Math  /  Numbers & Operations

QuestionEvaluate. 19(415)-\frac{1}{9}-\left(-\frac{4}{15}\right)
Write your answer in simplest form.

Studdy Solution

STEP 1

1. We are given the expression 19(415) -\frac{1}{9} - \left(-\frac{4}{15}\right) .
2. We need to evaluate this expression and simplify the result.

STEP 2

1. Simplify the expression by removing parentheses.
2. Find a common denominator.
3. Perform the subtraction.
4. Simplify the result.

STEP 3

Remove the parentheses by recognizing that subtracting a negative is the same as adding a positive.
19(415)=19+415-\frac{1}{9} - \left(-\frac{4}{15}\right) = -\frac{1}{9} + \frac{4}{15}

STEP 4

Identify the least common denominator (LCD) for the fractions 19\frac{1}{9} and 415\frac{4}{15}.
The denominators are 99 and 1515. The least common multiple of 99 and 1515 is 4545.

STEP 5

Convert each fraction to have the common denominator of 4545.
19=1×59×5=545-\frac{1}{9} = -\frac{1 \times 5}{9 \times 5} = -\frac{5}{45}
415=4×315×3=1245\frac{4}{15} = \frac{4 \times 3}{15 \times 3} = \frac{12}{45}

STEP 6

Perform the addition of the fractions.
545+1245=5+1245=745-\frac{5}{45} + \frac{12}{45} = \frac{-5 + 12}{45} = \frac{7}{45}
The simplified result of the expression is:
745\boxed{\frac{7}{45}}

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