PEMDAS Problems - Free Printable
Educational worksheet: PEMDAS Problems. Download and print for classroom or home learning activities.
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Step-by-step solution for: PEMDAS Problems
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Show Answer Key & Explanations
Step-by-step solution for: PEMDAS Problems
Of course! Let’s solve the problems on this “Using Parentheses Sheet 5:2” step by step.
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## Part 1: Work out these sample calculations
We’ll solve each expression using the correct order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
---
→ First, parentheses: 4 + 7 = 11
→ Then multiply: 11 × 3 = 33
✔ Answer: 33
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→ Parentheses: 8 – 5 = 3
→ Multiply: 11 × 3 = 33
✔ Answer: 33
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→ Parentheses: 60 ÷ 10 = 6
→ Subtract: 6 – 8 = -2
✔ Answer: -2
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→ Parentheses: 9 × 4 = 36
→ Add: 15 + 36 = 51
✔ Answer: 51
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→ Parentheses: 17 – 11 = 6
→ Multiply: 9 × 6 = 54
✔ Answer: 54
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→ Parentheses: 11 – 4 = 7
→ Add: 41 + 7 = 48
✔ Answer: 48
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→ Parentheses: 4 + 4 = 8
→ Subtract: 9 – 8 = 1
✔ Answer: 1
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→ Parentheses: 10 – 4 = 6
→ Multiply: 10 × 6 = 60
✔ Answer: 60
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→ Parentheses: 20 – 4 = 16
→ Multiply: 6 × 16 = 96
✔ Answer: 96
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→ Parentheses: 9 + 4 = 13
→ Subtract: 13 – 4 = 9
✔ Answer: 9
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→ Parentheses: 41 – 10 = 31
→ Subtract: 50 – 31 = 19
✔ Answer: 19
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→ Parentheses: 8 + 9 = 17
→ Subtract: 27 – 17 = 10
✔ Answer: 10
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→ First parentheses: 8 + 11 = 19
→ Second parentheses: 19 + 4 = 23
→ Subtract: 19 – 23 = -4
✔ Answer: -4
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→ First: 30 + 11 = 41
→ Second: 19 + 32 = 51
→ Subtract: 41 – 51 = -10
✔ Answer: -10
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→ First: 10 + 11 = 21
→ Second: 5 + 2 = 7
→ Subtract: 21 – 7 = 14
✔ Answer: 14
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→ Parentheses: 4 + 12 = 16
→ Multiply: 16 × 3 = 48
→ Add: 9 + 48 = 57
✔ Answer: 57
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## Part 2: Calculator Challenges
These are trickier because they involve multiple operations. We must follow order of operations carefully — especially multiplication before addition unless parentheses dictate otherwise.
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→ Left to right (same precedence):
87.5 – 12 = 75.5
75.5 + 91 = 166.5
✔ Answer: 166.5
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→ Parentheses: 17.8 + 27.4 = 45.2
→ Add: 45.2 + 19 = 64.2
✔ Answer: 64.2
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→ Left to right:
14000 – 137.98 = 13862.02
13862.02 + 121 = 13983.02
✔ Answer: 13983.02
---
→ Left to right:
3230.2 + 211 = 3441.2
3441.2 – 190.9 = 3250.3
✔ Answer: 3250.3
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→ Left to right:
3138 + 1161.75 = 4299.75
4299.75 + 41 = 4340.75
✔ Answer: 4340.75
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→ Left to right:
1350 – 1012.4 = 337.6
337.6 + 48 = 385.6
✔ Answer: 385.6
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→ Left to right:
370 – 35 = 335
335 + 105.4 = 440.4
✔ Answer: 440.4
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→ Left to right:
1300 + 117.5 = 1417.5
1417.5 + 9.7 = 1427.2
✔ Answer: 1427.2
---
## Part 3: Put these expressions in order from smallest to largest value
We are given three expressions:
> A) 1.75 – (8.1 ÷ 4)
> B) (0.21 x 11) – (1.5 ÷ 3)
> C) 8 – (5.6 ÷ 4)
Let’s compute each one.
---
→ Inside parentheses: 8.1 ÷ 4 = 2.025
→ Subtract: 1.75 – 2.025 = -0.275
✔ Value A = -0.275
---
→ First: 0.21 × 11 = 2.31
→ Second: 1.5 ÷ 3 = 0.5
→ Subtract: 2.31 – 0.5 = 1.81
✔ Value B = 1.81
---
→ Inside parentheses: 5.6 ÷ 4 = 1.4
→ Subtract: 8 – 1.4 = 6.6
✔ Value C = 6.6
---
A = -0.275 → B = 1.81 → C = 6.6
✔ Smallest to Largest: A, B, C
---
## ✔ Final Answers Summary:
1. 33
2. 33
3. -2
4. 51
5. 54
6. 48
7. 1
8. 60
9. 96
10. 9
11. 19
12. 10
13. -4
14. -10
15. 14
16. 57
17. 166.5
18. 64.2
19. 13983.02
20. 3250.3
21. 4340.75
22. 385.6
23. 440.4
24. 1427.2
Smallest: A → B → C (Largest)
---
Let me know if you’d like a printable version or explanations for any specific problem!
