review: all four operations (191–202)

  1. 191.27
  2. 192.17
  3. 193.−10
  4. 194.−110
  5. 195.54
  6. 196.−14
  7. 197.−156
  8. 198.10
  9. 199.5
  10. 200.8
  11. 201.11
  12. 202.−14