Evaluating Numerical Expressions with Fractions Worksheets - Free Printable

Problem: Evaluate each numerical expression involving fractions.

We will solve each expression step by step, following the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

---

#### 1) \( 8 - \frac{2}{3} \times 4 + \frac{1}{3} \)

1. Perform multiplication first:
\[
\frac{2}{3} \times 4 = \frac{2 \times 4}{3} = \frac{8}{3}
\]

2. Substitute back into the expression:
\[
8 - \frac{8}{3} + \frac{1}{3}
\]

3. Convert 8 to a fraction with a denominator of 3:
\[
8 = \frac{24}{3}
\]

4. Combine all terms:
\[
\frac{24}{3} - \frac{8}{3} + \frac{1}{3} = \frac{24 - 8 + 1}{3} = \frac{17}{3}
\]

Answer:
\[
\boxed{\frac{17}{3}}
\]

---

#### 2) \( 5 + \frac{5}{8} + 21 \)

1. Add the integers first:
\[
5 + 21 = 26
\]

2. Add the fraction:
\[
26 + \frac{5}{8} = 26 \frac{5}{8}
\]

Answer:
\[
\boxed{26 \frac{5}{8}}
\]

---

#### 3) \( \frac{1}{4} + 9 \times \frac{2}{3} \)

1. Perform multiplication first:
\[
9 \times \frac{2}{3} = \frac{9 \times 2}{3} = \frac{18}{3} = 6
\]

2. Add the result to \(\frac{1}{4}\):
\[
\frac{1}{4} + 6
\]

3. Convert 6 to a fraction with a denominator of 4:
\[
6 = \frac{24}{4}
\]

4. Combine the fractions:
\[
\frac{1}{4} + \frac{24}{4} = \frac{1 + 24}{4} = \frac{25}{4}
\]

Answer:
\[
\boxed{\frac{25}{4}}
\]

---

#### 4) \( 8 \times 5 - \frac{9}{2} + \frac{3}{4} \)

1. Perform multiplication first:
\[
8 \times 5 = 40
\]

2. Substitute back into the expression:
\[
40 - \frac{9}{2} + \frac{3}{4}
\]

3. Convert all terms to have a common denominator (LCM of 1, 2, and 4 is 4):
\[
40 = \frac{160}{4}, \quad \frac{9}{2} = \frac{18}{4}
\]

4. Substitute and combine:
\[
\frac{160}{4} - \frac{18}{4} + \frac{3}{4} = \frac{160 - 18 + 3}{4} = \frac{145}{4}
\]

Answer:
\[
\boxed{\frac{145}{4}}
\]

---

#### 5) \( 64 \div 6 - \frac{7}{9} \times \frac{3}{7} \)

1. Perform division and multiplication separately:
\[
64 \div 6 = \frac{64}{6} = \frac{32}{3}
\]
\[
\frac{7}{9} \times \frac{3}{7} = \frac{7 \times 3}{9 \times 7} = \frac{21}{63} = \frac{1}{3}
\]

2. Substitute back into the expression:
\[
\frac{32}{3} - \frac{1}{3}
\]

3. Combine the fractions:
\[
\frac{32}{3} - \frac{1}{3} = \frac{32 - 1}{3} = \frac{31}{3}
\]

Answer:
\[
\boxed{\frac{31}{3}}
\]

---

#### 6) \( 4 \times \frac{1}{7} + 5 \)

1. Perform multiplication first:
\[
4 \times \frac{1}{7} = \frac{4}{7}
\]

2. Add the result to 5:
\[
\frac{4}{7} + 5
\]

3. Convert 5 to a fraction with a denominator of 7:
\[
5 = \frac{35}{7}
\]

4. Combine the fractions:
\[
\frac{4}{7} + \frac{35}{7} = \frac{4 + 35}{7} = \frac{39}{7}
\]

Answer:
\[
\boxed{\frac{39}{7}}
\]

---

#### 7) \( \frac{5}{6} \times 18 - \frac{4}{3} \)

1. Perform multiplication first:
\[
\frac{5}{6} \times 18 = \frac{5 \times 18}{6} = \frac{90}{6} = 15
\]

2. Subtract \(\frac{4}{3}\):
\[
15 - \frac{4}{3}
\]

3. Convert 15 to a fraction with a denominator of 3:
\[
15 = \frac{45}{3}
\]

4. Combine the fractions:
\[
\frac{45}{3} - \frac{4}{3} = \frac{45 - 4}{3} = \frac{41}{3}
\]

Answer:
\[
\boxed{\frac{41}{3}}
\]

---

#### 8) \( 2 - \frac{4}{9} \times \frac{3}{8} + 1 \)

1. Perform multiplication first:
\[
\frac{4}{9} \times \frac{3}{8} = \frac{4 \times 3}{9 \times 8} = \frac{12}{72} = \frac{1}{6}
\]

2. Substitute back into the expression:
\[
2 - \frac{1}{6} + 1
\]

3. Combine the integers:
\[
2 + 1 = 3
\]

4. Subtract \(\frac{1}{6}\):
\[
3 - \frac{1}{6}
\]

5. Convert 3 to a fraction with a denominator of 6:
\[
3 = \frac{18}{6}
\]

6. Combine the fractions:
\[
\frac{18}{6} - \frac{1}{6} = \frac{18 - 1}{6} = \frac{17}{6}
\]

Answer:
\[
\boxed{\frac{17}{6}}
\]

---

#### 9) \( 82 - 9 \times \frac{7}{6} + \frac{5}{2} \)

1. Perform multiplication first:
\[
9 \times \frac{7}{6} = \frac{9 \times 7}{6} = \frac{63}{6} = \frac{21}{2}
\]

2. Substitute back into the expression:
\[
82 - \frac{21}{2} + \frac{5}{2}
\]

3. Convert 82 to a fraction with a denominator of 2:
\[
82 = \frac{164}{2}
\]

4. Combine all terms:
\[
\frac{164}{2} - \frac{21}{2} + \frac{5}{2} = \frac{164 - 21 + 5}{2} = \frac{148}{2} = 74
\]

Answer:
\[
\boxed{74}
\]

---

#### 10) \( 1 + 4 \times \frac{9}{0} \)

1. Note that division by zero (\(\frac{9}{0}\)) is undefined. Therefore, the entire expression is undefined.

Answer:
\[
\boxed{\text{Undefined}}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1) & \ \frac{17}{3} \\
2) & \ 26 \frac{5}{8} \\
3) & \ \frac{25}{4} \\
4) & \ \frac{145}{4} \\
5) & \ \frac{31}{3} \\
6) & \ \frac{39}{7} \\
7) & \ \frac{41}{3} \\
8) & \ \frac{17}{6} \\
9) & \ 74 \\
10) & \ \text{Undefined}
\end{aligned}
}
\]