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Math  /  Numbers & Operations

QuestionAdd. −13+59-\frac{1}{3}+\frac{5}{9}
Write your answer in simplest form.

Studdy Solution

STEP 1

1. We are adding two fractions: −13-\frac{1}{3} and 59\frac{5}{9}.
2. The result should be in its simplest form.

STEP 2

1. Find a common denominator.
2. Convert fractions to have the common denominator.
3. Add the fractions.
4. Simplify the result.

STEP 3

Identify the denominators of the fractions: 33 and 99.

STEP 4

Determine the least common denominator (LCD) of 33 and 99, which is 99.

STEP 5

Convert −13-\frac{1}{3} to an equivalent fraction with a denominator of 99.
−13=−1×33×3=−39 -\frac{1}{3} = -\frac{1 \times 3}{3 \times 3} = -\frac{3}{9}

STEP 6

Add the fractions −39-\frac{3}{9} and 59\frac{5}{9}.
−39+59=−3+59=29 -\frac{3}{9} + \frac{5}{9} = \frac{-3 + 5}{9} = \frac{2}{9}

STEP 7

Check if 29\frac{2}{9} is in its simplest form. Since 22 and 99 have no common factors other than 11, it is already simplified.
The sum of the fractions is:
29\boxed{\frac{2}{9}}

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