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QuestionTechnical Math Unit Test 2 Evaluate each expression. 6) (−334)−(−123)\left(-3 \frac{3}{4}\right)-\left(-1 \frac{2}{3}\right) A) −5712-5 \frac{7}{12} B) −2112-2 \frac{1}{12} C) −31112-3 \frac{11}{12} D) 131601 \frac{31}{60}

Studdy Solution

STEP 1

1. We are evaluating the expression (−334)−(−123)\left(-3 \frac{3}{4}\right)-\left(-1 \frac{2}{3}\right).
2. We need to convert mixed numbers to improper fractions for easier calculation.
3. We will perform subtraction of fractions.
4. The final answer should be converted back to a mixed number if necessary.

STEP 2

1. Convert mixed numbers to improper fractions.
2. Perform the subtraction operation.
3. Simplify the result if necessary.
4. Convert the result back to a mixed number.

STEP 3

Convert −334-3 \frac{3}{4} and −123-1 \frac{2}{3} to improper fractions.
−334=−(3×4+34)=−154-3 \frac{3}{4} = -\left(\frac{3 \times 4 + 3}{4}\right) = -\frac{15}{4}
−123=−(1×3+23)=−53-1 \frac{2}{3} = -\left(\frac{1 \times 3 + 2}{3}\right) = -\frac{5}{3}

STEP 4

Set up the subtraction of the two improper fractions.
−154−(−53)=−154+53-\frac{15}{4} - \left(-\frac{5}{3}\right) = -\frac{15}{4} + \frac{5}{3}

STEP 5

Find a common denominator to perform the addition.
The least common multiple of 44 and 33 is 1212.
Convert the fractions:
−154=−15×34×3=−4512-\frac{15}{4} = -\frac{15 \times 3}{4 \times 3} = -\frac{45}{12}
53=5×43×4=2012\frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12}

STEP 6

Add the fractions.
−4512+2012=−45+2012=−2512-\frac{45}{12} + \frac{20}{12} = \frac{-45 + 20}{12} = \frac{-25}{12}

STEP 7

Convert −2512\frac{-25}{12} back to a mixed number.
Divide 2525 by 1212:
25÷12=2remainder125 \div 12 = 2 \quad \text{remainder} \quad 1
So, −2512=−2112\frac{-25}{12} = -2 \frac{1}{12}.
The correct answer is:
−2112\boxed{-2 \frac{1}{12}}
This corresponds to option B.

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