Let’s solve each expression step by step, following the
order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
---
1) (1.05 + 2.2)²
→ First, add inside parentheses:
1.05 + 2.2 =
3.25
→ Then square it:
3.25² = 3.25 × 3.25
Let’s compute:
3.25 × 3.25
= (3 + 0.25)² = 9 + 2×3×0.25 + 0.0625 = 9 + 1.5 + 0.0625 =
10.5625
✔ Answer: 10.5625
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2) 3.504 − (3.8 − 2.041)
→ Inside parentheses:
3.8 − 2.041 =
1.759
→ Subtract from 3.504:
3.504 − 1.759 =
1.745
✔ Answer: 1.745
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3) 2.4 − (2.5 − 2.2)
→ Inside parentheses:
2.5 − 2.2 =
0.3
→ Subtract:
2.4 − 0.3 =
2.1
✔ Answer: 2.1
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4) (3.2 + 2.9) ÷ 1.9
→ Add inside parentheses:
3.2 + 2.9 =
6.1
→ Divide by 1.9:
6.1 ÷ 1.9
Let’s compute:
6.1 ÷ 1.9 = 61 ÷ 19 ≈
3.2105...
But let's do exact decimal division:
1.9 × 3.2 = 6.08 → 6.1 − 6.08 = 0.02
So 3.2 + (0.02 / 1.9) ≈ 3.2 + 0.0105 ≈
3.2105
Rounded to reasonable decimal places (since inputs have 1 or 2 decimals), we can say
3.21
But better to keep precision — 6.1 ÷ 1.9 =
61/19 = 3.210526...
✔ Answer: 3.2105 (or approximately 3.21)
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5) (4 − 2.1) × 3.9
→ Inside parentheses:
4 − 2.1 =
1.9
→ Multiply:
1.9 × 3.9
Compute:
1.9 × 3.9 = (2 − 0.1)(4 − 0.1) = 8 − 0.2 − 0.4 + 0.01 = 7.41? Wait — better direct:
1.9 × 3.9 = 1.9 × (4 − 0.1) = 7.6 − 0.19 =
7.41
✔ Answer: 7.41
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6) 3.9 + 2.8 ÷ 4
→ Division first:
2.8 ÷ 4 =
0.7
→ Add:
3.9 + 0.7 =
4.6
✔ Answer: 4.6
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7) 1.6 + 1.8 + (3.8 + 1.2)
→ Inside parentheses:
3.8 + 1.2 =
5.0
→ Now add all:
1.6 + 1.8 + 5.0 = (1.6 + 1.8) = 3.4 → 3.4 + 5.0 =
8.4
✔ Answer: 8.4
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8) 2.4 + 3.2 + 1.3³
→ First, exponent:
1.3³ = 1.3 × 1.3 × 1.3
1.3 × 1.3 = 1.69
1.69 × 1.3 = ?
1.69 × 1 = 1.69
1.69 × 0.3 = 0.507
Total = 1.69 + 0.507 =
2.197
→ Now add:
2.4 + 3.2 + 2.197 = (2.4 + 3.2) = 5.6 → 5.6 + 2.197 =
7.797
✔ Answer: 7.797
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9) (2³ + 3.7) × 1.2
→ Exponent first:
2³ = 8
→ Inside parentheses:
8 + 3.7 =
11.7
→ Multiply by 1.2:
11.7 × 1.2
Compute:
11.7 × 1 = 11.7
11.7 × 0.2 = 2.34
Total = 11.7 + 2.34 =
14.04
✔ Answer: 14.04
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10) (3.2 − (2.8 − 2)) ÷ 3.9
→ Innermost parentheses:
2.8 − 2 =
0.8
→ Next:
3.2 − 0.8 =
2.4
→ Divide by 3.9:
2.4 ÷ 3.9 = 24 ÷ 39 = 8 ÷ 13 ≈
0.61538...
✔ Answer: 0.6154 (rounded to 4 decimals)
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11) 2.9 × (2 + 3.7) / (2.7 − 2.1)
→ Numerator: 2 + 3.7 =
5.7
→ Denominator: 2.7 − 2.1 =
0.6
→ So: 2.9 × (5.7 ÷ 0.6)
First, 5.7 ÷ 0.6 = 57 ÷ 6 =
9.5
Then: 2.9 × 9.5
Compute:
2.9 × 9.5 = 2.9 × (10 − 0.5) = 29 − 1.45 =
27.55
✔ Answer: 27.55
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12) 2.71 / (3.5 − 3.1 + 3 − 2.4)
→ Simplify denominator:
3.5 − 3.1 = 0.4
0.4 + 3 = 3.4
3.4 − 2.4 =
1.0
→ So: 2.71 ÷ 1.0 =
2.71
✔ Answer: 2.71
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##
✔ Final Answers:
1)
10.5625
2)
1.745
3)
2.1
4)
3.2105 (or 3.21)
5)
7.41
6)
4.6
7)
8.4
8)
7.797
9)
14.04
10)
0.6154
11)
27.55
12)
2.71
Let me know if you’d like them rounded to specific decimal places!
Parent Tip: Review the logic above to help your child master the concept of decimal mixed operations worksheet.
