one third plus one-fourth
Understand the Problem
The question is asking to find the sum of one third and one fourth. We will need to find a common denominator to add these two fractions together.
Answer
The sum of one third and one fourth is $\frac{7}{12}$.
Answer for screen readers
The sum of one third and one fourth is $\frac{7}{12}$.
Steps to Solve
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Identify the fractions The fractions we need to add are $\frac{1}{3}$ and $\frac{1}{4}$.
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Find a common denominator The denominators are 3 and 4. The least common multiple (LCM) of 3 and 4 is 12.
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Convert the fractions We need to convert both fractions to have the common denominator of 12.
For $\frac{1}{3}$: $$ \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} $$
For $\frac{1}{4}$: $$ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} $$
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Add the fractions Now that both fractions have a common denominator, we can add them: $$ \frac{4}{12} + \frac{3}{12} = \frac{4+3}{12} = \frac{7}{12} $$
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State the final answer The sum of one third and one fourth is $\frac{7}{12}$.
The sum of one third and one fourth is $\frac{7}{12}$.
More Information
Adding fractions requires a common denominator, which simplifies the process and ensures that the values are accurately combined. The sum $\frac{7}{12}$ cannot be simplified further, as 7 and 12 have no common factors.
Tips
- Forgetting to find a common denominator before adding.
- Miscalculating the numerators when adding the fractions.
- Not converting to an equivalent fraction correctly.
