four fractions,decimals, order of operations Math Worksheets, Math ... - Free Printable

Let's solve each problem 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). We'll handle fractions, decimals, and mixed operations carefully.

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Problem 1:

$$
\frac{1}{6} - \frac{1}{3} \times 5 + 4 \times 2.3 \div 2
$$

Step-by-step:

1. Multiplication and Division first (left to right):

- $\frac{1}{3} \times 5 = \frac{5}{3}$
- $4 \times 2.3 = 9.2$, then $9.2 \div 2 = 4.6$

2. Now substitute:
$$
\frac{1}{6} - \frac{5}{3} + 4.6
$$

3. Convert all to decimals or common denominator:

- $\frac{1}{6} \approx 0.1667$
- $\frac{5}{3} \approx 1.6667$

So:
$$
0.1667 - 1.6667 + 4.6 = (-1.5) + 4.6 = 3.1
$$

✔ Answer: 3.1

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Problem 2:

$$
5.7 - 2.7 \times 4 - 6 \times 2.1 \div 3
$$

Step-by-step:

1. Multiplication and division:
- $2.7 \times 4 = 10.8$
- $6 \times 2.1 = 12.6$, then $12.6 \div 3 = 4.2$

2. Substitute:
$$
5.7 - 10.8 - 4.2
$$

3. Left to right:
- $5.7 - 10.8 = -5.1$
- $-5.1 - 4.2 = -9.3$

✔ Answer: -9.3

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Problem 3:

$$
\frac{1}{2} - 9 \times \frac{1}{3} \div 3 + 2 \times 2.3
$$

Step-by-step:

1. Multiplication and division:
- $9 \times \frac{1}{3} = 3$, then $3 \div 3 = 1$
- $2 \times 2.3 = 4.6$

2. Now:
$$
\frac{1}{2} - 1 + 4.6 = 0.5 - 1 + 4.6 = -0.5 + 4.6 = 4.1
$$

✔ Answer: 4.1

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Problem 4:

$$
\frac{1}{3} - \frac{1}{5} - 5 \times 3.9
$$

Step-by-step:

1. Multiplication:
- $5 \times 3.9 = 19.5$

2. Fractions:
- $\frac{1}{3} \approx 0.333$, $\frac{1}{5} = 0.2$

So:
$$
0.333 - 0.2 - 19.5 = 0.133 - 19.5 = -19.367
$$

Or exact fraction:
- $\frac{1}{3} - \frac{1}{5} = \frac{5 - 3}{15} = \frac{2}{15}$

Then:
$$
\frac{2}{15} - 19.5 = \frac{2}{15} - \frac{39}{2} = \text{common denominator } 30
$$
$$
\frac{4}{30} - \frac{585}{30} = -\frac{581}{30} \approx -19.3667
$$

✔ Answer: -19.37 (rounded)

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Problem 5:

$$
3.3 - 4 \times \frac{1}{2} \div 2 - 4 \times 4.8
$$

Step-by-step:

1. Multiplication and division:
- $4 \times \frac{1}{2} = 2$, then $2 \div 2 = 1$
- $4 \times 4.8 = 19.2$

2. Now:
$$
3.3 - 1 - 19.2 = 2.3 - 19.2 = -16.9
$$

✔ Answer: -16.9

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Problem 6:

$$
\frac{3}{5} + \frac{1}{3} \times 5 + 8 \times \frac{1}{3} \div 4
$$

Step-by-step:

1. Multiplication and division:
- $\frac{1}{3} \times 5 = \frac{5}{3}$
- $8 \times \frac{1}{3} = \frac{8}{3}$, then $\frac{8}{3} \div 4 = \frac{8}{3} \times \frac{1}{4} = \frac{2}{3}$

2. Now:
$$
\frac{3}{5} + \frac{5}{3} + \frac{2}{3}
$$

3. Combine $\frac{5}{3} + \frac{2}{3} = \frac{7}{3}$

4. Add $\frac{3}{5} + \frac{7}{3}$ → common denominator = 15:
- $\frac{3}{5} = \frac{9}{15}$, $\frac{7}{3} = \frac{35}{15}$
- Total: $\frac{44}{15} \approx 2.933$

✔ Answer: $\frac{44}{15}$ or 2.933

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Problem 7:

$$
4.7 + 5.8 + 5 \times \frac{3}{5}
$$

Step-by-step:

1. $5 \times \frac{3}{5} = 3$

2. Now:
$$
4.7 + 5.8 + 3 = 10.5 + 3 = 13.5
$$

✔ Answer: 13.5

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Problem 8:

$$
\frac{1}{4} - 20 \times \frac{1}{4} \div 4 - 5 \times 3.7
$$

Step-by-step:

1. Multiplication and division:
- $20 \times \frac{1}{4} = 5$, then $5 \div 4 = 1.25$
- $5 \times 3.7 = 18.5$

2. Now:
$$
\frac{1}{4} - 1.25 - 18.5 = 0.25 - 1.25 - 18.5 = -1 - 18.5 = -19.5
$$

✔ Answer: -19.5

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Problem 9:

$$
2.7 - 6 \times 3 \div 2 + 3 \times \frac{1}{3}
$$

Step-by-step:

1. Multiplication and division:
- $6 \times 3 = 18$, $18 \div 2 = 9$
- $3 \times \frac{1}{3} = 1$

2. Now:
$$
2.7 - 9 + 1 = -6.3 + 1 = -5.3
$$

✔ Answer: -5.3

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Problem 10:

$$
5.7 + 4 \times \frac{1}{2} \div 2 - 3 \times 3.4
$$

Step-by-step:

1. Multiplication and division:
- $4 \times \frac{1}{2} = 2$, then $2 \div 2 = 1$
- $3 \times 3.4 = 10.2$

2. Now:
$$
5.7 + 1 - 10.2 = 6.7 - 10.2 = -3.5
$$

✔ Answer: -3.5

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 3.1 |
| 2 | -9.3 |
| 3 | 4.1 |
| 4 | -19.37 (or $-\frac{581}{30}$) |
| 5 | -16.9 |
| 6 | $\frac{44}{15}$ or 2.933 |
| 7 | 13.5 |
| 8 | -19.5 |
| 9 | -5.3 |
| 10 | -3.5 |

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