Question
b) \( \frac{2}{5}+\frac{1}{2} \) e) \( \frac{2}{4}+\frac{2}{3} \)
Ask by Guerrero Mejia. in South Africa
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
b) \( \frac{9}{10} \)
e) \( \frac{7}{6} \)
Solution
### b) \( \frac{2}{5}+\frac{1}{2} \)
1. Find the least common denominator (LCD) of \(5\) and \(2\).
The LCD is \(10\).
2. Rewrite each fraction with the denominator \(10\):
\[
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}, \quad \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\]
3. Add the fractions:
\[
\frac{4}{10} + \frac{5}{10} = \frac{4+5}{10} = \frac{9}{10}
\]
### e) \( \frac{2}{4}+\frac{2}{3} \)
1. Notice that \( \frac{2}{4} \) can be simplified:
\[
\frac{2}{4} = \frac{1}{2}
\]
Now, the expression becomes \( \frac{1}{2}+\frac{2}{3} \).
2. Find the least common denominator (LCD) of \(2\) and \(3\).
The LCD is \(6\).
3. Rewrite each fraction with the denominator \(6\):
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}, \quad \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]
4. Add the fractions:
\[
\frac{3}{6} + \frac{4}{6} = \frac{3+4}{6} = \frac{7}{6}
\]
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Simplify this solution The Deep Dive
To add \( \frac{2}{5} + \frac{1}{2} \), first find a common denominator. The least common multiple of 5 and 2 is 10. Convert the fractions: \( \frac{2}{5} = \frac{4}{10} \) and \( \frac{1}{2} = \frac{5}{10} \). Now, add: \( \frac{4}{10} + \frac{5}{10} = \frac{9}{10} \). For \( \frac{2}{4} + \frac{2}{3} \), simplify \( \frac{2}{4} \) to \( \frac{1}{2} \). The least common multiple of 2 and 3 is 6. Convert: \( \frac{1}{2} = \frac{3}{6} \) and \( \frac{2}{3} = \frac{4}{6} \). Add them together: \( \frac{3}{6} + \frac{4}{6} = \frac{7}{6} \) or \( 1 \frac{1}{6} \).
