Mathematics worksheet for Grade 4 students focusing on adding and subtracting dissimilar fractions.

Problem: Addition and Subtraction of Dissimilar Fractions

The task is to add or subtract the given fractions and simplify the answers if possible. Let's solve each problem step by step.

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#### 1. \( \frac{9}{20} + \frac{1}{4} \)

Step 1: Find a common denominator.

- The denominators are 20 and 4.
- The least common multiple (LCM) of 20 and 4 is 20.

Step 2: Rewrite the fractions with the common denominator.

- For \( \frac{1}{4} \):
\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\]

- So, the expression becomes:
\[
\frac{9}{20} + \frac{5}{20}
\]

Step 3: Add the numerators.

\[
\frac{9}{20} + \frac{5}{20} = \frac{9 + 5}{20} = \frac{14}{20}
\]

Step 4: Simplify the fraction.

- The greatest common divisor (GCD) of 14 and 20 is 2.
- Simplify:
\[
\frac{14}{20} = \frac{14 \div 2}{20 \div 2} = \frac{7}{10}
\]

Final Answer:
\[
\boxed{\frac{7}{10}}
\]

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#### 2. \( \frac{6}{9} + \frac{2}{3} \)

Step 1: Simplify the fractions if possible.

- \( \frac{6}{9} \) can be simplified:
\[
\frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3}
\]

- So, the expression becomes:
\[
\frac{2}{3} + \frac{2}{3}
\]

Step 2: Add the fractions.

- Since the denominators are the same, add the numerators:
\[
\frac{2}{3} + \frac{2}{3} = \frac{2 + 2}{3} = \frac{4}{3}
\]

Final Answer:
\[
\boxed{\frac{4}{3}}
\]

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#### 3. \( \frac{7}{8} + \frac{2}{3} \)

Step 1: Find a common denominator.

- The denominators are 8 and 3.
- The least common multiple (LCM) of 8 and 3 is 24.

Step 2: Rewrite the fractions with the common denominator.

- For \( \frac{7}{8} \):
\[
\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}
\]

- For \( \frac{2}{3} \):
\[
\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}
\]

- So, the expression becomes:
\[
\frac{21}{24} + \frac{16}{24}
\]

Step 3: Add the numerators.

\[
\frac{21}{24} + \frac{16}{24} = \frac{21 + 16}{24} = \frac{37}{24}
\]

Final Answer:
\[
\boxed{\frac{37}{24}}
\]

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#### 4. \( \frac{20}{40} - \frac{1}{2} \)

Step 1: Simplify the fractions if possible.

- \( \frac{20}{40} \) can be simplified:
\[
\frac{20}{40} = \frac{20 \div 20}{40 \div 20} = \frac{1}{2}
\]

- So, the expression becomes:
\[
\frac{1}{2} - \frac{1}{2}
\]

Step 2: Subtract the fractions.

- Since the denominators are the same, subtract the numerators:
\[
\frac{1}{2} - \frac{1}{2} = \frac{1 - 1}{2} = \frac{0}{2} = 0
\]

Final Answer:
\[
\boxed{0}
\]

---

#### 5. \( \frac{8}{9} - \frac{1}{3} \)

Step 1: Find a common denominator.

- The denominators are 9 and 3.
- The least common multiple (LCM) of 9 and 3 is 9.

Step 2: Rewrite the fractions with the common denominator.

- For \( \frac{1}{3} \):
\[
\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}
\]

- So, the expression becomes:
\[
\frac{8}{9} - \frac{3}{9}
\]

Step 3: Subtract the numerators.

\[
\frac{8}{9} - \frac{3}{9} = \frac{8 - 3}{9} = \frac{5}{9}
\]

Final Answer:
\[
\boxed{\frac{5}{9}}
\]

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Final Answers:

1. \( \boxed{\frac{7}{10}} \)
2. \( \boxed{\frac{4}{3}} \)
3. \( \boxed{\frac{37}{24}} \)
4. \( \boxed{0} \)
5. \( \boxed{\frac{5}{9}} \)