Here are the step-by-step solutions for each problem on the worksheet. Remember to follow the order of operations: first solve anything inside parentheses `( )`, then do multiplication `×` and division `÷` from left to right, and finally do addition `+` and subtraction `-`.
Left Column:
1.
(1.2 + 0.4) × (3.2 ÷ 0.4)
* First, solve inside the parentheses: $1.2 + 0.4 = 1.6$ and $3.2 \div 0.4 = 8$.
* Now multiply the results: $1.6 \times 8 = 12.8$.
2.
(2.6 – (0.1 – 1)) × 1.6
* Start with the innermost parentheses: $0.1 - 1 = -0.9$.
* Now the expression is $(2.6 - (-0.9)) \times 1.6$. Subtracting a negative is like adding: $2.6 + 0.9 = 3.5$.
* Finally, multiply: $3.5 \times 1.6 = 5.6$.
3.
(1.3 – 0.7) × (4.5 ÷ 1.8)
* Solve the first parentheses: $1.3 - 0.7 = 0.6$.
* Solve the second parentheses: $4.5 \div 1.8 = 2.5$.
* Multiply the results: $0.6 \times 2.5 = 1.5$.
4.
((3.1 + 3.2) ÷ 3) × 3
* Solve the inner parentheses first: $3.1 + 3.2 = 6.3$.
* Now divide by 3: $6.3 \div 3 = 2.1$.
* Finally, multiply by 3: $2.1 \times 3 = 6.3$.
5.
1.5 × (0.3 + 0.5 – 0.2)
* Solve inside the parentheses from left to right: $0.3 + 0.5 = 0.8$, then $0.8 - 0.2 = 0.6$.
* Multiply: $1.5 \times 0.6 = 0.9$.
6.
(1.1 + 0.9) ÷ 4 + 2.7
* Solve the parentheses: $1.1 + 0.9 = 2.0$.
* Divide by 4: $2.0 \div 4 = 0.5$.
* Add 2.7: $0.5 + 2.7 = 3.2$.
Right Column:
7.
1.1 × (0.2 + 0.5 + 3.3)
* Solve inside the parentheses: $0.2 + 0.5 = 0.7$, then $0.7 + 3.3 = 4.0$.
* Multiply: $1.1 \times 4.0 = 4.4$.
8.
(2.4 ÷ 1.2 + 6.8) ÷ 2.2
* Inside the parentheses, do division first: $2.4 \div 1.2 = 2$.
* Then add: $2 + 6.8 = 8.8$.
* Finally, divide by 2.2: $8.8 \div 2.2 = 4$.
9.
0.6 × (4 – (1.3 + 0.2))
* Start with the innermost parentheses: $1.3 + 0.2 = 1.5$.
* Subtract that from 4: $4 - 1.5 = 2.5$.
* Multiply: $0.6 \times 2.5 = 1.5$.
10.
1.2 × (3 ÷ 2) – 1.3
* Solve the parentheses: $3 \div 2 = 1.5$.
* Multiply: $1.2 \times 1.5 = 1.8$.
* Subtract: $1.8 - 1.3 = 0.5$.
11.
(1.8 + 7) ÷ (1.7 – 0.1)
* Solve the first parentheses: $1.8 + 7 = 8.8$.
* Solve the second parentheses: $1.7 - 0.1 = 1.6$.
* Divide: $8.8 \div 1.6 = 5.5$.
12.
(1.5 ÷ 0.5) × (1.2 + 0.8)
* Solve the first parentheses: $1.5 \div 0.5 = 3$.
* Solve the second parentheses: $1.2 + 0.8 = 2$.
* Multiply: $3 \times 2 = 6$.
Final Answer:
(1.2 + 0.4) × (3.2 ÷ 0.4) =
12.8
(2.6 – (0.1 – 1)) × 1.6 =
5.6
(1.3 – 0.7) × (4.5 ÷ 1.8) =
1.5
((3.1 + 3.2) ÷ 3) × 3 =
6.3
1.5 × (0.3 + 0.5 – 0.2) =
0.9
(1.1 + 0.9) ÷ 4 + 2.7 =
3.2
1.1 × (0.2 + 0.5 + 3.3) =
4.4
(2.4 ÷ 1.2 + 6.8) ÷ 2.2 =
4
0.6 × (4 – (1.3 + 0.2)) =
1.5
1.2 × (3 ÷ 2) – 1.3 =
0.5
(1.8 + 7) ÷ (1.7 – 0.1) =
5.5
(1.5 ÷ 0.5) × (1.2 + 0.8) =
6
Parent Tip: Review the logic above to help your child master the concept of mixed operations with decimals worksheet.
