Question

The sum of 1/6,2/3, and 1/4 is

Answer 1

When adding, find a common denominator first, which is 12, then make each fraction into x/12, which are 2/12+8/12+3/12, which is 13/12 or 1 1/12

Answer 2

¹³/₁₂

Further explanation

Given:

$\boxed{ \ \frac{1}{6} + \frac{2}{3} + \frac{1}{4} = ? \ }$

• A fraction represents part of a whole.
• A fraction consists of a numerator and a denominator. i.e., $\boxed{ \ \frac{numerator}{denominator} \ }$.
• The numerator = the number of equal parts of a whole.
• The denominator = the total number of parts that make up said whole.

From the problems above, the denominator or the bottom numbers are still different. We use the Least Common Multiple (or LCM) to equalize the denominator.

• Multiples of 3: $\boxed{ \ \{3, 6, 9, 12, 15, ... \} \ }$
• Multiples of 4: $\boxed{ \ \{4, 8, 12, 16, ... \} \ }$
• Multiples of 6: $\boxed{ \ \{6, 12, 18, ... \} \ }$

Hence, the LCM for 3, 4, and 6 is 12.

We change the denominator for each fraction to 12.

$\boxed{ \ \frac{1}{6} \rightarrow \frac{multiply \ by \ 2}{multiply \ by \ 2} \rightarrow \frac{2}{12} \ }$

$\boxed{ \ \frac{2}{3} \rightarrow \frac{multiply \ by \ 4}{multiply \ by \ 4} \rightarrow \frac{8}{12} \ }$

$\boxed{ \ \frac{1}{4} \rightarrow \frac{multiply \ by \ 3}{multiply \ by \ 3} \rightarrow \frac{3}{12} \ }$

Then we continue adding fractions.

$\boxed{ \ \frac{1}{6} + \frac{2}{3} + \frac{1}{4} = \frac{2}{12} + \frac{8}{12} + \frac{3}{12} \ }$

$\boxed{ \ \frac{1}{6} + \frac{2}{3} + \frac{1}{4} = \boxed{ \ \frac{13}{12} \ } \ }$

Thus, the result is $\boxed{ \ \frac{13}{12} \ or \ 1\frac{1}{12}\ }$

Learn more

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Keywords: the sum of ¹/₆, ²/₃, and ¹/₄, fraction, adding, numerator, denominator, still different, LCM