Question

1/2 + 1/3 + 1/5 =

• A. 1
• B. 1 1/30
• C. 1 1/10
• D. 1 4/15
• E. 1 11/30

Hint:

For sums of unit fractions (fractions with a numerator of 1), you can use the formula for two fractions: \(\frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab}\). You can apply this twice, but finding the LCM for all denominators at once is usually more efficient for three or more fractions.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The question requires the addition of three fractions with different denominators.
Step 2: Key Formula or Approach:
To add fractions, we must find a common denominator, which is the Least Common Multiple (LCM) of the individual denominators.
Step 3: Detailed Explanation:
The denominators are 2, 3, and 5. Since these are all prime numbers, their LCM is their product.
\[ \text{LCM}(2, 3, 5) = 2 \times 3 \times 5 = 30 \]
Now, convert each fraction to an equivalent fraction with a denominator of 30:
\[ \frac{1}{2} = \frac{1 \times 15}{2 \times 15} = \frac{15}{30} \]
\[ \frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30} \]
\[ \frac{1}{5} = \frac{1 \times 6}{5 \times 6} = \frac{6}{30} \]
Now, add the numerators:
\[ \frac{15}{30} + \frac{10}{30} + \frac{6}{30} = \frac{15 + 10 + 6}{30} = \frac{31}{30} \]
This is an improper fraction. To convert it to a mixed number, divide 31 by 30.
\[ 31 \div 30 = 1 \text{ with a remainder of } 1 \]
So, the mixed number is \(1 \frac{1}{30}\).
Step 4: Final Answer:
The sum is \(1 \frac{1}{30}\), which corresponds to option (B).