---
## Part 1: Work out these sample calculations
We’ll solve each expression using the correct order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
---
1) (4 + 7) x 3 =
→ First, parentheses: 4 + 7 = 11
→ Then multiply: 11 × 3 = 33
✔ Answer: 33
---
2) 11 x (8 – 5) =
→ Parentheses: 8 – 5 = 3
→ Multiply: 11 × 3 = 33
✔ Answer: 33
---
3) (60 ÷ 10) – 8 =
→ Parentheses: 60 ÷ 10 = 6
→ Subtract: 6 – 8 = -2
✔ Answer: -2
---
4) 15 + (9 × 4) =
→ Parentheses: 9 × 4 = 36
→ Add: 15 + 36 = 51
✔ Answer: 51
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5) 9 x (17 – 11) =
→ Parentheses: 17 – 11 = 6
→ Multiply: 9 × 6 = 54
✔ Answer: 54
---
6) 41 + (11 – 4) =
→ Parentheses: 11 – 4 = 7
→ Add: 41 + 7 = 48
✔ Answer: 48
---
7) 9 – (4 + 4) =
→ Parentheses: 4 + 4 = 8
→ Subtract: 9 – 8 = 1
✔ Answer: 1
---
8) 10 x (10 – 4) =
→ Parentheses: 10 – 4 = 6
→ Multiply: 10 × 6 = 60
✔ Answer: 60
---
9) 6 x (20 – 4) =
→ Parentheses: 20 – 4 = 16
→ Multiply: 6 × 16 = 96
✔ Answer: 96
---
10) (9 + 4) – 4 =
→ Parentheses: 9 + 4 = 13
→ Subtract: 13 – 4 = 9
✔ Answer: 9
---
11) 50 – (41 – 10) =
→ Parentheses: 41 – 10 = 31
→ Subtract: 50 – 31 = 19
✔ Answer: 19
---
12) 27 – (8 + 9) =
→ Parentheses: 8 + 9 = 17
→ Subtract: 27 – 17 = 10
✔ Answer: 10
---
13) (8 + 11) – (19 + 4) =
→ First parentheses: 8 + 11 = 19
→ Second parentheses: 19 + 4 = 23
→ Subtract: 19 – 23 = -4
✔ Answer: -4
---
14) (30 + 11) – (19 + 32) =
→ First: 30 + 11 = 41
→ Second: 19 + 32 = 51
→ Subtract: 41 – 51 = -10
✔ Answer: -10
---
15) (10 + 11) – (5 + 2) =
→ First: 10 + 11 = 21
→ Second: 5 + 2 = 7
→ Subtract: 21 – 7 = 14
✔ Answer: 14
---
16) 9 + (4 + 12) x 3 =
→ Parentheses: 4 + 12 = 16
→ Multiply: 16 × 3 = 48
→ Add: 9 + 48 = 57
✔ Answer: 57
---
## Part 2: Calculator Challenges
These are trickier because they involve multiple operations. We must follow order of operations carefully — especially multiplication before addition unless parentheses dictate otherwise.
---
17) 87.5 – 12 + 91 =
→ Left to right (same precedence):
87.5 – 12 = 75.5
75.5 + 91 = 166.5
✔ Answer: 166.5
---
18) (17.8 + 27.4) + 19 =
→ Parentheses: 17.8 + 27.4 = 45.2
→ Add: 45.2 + 19 = 64.2
✔ Answer: 64.2
---
19) 14000 – 137.98 + 121 =
→ Left to right:
14000 – 137.98 = 13862.02
13862.02 + 121 = 13983.02
✔ Answer: 13983.02
---
20) 3230.2 + 211 – 190.9 =
→ Left to right:
3230.2 + 211 = 3441.2
3441.2 – 190.9 = 3250.3
✔ Answer: 3250.3
---
21) 3138 + 1161.75 + 41 =
→ Left to right:
3138 + 1161.75 = 4299.75
4299.75 + 41 = 4340.75
✔ Answer: 4340.75
---
22) 1350 – 1012.4 + 48 =
→ Left to right:
1350 – 1012.4 = 337.6
337.6 + 48 = 385.6
✔ Answer: 385.6
---
23) 370 – 35 + 105.4 =
→ Left to right:
370 – 35 = 335
335 + 105.4 = 440.4
✔ Answer: 440.4
---
24) 1300 + 117.5 + 9.7 =
→ Left to right:
1300 + 117.5 = 1417.5
1417.5 + 9.7 = 1427.2
✔ Answer: 1427.2
---
## Part 3: Put these expressions in order from smallest to largest value
We are given three expressions:
> A) 1.75 – (8.1 ÷ 4)
> B) (0.21 x 11) – (1.5 ÷ 3)
> C) 8 – (5.6 ÷ 4)
Let’s compute each one.
---
Expression A: 1.75 – (8.1 ÷ 4)
→ Inside parentheses: 8.1 ÷ 4 = 2.025
→ Subtract: 1.75 – 2.025 = -0.275
✔ Value A = -0.275
---
Expression B: (0.21 × 11) – (1.5 ÷ 3)
→ First: 0.21 × 11 = 2.31
→ Second: 1.5 ÷ 3 = 0.5
→ Subtract: 2.31 – 0.5 = 1.81
✔ Value B = 1.81
---
Expression C: 8 – (5.6 ÷ 4)
→ Inside parentheses: 5.6 ÷ 4 = 1.4
→ Subtract: 8 – 1.4 = 6.6
✔ Value C = 6.6
---
Now, order from smallest to largest:
A = -0.275 → B = 1.81 → C = 6.6
✔ Smallest to Largest: A, B, C
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## ✔ Final Answers Summary:
Part 1: Sample Calculations
1. 33
2. 33
3. -2
4. 51
5. 54
6. 48
7. 1
8. 60
9. 96
10. 9
11. 19
12. 10
13. -4
14. -10
15. 14
16. 57
Part 2: Calculator Challenges
17. 166.5
18. 64.2
19. 13983.02
20. 3250.3
21. 4340.75
22. 385.6
23. 440.4
24. 1427.2
Part 3: Order Smallest to Largest
Smallest: A → B → C (Largest)
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Let me know if you’d like a printable version or explanations for any specific problem!
Parent Tip: Review the logic above to help your child master the concept of free printable math worksheets bedmas.
