Order of Operations (PEDMAS with division of integers) worksheet ... - Free Printable

Problem Analysis

The task involves solving a series of division problems involving positive and negative integers. The key rules for division of integers are as follows:

1. Same Signs: When dividing two integers with the same sign (both positive or both negative), the result is positive.
- \( (+a) \div (+b) = +\left(\frac{a}{b}\right) \)
- \( (-a) \div (-b) = +\left(\frac{a}{b}\right) \)

2. Different Signs: When dividing two integers with different signs (one positive and one negative), the result is negative.
- \( (+a) \div (-b) = -\left(\frac{a}{b}\right) \)
- \( (-a) \div (+b) = -\left(\frac{a}{b}\right) \)

We will solve each problem step by step using these rules.

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Solution to Each Problem

#### Problems 1–10

1. \( (-10) \div (+2) \)
- Different signs: Result is negative.
- \( \frac{-10}{2} = -5 \)
- Answer: \(-5\)

2. \( (-77) \div (+7) \)
- Different signs: Result is negative.
- \( \frac{-77}{7} = -11 \)
- Answer: \(-11\)

3. \( (-56) \div (+7) \)
- Different signs: Result is negative.
- \( \frac{-56}{7} = -8 \)
- Answer: \(-8\)

4. \( (-27) \div (-3) \)
- Same signs: Result is positive.
- \( \frac{-27}{-3} = 9 \)
- Answer: \(9\)

5. \( (+45) \div (+5) \)
- Same signs: Result is positive.
- \( \frac{45}{5} = 9 \)
- Answer: \(9\)

6. \( (-4) \div (+2) \)
- Different signs: Result is negative.
- \( \frac{-4}{2} = -2 \)
- Answer: \(-2\)

7. \( (+110) \div (-11) \)
- Different signs: Result is negative.
- \( \frac{110}{-11} = -10 \)
- Answer: \(-10\)

8. \( (+70) \div (+7) \)
- Same signs: Result is positive.
- \( \frac{70}{7} = 10 \)
- Answer: \(10\)

9. \( (+50) \div (+10) \)
- Same signs: Result is positive.
- \( \frac{50}{10} = 5 \)
- Answer: \(5\)

10. \( (-70) \div (+10) \)
- Different signs: Result is negative.
- \( \frac{-70}{10} = -7 \)
- Answer: \(-7\)

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#### Problems 11–20

11. \( (-20) \div (-2) \)
- Same signs: Result is positive.
- \( \frac{-20}{-2} = 10 \)
- Answer: \(10\)

12. \( (+72) \div (+9) \)
- Same signs: Result is positive.
- \( \frac{72}{9} = 8 \)
- Answer: \(8\)

13. \( (+30) \div (+6) \)
- Same signs: Result is positive.
- \( \frac{30}{6} = 5 \)
- Answer: \(5\)

14. \( (-42) \div (-7) \)
- Same signs: Result is positive.
- \( \frac{-42}{-7} = 6 \)
- Answer: \(6\)

15. \( (+35) \div (+7) \)
- Same signs: Result is positive.
- \( \frac{35}{7} = 5 \)
- Answer: \(5\)

16. \( (-48) \div (+6) \)
- Different signs: Result is negative.
- \( \frac{-48}{6} = -8 \)
- Answer: \(-8\)

17. \( (-36) \div (+6) \)
- Different signs: Result is negative.
- \( \frac{-36}{6} = -6 \)
- Answer: \(-6\)

18. \( (-18) \div (+6) \)
- Different signs: Result is negative.
- \( \frac{-18}{6} = -3 \)
- Answer: \(-3\)

19. \( (+72) \div (+8) \)
- Same signs: Result is positive.
- \( \frac{72}{8} = 9 \)
- Answer: \(9\)

20. \( (-110) \div (-11) \)
- Same signs: Result is positive.
- \( \frac{-110}{-11} = 10 \)
- Answer: \(10\)

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#### Problems 21–30

21. \( (-10) \div (-5) \)
- Same signs: Result is positive.
- \( \frac{-10}{-5} = 2 \)
- Answer: \(2\)

22. \( (-44) \div (+11) \)
- Different signs: Result is negative.
- \( \frac{-44}{11} = -4 \)
- Answer: \(-4\)

23. \( (+77) \div (-7) \)
- Different signs: Result is negative.
- \( \frac{77}{-7} = -11 \)
- Answer: \(-11\)

24. \( (+21) \div (+7) \)
- Same signs: Result is positive.
- \( \frac{21}{7} = 3 \)
- Answer: \(3\)

25. \( (+27) \div (+3) \)
- Same signs: Result is positive.
- \( \frac{27}{3} = 9 \)
- Answer: \(9\)

26. \( (+18) \div (+3) \)
- Same signs: Result is positive.
- \( \frac{18}{3} = 6 \)
- Answer: \(6\)

27. \( (+30) \div (-5) \)
- Different signs: Result is negative.
- \( \frac{30}{-5} = -6 \)
- Answer: \(-6\)

28. \( (-36) \div (-4) \)
- Same signs: Result is positive.
- \( \frac{-36}{-4} = 9 \)
- Answer: \(9\)

29. \( (-21) \div (-7) \)
- Same signs: Result is positive.
- \( \frac{-21}{-7} = 3 \)
- Answer: \(3\)

30. \( (+24) \div (+6) \)
- Same signs: Result is positive.
- \( \frac{24}{6} = 4 \)
- Answer: \(4\)

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Final Answers

\[
\boxed{
\begin{array}{ll}
1. & -5 \\
2. & -11 \\
3. & -8 \\
4. & 9 \\
5. & 9 \\
6. & -2 \\
7. & -10 \\
8. & 10 \\
9. & 5 \\
10. & -7 \\
11. & 10 \\
12. & 8 \\
13. & 5 \\
14. & 6 \\
15. & 5 \\
16. & -8 \\
17. & -6 \\
18. & -3 \\
19. & 9 \\
20. & 10 \\
21. & 2 \\
22. & -4 \\
23. & -11 \\
24. & 3 \\
25. & 9 \\
26. & 6 \\
27. & -6 \\
28. & 9 \\
29. & 3 \\
30. & 4 \\
\end{array}
}
\]