Below zero
- 1.Put these in order from smallest to largest: 3 −5 0 −1
- 2.What is the opposite of −6?
- 3.What is the absolute value of −9? (Written |−9|.)
- 4.Which is colder: −4°F or −12°F?
Adding signed numbers
- 5.−8 + 3 =
- 6.6 + (−10) =
- 7.−7 + (−4) =
- 8.−5 + 5 =
Subtracting signed numbers
- 9.4 − 9 =
- 10.−3 − 6 =
- 11.5 − (−3) =
- 12.−2 − (−8) =
- 13.Which of these means the same as 7 − (−2)?
Multiplying signed numbers
- 14.−4 × 6 =
- 15.−7 × (−3) =
- 16.Which of these products is positive?
- 17.2 × (−3) × (−5) =
Dividing signed numbers
- 18.−24 ÷ 6 =
- 19.−36 ÷ (−4) =
- 20.−459 =
Mixed practice
- 21.−3 + 4 × (−2) =
- 22.At dawn the temperature is −8°F. By noon it has risen 15 degrees. What is the temperature at noon?
- 23.Your bank account is overdrawn by $30, so the balance shows as −$30. You deposit $50. What is the balance now?
- 24.On three plays in a row, a football team loses 4 yards each time. What is the total change in yards?
- 25.One day in the Bronx, the high was 12°F and the low was −7°F. How many degrees apart are they?
- 26.The low temperatures over four nights were −6°, −2°, 2°, and −10°. What was the mean (average) low?
Or check one topic at a time, with the button under it.
Where to go next
| Topic | Questions | Right | Deep Sea quiz and apps | Practice |
|---|---|---|---|---|
| 1. Below zero | 1–4 | of 4 | Quiz 20 | |
| 2. Adding signed numbers | 5–8 | of 4 | Quiz 21Math Path · Temperature Vat · Ballast | |
| 3. Subtracting signed numbers | 9–13 | of 5 | Quiz 21Math Path · Temperature Vat · Ballast | |
| 4. Multiplying signed numbers | 14–17 | of 4 | Quiz 22 | |
| 5. Dividing signed numbers | 18–20 | of 3 | Quiz 22 | |
| 6. Mixed practice | 21–26 | of 6 | Quiz 21 and Quiz 22 |
The Deep Sea quizzes and the three Mazarine apps are at thepeoplesshare.org/ged/math.
The key prints only when it is showing, and it starts on its own page. After you check a topic, each question you missed offers its own reasoning with the Why? button.
Answers, with the reasoning in brief
- 1.−5, −1, 0, 3. On the number line, a number further to the left is smaller. −5 is the furthest below zero, so it comes first, then −1, then 0, then 3.
- 2.6. Opposites sit the same distance from zero, one on each side. The opposite of −6 is 6, and the opposite of 6 is −6.
- 3.9. Absolute value is a number's distance from zero, and a distance is never negative. −9 is 9 steps from zero.
- 4.−12°F. Both are below zero, and −12 is further below. Twelve degrees below zero is colder than four degrees below.
- 5.−5. Start at −8 and go up 3: −7, −6, −5. You are still below zero, because you climbed only 3 of the 8.
- 6.−4. Start at 6 and go down 10. Six of those steps bring you to 0; the other four take you to −4.
- 7.−11. Both numbers are below zero, and adding a negative takes you further down: from −7, go down 4 more to −11.
- 8.0. −5 and 5 are opposites, and opposites add to zero. A pair like this is called a zero pair.
- 9.−5. Start at 4 and go down 9. Four steps bring you to 0; five more take you to −5. Written another way, 4 − 9 = 4 + (−9).
- 10.−9. Start at −3 and go down 6 more: −9. Subtracting a positive always takes you down.
- 11.8. Subtracting a negative is the same as adding a positive: 5 − (−3) = 5 + 3 = 8. Taking away a debt of 3 leaves you 3 better off.
- 12.6. Rewrite it first: −2 − (−8) = −2 + 8. Start at −2 and go up 8: two steps bring you to 0, and six more take you to 6.
- 13.(a) 7 + 2. Subtracting a negative is the same as adding its opposite, so −(−2) becomes +2. Both expressions equal 9.
- 14.−24. Multiply the sizes: 4 × 6 = 24. The signs differ (one negative, one positive), so the product is negative.
- 15.21. Multiply the sizes: 7 × 3 = 21. The signs match (both negative), so the product is positive.
- 16.(b) −3 × (−4) = 12. Matching signs give a positive product. Choices (a) and (c) each mix a negative with a positive, so each equals −12.
- 17.30. Multiply the sizes first: 2 × 3 × 5 = 30. Then count the negative signs: there are two. An even number of negatives makes the answer positive; an odd number makes it negative.
- 18.−4. 24 ÷ 6 = 4. The signs differ (negative divided by positive), so the answer is negative.
- 19.9. 36 ÷ 4 = 9. The signs match (negative divided by negative), so the answer is positive.
- 20.−5. The fraction bar means divide: 45 ÷ 9 = 5. Negative divided by positive is negative.
- 21.−11. Multiply before you add: 4 × (−2) = −8. Then −3 + (−8) = −11. Adding first gives 1 × (−2) = −2, which is wrong.
- 22.7°F. −8 + 15 = 7. The first 8 degrees of the rise bring the temperature up to zero; the other 7 take it above zero.
- 23.$20. −30 + 50 = 20. The first $30 of the deposit clears the overdraft; the other $20 is yours.
- 24.−12 yards, a loss of 12. Three losses of 4 yards: 3 × (−4) = −12.
- 25.19 degrees. 12 − (−7) = 12 + 7 = 19. From −7 up to 0 is 7 degrees, and from 0 up to 12 is 12 more.
- 26.−4°. Add the four lows: −6 + (−2) + 2 + (−10) = −16. The −2 and the 2 cancel, which makes the adding easier. Then divide by the number of nights: −16 ÷ 4 = −4.