Comparing and Ordering Integers Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Ordering Integers" that contains several problems involving ordering integers. Let's go through each section step by step and solve the problems.

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Problem 1: Order each set of integers from least to greatest

#### a) 36, 18, 72, 25
- List the numbers: 36, 18, 72, 25
- Order them from smallest to largest:
- 18 < 25 < 36 < 72
- ✔ Answer: 18, 25, 36, 72

#### b) -42, -15, -90, -62, -83
- These are all negative numbers. Remember: The greater the absolute value, the smaller the number.
- Absolute values: 42, 15, 90, 62, 83 → so order from smallest to largest (most negative to least negative):
- -90 < -83 < -62 < -42 < -15
- ✔ Answer: -90, -83, -62, -42, -15

#### c) -17, -19, -82, -38, -39
- Compare absolute values: 17, 19, 82, 38, 39
- So order from most negative to least negative:
- -82 < -39 < -38 < -19 < -17
- ✔ Answer: -82, -39, -38, -19, -17

#### d) -31, -29, -32, -30, -37
- Absolute values: 31, 29, 32, 30, 37 → order from largest to smallest (to get increasing order of negatives):
- -37 < -32 < -31 < -30 < -29
- ✔ Answer: -37, -32, -31, -30, -29

#### e) -11, -13, -15, -14, -12
- Absolute values: 11, 13, 15, 14, 12 → order from largest to smallest:
- -15 < -14 < -13 < -12 < -11
- ✔ Answer: -15, -14, -13, -12, -11

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Problem 2: Order each set of integers from greatest to least

#### a) -48, -44, -53, -30, -26
- All negative. Greatest means closest to zero.
- Order from least negative (greatest) to most negative (least):
- -26 > -30 > -44 > -48 > -53
- ✔ Answer: -26, -30, -44, -48, -53

#### b) -20, -24, -18, -23, -28
- From greatest to least:
- -18 > -20 > -23 > -24 > -28
- ✔ Answer: -18, -20, -23, -24, -28

#### c) 8, 40, 25, 18, 32
- Positive numbers only. Order from greatest to least:
- 40 > 32 > 25 > 18 > 8
- ✔ Answer: 40, 32, 25, 18, 8

#### d) -6, 22, 15, 10, 32
- Mix of negative and positive. Positive numbers are greater than negative.
- First list positives in descending order: 32, 22, 15, 10
- Then negative: -6
- So: 32 > 22 > 15 > 10 > -6
- ✔ Answer: 32, 22, 15, 10, -6

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Problem 3: Use the table to answer the average temperature for cities in the month of January. Order the cities from coldest to warmest temperatures.

We are given a table:

| City | Temperature |
|----------------|-------------|
| San Diego | 57 |
| Miami | 65 |
| New Orleans | 47 |
| Minneapolis | -7 |
| Chicago | -12 |
| Boston | 24 |

Now, order the cities from coldest to warmest, i.e., lowest temperature to highest.

Let’s list temperatures in ascending order:
- -12 (Chicago)
- -7 (Minneapolis)
- 24 (Boston)
- 47 (New Orleans)
- 57 (San Diego)
- 65 (Miami)

So the order from coldest to warmest is:
1. Chicago (-12)
2. Minneapolis (-7)
3. Boston (24)
4. New Orleans (47)
5. San Diego (57)
6. Miami (65)

✔ Final Answer:
Chicago, Minneapolis, Boston, New Orleans, San Diego, Miami

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✔ Summary of Answers:

#### 1. Order from least to greatest
a) 18, 25, 36, 72
b) -90, -83, -62, -42, -15
c) -82, -39, -38, -19, -17
d) -37, -32, -31, -30, -29
e) -15, -14, -13, -12, -11

#### 2. Order from greatest to least
a) -26, -30, -44, -48, -53
b) -18, -20, -23, -24, -28
c) 40, 32, 25, 18, 8
d) 32, 22, 15, 10, -6

#### 3. Order cities from coldest to warmest
Chicago, Minneapolis, Boston, New Orleans, San Diego, Miami

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