Q. \( \frac{1}{3} + \left(-\frac{2}{3}\right) = -\frac{1}{3} \).

Q: How do I add \frac{1}{3} and -\frac{2}{3} ?

Same denominator, add numerators: 1 + (-2) = -1, so the sum is -\frac{1}{3} (already simplified).

Q: Is \frac{1}{3} + -\frac{2}{3} the same as \frac{1}{3} - \frac{2}{3} ?

Yes. Adding a negative equals subtracting the positive: \frac{1}{3} + -\frac{2}{3} = \frac{1}{3} - \frac{2}{3} = -\frac{1}{3} ..

Q: How can I see \frac{1}{3} + -\frac{2}{3} on the number line?

Start at 0, move right \frac{1}{3} , then left \frac{2}{3} . Net movement is left \frac{1}{3} , landing at -\frac{1}{3} ..

Q: How would I add \frac{1}{3} and -\frac{2}{5} (different denominators)?

Find common denominator: convert to fifteenths: \frac{1}{3}=\frac{5}{15}, -\frac{2}{5}=-\frac{6}{15}. Add: \frac{5-6}{15}=-\frac{1}{15}.

Answer

\[
\frac{1}{3}+\left(-\frac{2}{3}\right)=\frac{1+(-2)}{3}=-\frac{1}{3}
\]

Final result: \(-\frac{1}{3}\)

Detailed Explanation

Step-by-step solution

Write the expression to be evaluated:
\( \frac{1}{3} + \left(-\frac{2}{3}\right) \)
Note the denominators are the same (3). When adding fractions with the same denominator, keep the denominator and add the numerators:
\( \frac{1}{3} + \left(-\frac{2}{3}\right) = \frac{1 + (-2)}{3} \)
Compute the numerator. Adding a negative number is the same as subtraction:
\( 1 + (-2) = 1 – 2 = -1 \)

So the fraction becomes

\( \frac{-1}{3} \)
Put the negative sign in conventional form and check for simplification:
\( -\frac{1}{3} \)

The fraction \( \frac{1}{3} \) is already in lowest terms, so no further simplification is possible.
(Alternative viewpoint) Interpret the original expression as subtraction:
\( \frac{1}{3} + \left(-\frac{2}{3}\right) = \frac{1}{3} – \frac{2}{3} = -\frac{1}{3} \)

Answer: \( -\frac{1}{3} \)

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Arithmetic FAQs

How do I add \( \frac{1}{3} \) and \( -\frac{2}{3} \)?

Same denominator, add numerators: \(1 + (-2) = -1\), so the sum is \(-\frac{1}{3}\) (already simplified).

Why can I just add the numerators for \( \frac{1}{3} + -\frac{2}{3} \)?.

When denominators match you add numerators with their signs. Here both denominators are \(3\), so add \(1\) and \(-2\) to get \(-1\) over \(3\): \(-\frac{1}{3}\)..

Is \( \frac{1}{3} + -\frac{2}{3} \) the same as \( \frac{1}{3} - \frac{2}{3} \)?

Yes. Adding a negative equals subtracting the positive: \( \frac{1}{3} + -\frac{2}{3} = \frac{1}{3} - \frac{2}{3} = -\frac{1}{3} \)..

How can I see \( \frac{1}{3} + -\frac{2}{3} \) on the number line?

Start at 0, move right \( \frac{1}{3} \), then left \( \frac{2}{3} \). Net movement is left \( \frac{1}{3} \), landing at \( -\frac{1}{3} \)..

How do I check the result with decimals?

Convert: \(\frac{1}{3}=0.333...\), \(-\frac{2}{3}=-0.666...\), sum \(=-0.333...\) which equals \(-\frac{1}{3}...\).

Why is the result negative?

How would I add \(\frac{1}{3}\) and \(-\frac{2}{5}\) (different denominators)?

Find common denominator: convert to fifteenths: \( \frac{1}{3}=\frac{5}{15}, -\frac{2}{5}=-\frac{6}{15}. \) Add: \( \frac{5-6}{15}=-\frac{1}{15}. \)

Is \(-\frac{1}{3}\) in simplest form?

Yes. Numerator 1 and denominator 3 have no common factors other than 1, so \(-\frac{1}{3}\) is fully simplified.

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