Ordering Integers

Show your work for each problem.

1.
Which list shows the integers in ascending order (least to greatest)?
1. a) $7, 3, 0, -2, -5$
2. b) $-5, -2, 0, 3, 7$
3. c) $0, -2, 3, -5, 7$
4. d) $-2, -5, 0, 3, 7$
Answer: $-5, -2, 0, 3, 7$
$-5, -2, 0, 3, 7$ is correct. Starting from $-5$ (the smallest), we go through $-2$ , then $0$ , then $3$ , and finally $7$ (the largest).
2.
What does "descending order" mean?
1. a)From least to greatest
2. b)From greatest to least
3. c)Random order
4. d)From zero outward
Answer: From greatest to least
Descending order means arranging from greatest to least. Think of "descending" like going DOWN - starting with the largest value.
3.
What is the smallest integer in this set? $\{3, -8, 5, -2, 0\}$
Answer: -8
$-8$ is the smallest because it is the furthest left on the number line. Remember: the further a negative number is from zero, the smaller it is!
4.
What is the largest integer in this set? $\{-4, -9, -1, -6\}$
Answer: -1
$-1$ is the largest because it is closest to zero. On the number line, $-1$ is to the right of $-4$ , $-6$ , and $-9$ .
5.
Where does zero belong when ordering integers in ascending order?
1. a)It can go anywhere
2. b)At the very beginning
3. c)At the very end
4. d)After all negatives, before all positives
Answer: After all negatives, before all positives
In ascending order, zero comes after all negative numbers and before all positive numbers. Zero is neither positive nor negative - it's the boundary!
6.
Order these integers from least to greatest: $2$ , $-7$ , $4$ , $-3$ , $0$
Answer: -7, -3, 0, 2, 4
1. What is the smallest (most negative) integer? -7
2. What is the next smallest integer? -3
3. What comes after the negative numbers? 0
4. Which integer comes fourth? 2
7.
Order these integers from greatest to least: $-5$ , $1$ , $-2$ , $6$ , $-9$
Answer: 6, 1, -2, -5, -9
1. What is the largest (most positive) integer? 6
2. What is the next largest integer? 1
3. Which integer comes third? -2
8.
Order these temperatures from coldest to warmest: $3°C$ , $-6°C$ , $-1°C$ , $8°C$ , $-4°C$ . Which temperature comes third? Type only the number.
Answer: -1
From coldest to warmest: $-6°C, -4°C, -1°C, 3°C, 8°C$ . The most negative temperature is the coldest! The third one is $-1°C$ .
9.
Golf scores: Ali $-3$ , Ben $+2$ , Cara $-5$ , Dan $0$ . Who won (lowest score)?
1. a)Ali ( $-3$ )
2. b)Ben ( $+2$ )
3. c)Cara ( $-5$ )
4. d)Dan ( $0$ )
Answer: Cara ( $-5$ )
Cara won with $-5$ because it's the smallest (most negative) score. In ascending order: $-5, -3, 0, +2$ .
10.
Which list shows these integers from greatest to least: $-12$ , $-3$ , $-8$ , $-1$ , $-15$ ?
1. a) $-3, -1, -8, -12, -15$
2. b) $-1, -3, -8, -12, -15$
3. c) $-15, -12, -8, -3, -1$
4. d) $-1, -3, -12, -8, -15$
Answer: $-1, -3, -8, -12, -15$
From greatest to least: $-1, -3, -8, -12, -15$ . Remember: $-1$ is closest to zero, so it's the greatest negative number here. The list $-15, -12, -8, -3, -1$ is the reverse: least to greatest.
11.
Five elevations are recorded: Sea level ( $0$ m), Mountain peak ( $850$ m), Cave ( $-45$ m), Valley ( $-120$ m), Hill ( $200$ m). Order from lowest to highest.
Answer: -120, -45, 0, 200, 850
1. Which location is the lowest (most negative)? -120
2. What is the next lowest elevation? -45
3. What elevation represents sea level? 0
4. Which elevation comes fourth? 200
12.
Order these integers from least to greatest: $-14$ , $7$ , $-7$ , $0$ , $14$ , $-21$ , $21$
Answer: -21, -14, -7, 0, 7, 14, 21
1. What is the smallest (most negative) integer? -21
2. Which integer comes second? -14
3. What comes next after all negatives? 0
4. Which integer comes right after zero? 7
13.
Bank account balances (in dollars): Carla $-85$ , Diana $120$ , Erik $-30$ , Fiona $-150$ , George $45$ . Order them from poorest (most debt) to richest. Which balance comes second? Type only the number.
Answer: -85
From poorest to richest: Fiona ( $-150$ dollars), Carla ( $-85$ dollars), Erik ( $-30$ dollars), George ( $45$ dollars), Diana ( $120$ dollars). Carla's $-85$ dollars comes second. Negative balances mean debt!
14.
Which statement about ordering integers is FALSE?
1. a) $-5$ is greater than $-2$ because 5 is greater than 2
2. b)On a number line, numbers increase from left to right
3. c)Of two negative numbers, the smaller one is further from zero
4. d)Zero comes between negative and positive numbers
Answer: $-5$ is greater than $-2$ because 5 is greater than 2
The FALSE statement is that $-5 > -2$ . Actually, $-2 > -5$ because $-2$ is closer to zero. With negative numbers, the one closer to zero is greater!
15.
Weekly stock price changes: Mon $+3$ , Tue $-8$ , Wed $+5$ , Thu $-2$ , Fri $-6$ . Order the days from worst to best performance.
Answer: -8, -6, -2, +3, +5
1. What was the worst day (biggest loss)? -8
2. What was the second worst day? -6
3. What was the third worst day? -2
4. Which change comes fourth? +3
16.
Order from greatest to least: $-25$ , $-100$ , $50$ , $-5$ , $0$ , $25$ , $-50$ . Which integer comes fourth in your list?
Answer: -5
Descending order: $50, 25, 0, -5, -25, -50, -100$ . Notice: $50$ is the greatest, then $25$ , then $0$ , then negative numbers in order of how close they are to zero. The fourth integer is $-5$ , the negative number closest to zero.