Question

Simplify: $1 + \frac{1}{3} + \frac{1}{6} + \frac{1}{8} + \frac{1}{12} + \frac{1}{24}$

• A. 1.5
• B. 1.75
• C. 1.25
• D. 2

Answer 1

Answer:

B. 1.75

The simplified value of the expression is $\frac{7}{4}$ (or $1\frac{3}{4}$, which is $1.75$).

The given expression is:
$1 + \frac{1}{3} + \frac{1}{6} + \frac{1}{8} + \frac{1}{12} + \frac{1}{24}$

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Step 1: Find the Lowest Common Multiple (LCM)

Find the LCM of the denominators (3, 6, 8, 12, and 24).

• The LCM is 24.

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Step 2: Convert fractions to have a common denominator

Rewrite each term with a denominator of 24:

• $1 = \frac{24}{24}$

• $\frac{1}{3} = \frac{8}{24}$

• $\frac{1}{6} = \frac{4}{24}$

• $\frac{1}{8} = \frac{3}{24}$

• $\frac{1}{12} = \frac{2}{24}$

• $\frac{1}{24} = \frac{1}{24}$

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Step 3: Add the numerators together

Combine everything over the single common denominator:
$\frac{24 + 8 + 4 + 3 + 2 + 1}{24} = \frac{42}{24}$

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Step 4: Reduce to lowest terms

Divide both the numerator and the denominator by their greatest common divisor, which is 6:

• $42 \div 6 = 7$

• $24 \div 6 = 4$

This gives the final result: $\frac{7}{4}$ (or $1.75$).