Let's solve each expression step by step using the
order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
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1. $(5.9 - 5.3) \times 7.2 + (1.4)^2$
-
Step 1: Parentheses
- $5.9 - 5.3 = 0.6$
- $(1.4)^2 = 1.4 \times 1.4 = 1.96$
-
Step 2: Multiplication
- $0.6 \times 7.2 = 4.32$
-
Step 3: Addition
- $4.32 + 1.96 = 6.28$
✔ Answer: $6.28$
---
2. $((2.1)^2 + 5.2 - 7.2) \times 7.1$
-
Step 1: Exponent
- $(2.1)^2 = 4.41$
-
Step 2: Parentheses (left to right)
- $4.41 + 5.2 = 9.61$
- $9.61 - 7.2 = 2.41$
-
Step 3: Multiplication
- $2.41 \times 7.1 = ?$
Let’s compute:
- $2.41 \times 7.1 = 2.41 \times (7 + 0.1) = 2.41 \times 7 + 2.41 \times 0.1 = 16.87 + 0.241 = 17.111$
✔ Answer: $17.111$
---
3. $8.5 \times ((1.6)^2 + 2.4 - 2.1)$
-
Step 1: Exponent
- $(1.6)^2 = 2.56$
-
Step 2: Parentheses
- $2.56 + 2.4 = 4.96$
- $4.96 - 2.1 = 2.86$
-
Step 3: Multiplication
- $8.5 \times 2.86 = ?$
Compute:
- $8.5 \times 2.86 = 8.5 \times (2 + 0.8 + 0.06) = 17 + 6.8 + 0.51 = 24.31$
✔ Answer: $24.31$
---
4. $(7.9)^2 + 4.2 \times (6.5 - 5.7)$
-
Step 1: Exponent
- $(7.9)^2 = 62.41$
-
Step 2: Parentheses
- $6.5 - 5.7 = 0.8$
-
Step 3: Multiplication
- $4.2 \times 0.8 = 3.36$
-
Step 4: Addition
- $62.41 + 3.36 = 65.77$
✔ Answer: $65.77$
---
5. $(7.3)^2 + 9.1 + (8.7 - 6.1)$
-
Step 1: Exponent
- $(7.3)^2 = 53.29$
-
Step 2: Parentheses
- $8.7 - 6.1 = 2.6$
-
Step 3: Addition (left to right)
- $53.29 + 9.1 = 62.39$
- $62.39 + 2.6 = 64.99$
✔ Answer: $64.99$
---
6. $(3.2)^2 \times (1.6 - 1.4 + 8.3)$
-
Step 1: Exponent
- $(3.2)^2 = 10.24$
-
Step 2: Parentheses (left to right)
- $1.6 - 1.4 = 0.2$
- $0.2 + 8.3 = 8.5$
-
Step 3: Multiplication
- $10.24 \times 8.5 = ?$
Break it down:
- $10.24 \times 8 = 81.92$
- $10.24 \times 0.5 = 5.12$
- Total: $81.92 + 5.12 = 87.04$
✔ Answer: $87.04$
---
7. $(5.2 + 6.6 - 9.3)^2 \times 3.8$
-
Step 1: Parentheses
- $5.2 + 6.6 = 11.8$
- $11.8 - 9.3 = 2.5$
-
Step 2: Exponent
- $(2.5)^2 = 6.25$
-
Step 3: Multiplication
- $6.25 \times 3.8 = ?$
Calculate:
- $6.25 \times 3.8 = 6.25 \times (3 + 0.8) = 18.75 + 5.00 = 23.75$
✔ Answer: $23.75$
---
8. $3.8 \times (9.5 + (2.5)^2 - 2.4)$
-
Step 1: Exponent
- $(2.5)^2 = 6.25$
-
Step 2: Parentheses (left to right)
- $9.5 + 6.25 = 15.75$
- $15.75 - 2.4 = 13.35$
-
Step 3: Multiplication
- $3.8 \times 13.35 = ?$
Break it down:
- $3.8 \times 13.35 = 3.8 \times (13 + 0.35) = 3.8 \times 13 = 49.4$, and $3.8 \times 0.35 = 1.33$
- Total: $49.4 + 1.33 = 50.73$
✔ Answer: $50.73$
---
✔ Final Answers:
1. $6.28$
2. $17.111$
3. $24.31$
4. $65.77$
5. $64.99$
6. $87.04$
7. $23.75$
8. $50.73$
Let me know if you'd like these rounded or formatted differently!
Parent Tip: Review the logic above to help your child master the concept of order of operations with decimals worksheet.
