The task involves solving a series of fraction problems. Let's go through each problem step by step.
Problem 1: \( \frac{1}{2} + \frac{1}{4} \)
To add fractions, we need a common denominator. The denominators here are 2 and 4. The least common denominator (LCD) is 4.
- Convert \( \frac{1}{2} \) to a fraction with a denominator of 4:
\[
\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
\]
- Now add the fractions:
\[
\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4} = \frac{3}{4}
\]
Answer: \( \frac{3}{4} \)
---
Problem 2: \( \frac{3}{5} - \frac{1}{5} \)
Here, the denominators are already the same (both are 5), so we can directly subtract the numerators.
\[
\frac{3}{5} - \frac{1}{5} = \frac{3 - 1}{5} = \frac{2}{5}
\]
Answer: \( \frac{2}{5} \)
---
Problem 3: \( \frac{2}{3} + \frac{1}{6} \)
The denominators are 3 and 6. The least common denominator (LCD) is 6.
- Convert \( \frac{2}{3} \) to a fraction with a denominator of 6:
\[
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]
- Now add the fractions:
\[
\frac{4}{6} + \frac{1}{6} = \frac{4 + 1}{6} = \frac{5}{6}
\]
Answer: \( \frac{5}{6} \)
---
Problem 4: \( \frac{5}{8} - \frac{1}{4} \)
The denominators are 8 and 4. The least common denominator (LCD) is 8.
- Convert \( \frac{1}{4} \) to a fraction with a denominator of 8:
\[
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
\]
- Now subtract the fractions:
\[
\frac{5}{8} - \frac{2}{8} = \frac{5 - 2}{8} = \frac{3}{8}
\]
Answer: \( \frac{3}{8} \)
---
Problem 5: \( \frac{3}{7} + \frac{2}{7} \)
Here, the denominators are already the same (both are 7), so we can directly add the numerators.
\[
\frac{3}{7} + \frac{2}{7} = \frac{3 + 2}{7} = \frac{5}{7}
\]
Answer: \( \frac{5}{7} \)
---
Problem 6: \( \frac{4}{9} - \frac{1}{3} \)
The denominators are 9 and 3. The least common denominator (LCD) is 9.
- Convert \( \frac{1}{3} \) to a fraction with a denominator of 9:
\[
\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}
\]
- Now subtract the fractions:
\[
\frac{4}{9} - \frac{3}{9} = \frac{4 - 3}{9} = \frac{1}{9}
\]
Answer: \( \frac{1}{9} \)
---
Final Answers:
\[
\boxed{\frac{3}{4}, \frac{2}{5}, \frac{5}{6}, \frac{3}{8}, \frac{5}{7}, \frac{1}{9}}
\]
Parent Tip: Review the logic above to help your child master the concept of 2nd grade fraction worksheet.
