Introduction to Negative Numbers

Show your work for each problem.

1.
Which number is negative?
1. a)12
2. b)-3
3. c)0
4. d)5
Answer: -3
is the only negative number because it has a minus sign. and are positive, and is neither.
2.
What is the opposite of ?
Answer: -7
The opposite of is . Both are 7 units from zero, but on opposite sides of the number line.
3.
Place these numbers in order from least to greatest: , , ,
Answer: -5, -2, 0, 3
1. Which number is furthest left on the number line (smallest)? -5
2. Which negative number comes next? -2
3. What comes after the negative numbers? 0
4. What is the largest number? 3
4.
Where are negative numbers located on a number line?
1. a)Above zero
2. b)To the right of zero
3. c)At zero
4. d)To the left of zero
Answer: To the left of zero
Negative numbers are located to the LEFT of zero on a number line. Positive numbers are to the right.
5.
A thermometer shows . How many degrees below zero is this?
Answer: 4
means 4 degrees below zero. The 4 tells us the distance from zero.
6.
Compare: Which is greater, or ?
Answer: -3
1. On a number line, which is closer to zero: or ? -3
2. Which number is further to the RIGHT on the number line? -3
3. So which number is GREATER? -3
7.
Which statement is TRUE?
1. a)
2. b)
3. c)
4. d)
Answer:
is TRUE because is closer to zero than . The others: , , .
8.
What is the opposite of ?
Answer: 12
The opposite of is . They are both 12 units from zero, but on opposite sides of the number line.
9.
A submarine is at meters. It rises 30 meters. What is its new depth?
Answer: -20
1. The submarine starts at meters. Rising means moving toward zero. We add 30. What is ? -20
10.
The temperature was in the morning. By afternoon, it rose 12 degrees. What is the afternoon temperature?
1. a)
2. b)
3. c)
4. d)
Answer:
. Starting at and adding 12: first add 7 to reach 0, then add the remaining 5 to reach .
11.
Your bank balance is euros. You deposit 40 euros. What is your new balance?
Answer: 25
1. You owe 15 euros (that is ). You add 40 euros. First, how much covers the debt? 15
2. After paying the 15 euro debt, how much of the 40 euros remains? 25
3. So what is your final balance? 25
12.
List all integers between and (not including and ).
Answer: -3, -2, -1, 0, 1
The integers between and (not including endpoints) are: , , , , . That is 5 integers.
13.
An elevator starts at floor (basement), goes up 7 floors, then down 4 floors. What floor is it on now?
Answer: 0
1. Start at floor . Go UP 7 floors. What floor are you on? (Calculate ) 4
2. Now from floor , go DOWN 4 floors. What floor are you on? 0
14.
Which list shows numbers in order from GREATEST to LEAST?
1. a)
2. b)
3. c)
4. d)
Answer:
is correct. It goes from greatest (5) to least (). Option A mixes the order incorrectly. Options C and D both show numbers from least to greatest.
15.
A diver is at meters. She needs to reach the surface ( meters). If she rises at 6 meters per minute, how many minutes will it take?
Answer: 3
1. How far does she need to travel to reach the surface? (Distance from to ) 18
2. She rises 6 meters each minute. How many minutes to travel 18 meters? 3
16.
At midnight, the temperature was . By 6 AM it dropped 5 degrees, and by noon it rose 11 degrees. What was the noon temperature?
1. a)
2. b)
3. c)
4. d)
Answer:
Midnight: . Dropped 5°: . Rose 11°: . The noon temperature was .
17.
A golfer scores (under par) in round 1, (over par) in round 2, and in round 3. What is the total score relative to par?
Answer: 0
1. Add the first two rounds: 1
2. Now add round 3: 0
18.
What integer is exactly halfway between and on a number line?
Answer: -2
To find the midpoint: add the two numbers and divide by 2. . The integer exactly halfway between and is .