Integer comparison worksheet for identifying smaller and larger numbers in given pairs.

Problem Analysis:

The task involves comparing pairs of integers to determine which number is smaller or larger in each pair. This requires understanding the concept of integers, including positive and negative numbers, and their relative magnitudes.

#### Key Concepts:
1. Positive Integers: Numbers greater than zero (e.g., 12, 25).
2. Negative Integers: Numbers less than zero (e.g., -45, -36).
3. Comparison Rules:
- Among negative integers, the number with the larger absolute value is actually smaller.
- Among positive integers, the number with the larger absolute value is larger.
- Any positive integer is always larger than any negative integer.

Solution:

#### Part 1: Which number is smaller in each of the following pairs?

1. (i) -45, -36
- Both numbers are negative.
- The absolute values are 45 and 36.
- Since 45 > 36, -45 is smaller than -36.
- Answer: -45

2. (ii) 12, -25
- One number is positive (12), and the other is negative (-25).
- Any positive number is larger than any negative number.
- Therefore, -25 is smaller.
- Answer: -25

3. (iii) -96, -88
- Both numbers are negative.
- The absolute values are 96 and 88.
- Since 96 > 88, -96 is smaller than -88.
- Answer: -96

4. (iv) -17, -25
- Both numbers are negative.
- The absolute values are 17 and 25.
- Since 25 > 17, -25 is smaller than -17.
- Answer: -25

5. (v) -109, -125
- Both numbers are negative.
- The absolute values are 109 and 125.
- Since 125 > 109, -125 is smaller than -109.
- Answer: -125

6. (vi) -48, -24
- Both numbers are negative.
- The absolute values are 48 and 24.
- Since 48 > 24, -48 is smaller than -24.
- Answer: -48

7. (vii) -15, 0
- One number is negative (-15), and the other is zero.
- Any negative number is smaller than zero.
- Answer: -15

8. (viii) -46, 125
- One number is negative (-46), and the other is positive (125).
- Any negative number is smaller than any positive number.
- Answer: -46

9. (xi) -23, -24
- Both numbers are negative.
- The absolute values are 23 and 24.
- Since 24 > 23, -24 is smaller than -23.
- Answer: -24

#### Part 2: Which number is larger in each of the following pairs?

1. (i) -1, 0
- One number is negative (-1), and the other is zero.
- Any negative number is smaller than zero.
- Therefore, 0 is larger.
- Answer: 0

2. (ii) -7, -8
- Both numbers are negative.
- The absolute values are 7 and 8.
- Since 7 < 8, -7 is larger than -8.
- Answer: -7

3. (iii) -36, 25
- One number is negative (-36), and the other is positive (25).
- Any positive number is larger than any negative number.
- Answer: 25

4. (iv) -17, -25
- Both numbers are negative.
- The absolute values are 17 and 25.
- Since 17 < 25, -17 is larger than -25.
- Answer: -17

5. (v) 17, -19
- One number is positive (17), and the other is negative (-19).
- Any positive number is larger than any negative number.
- Answer: 17

6. (vi) -49, 48
- One number is negative (-49), and the other is positive (48).
- Any positive number is larger than any negative number.
- Answer: 48

7. (vii) -36, -55
- Both numbers are negative.
- The absolute values are 36 and 55.
- Since 36 < 55, -36 is larger than -55.
- Answer: -36

8. (viii) 10, -9
- One number is positive (10), and the other is negative (-9).
- Any positive number is larger than any negative number.
- Answer: 10

9. (xi) -317, -603
- Both numbers are negative.
- The absolute values are 317 and 603.
- Since 317 < 603, -317 is larger than -603.
- Answer: -317

Final Answers:

#### Part 1: Smaller Numbers
(i) -45
(ii) -25
(iii) -96
(iv) -25
(v) -125
(vi) -48
(vii) -15
(viii) -46
(xi) -24

#### Part 2: Larger Numbers
(i) 0
(ii) -7
(iii) 25
(iv) -17
(v) 17
(vi) 48
(vii) -36
(viii) 10
(xi) -317

Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Part 1:} & \text{(i) -45, (ii) -25, (iii) -96, (iv) -25, (v) -125, (vi) -48, (vii) -15, (viii) -46, (xi) -24} \\
\text{Part 2:} & \text{(i) 0, (ii) -7, (iii) 25, (iv) -17, (v) 17, (vi) 48, (vii) -36, (viii) 10, (xi) -317}
\end{array}
}
\]