Q. One third plus one third equals \( \frac{1}{3} + \frac{1}{3} = \frac{2}{3} \).

Q: What is \frac{1}{3} + \frac{1}{3}?

What is \frac{1}{3} + \frac{1}{3}?

Q: What is \frac{1}{3} + \frac{1}{3} as a decimal?

\frac{1}{3} \approx 0.333..., so 0.333... + 0.333... = 0.666... which equals \frac{2}{3}.

Q: How do I add \frac{1}{3} to a fraction with a different denominator, like \frac{1}{4}?

Find a common denominator (LCM 12): convert \frac{1}{3} = \frac{4}{12} and \frac{1}{4} = \frac{3}{12}, then add: \frac{4}{12} + \frac{3}{12} = \frac{7}{12}.

Q: Is \frac{2}{3} in simplest form?

Yes. 2 and 3 have no common factors besides 1, so \frac{2}{3} is fully simplified.

Q: How can I picture \frac{1}{3} + \frac{1}{3}?

How can I picture \frac{1}{3} + \frac{1}{3}?

Q: What happens if I add three \frac{1}{3} terms: \frac{1}{3}+\frac{1}{3}+\frac{1}{3}?

\frac{1}{3}+\frac{1}{3}+\frac{1}{3} = \frac{3}{3} = 1, so three one-thirds make a whole.

Q: How do I subtract to undo \frac{1}{3} + \frac{1}{3}?

To reverse it, subtract one of the thirds: \frac{2}{3} - \frac{1}{3} = \frac{1}{3}. Subtract numerators when denominators match.

Answer

\[\frac{1}{3} + \frac{1}{3} = \frac{2}{3}\]

Since the denominators are equal, add numerators: 1 + 1 = 2, over 3.

Detailed Explanation

We will compute one third plus one third step by step.

Write the sum in fraction form

Start by expressing the problem using fraction notation:
\( \frac{1}{3} + \frac{1}{3} \).
Identify the denominators

Both fractions have the same denominator 3, because each is one third.

Explanation: When adding fractions with the same denominator, you keep the denominator and add the numerators.
Add the numerators and keep the denominator

Apply the rule for adding like denominators:
\[ \frac{1}{3} + \frac{1}{3} = \frac{1 + 1}{3}. \]

Explanation: We add the numerators 1 and 1 while the denominator remains 3.
Simplify the numerator

Compute the sum in the numerator:
\[ \frac{1 + 1}{3} = \frac{2}{3}. \]

Explanation: 1 plus 1 equals 2, so the fraction becomes two thirds.
Reduce the fraction if possible

Check for common factors of 2 and 3. The greatest common divisor of 2 and 3 is 1, so the fraction is already in lowest terms:
\[ \frac{2}{3}. \]

Explanation: There is no integer greater than 1 that divides both 2 and 3, so the fraction cannot be simplified further.

Final answer: \( \frac{2}{3} \)

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FAQs

What is \(\frac{1}{3} + \frac{1}{3}\)?

Why can I just add the numerators when denominators match?

When denominators are equal, each fraction counts equal-sized parts. Adding numerators counts how many of those parts you have: \(\frac{a}{n} + \frac{b}{n} = \frac{a+b}{n}\).

What is \(\frac{1}{3} + \frac{1}{3}\) as a decimal?

\(\frac{1}{3} \approx 0.333...\), so \(0.333... + 0.333... = 0.666...\) which equals \(\frac{2}{3}\).

How do I add \(\frac{1}{3}\) to a fraction with a different denominator, like \(\frac{1}{4}\)?

Find a common denominator (LCM 12): convert \(\frac{1}{3} = \frac{4}{12}\) and \(\frac{1}{4} = \frac{3}{12}\), then add: \(\frac{4}{12} + \frac{3}{12} = \frac{7}{12}\).

Is \(\frac{2}{3}\) in simplest form?

Yes. 2 and 3 have no common factors besides 1, so \(\frac{2}{3}\) is fully simplified.

How can I picture \(\frac{1}{3} + \frac{1}{3}\)?

What happens if I add three \(\frac{1}{3}\) terms: \(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\)?

\(\frac{1}{3}+\frac{1}{3}+\frac{1}{3} = \frac{3}{3} = 1\), so three one-thirds make a whole.

How do I subtract to undo \(\frac{1}{3} + \frac{1}{3}\)?

To reverse it, subtract one of the thirds: \(\frac{2}{3} - \frac{1}{3} = \frac{1}{3}\). Subtract numerators when denominators match.

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