Math

QuestionFind the value of 26.95÷51226.95 \div -5 \frac{1}{2}.

Studdy Solution

STEP 1

Assumptions1. The expression to be solved is 26.95÷5126.95 \div -5 \frac{1}{}. . The division operation should be performed between the decimal number and the mixed number.
3. The mixed number should be converted to an improper fraction before performing the division.

STEP 2

First, we need to convert the mixed number 512-5 \frac{1}{2} to an improper fraction. The formula to convert a mixed number to an improper fraction isImproper fraction=Whole number×Denominator+umerator\text{Improper fraction} = \text{Whole number} \times \text{Denominator} + \text{umerator}

STEP 3

Now, plug in the given values for the whole number, denominator, and numerator to calculate the improper fraction.
Improper fraction=5×2+1\text{Improper fraction} = -5 \times2 +1

STEP 4

Calculate the improper fraction.
Improper fraction=×2+1=11\text{Improper fraction} = - \times2 +1 = -11So, 12- \frac{1}{2} is equivalent to 112-\frac{11}{2}.

STEP 5

Now that we have the improper fraction, we can perform the division operation. The division of two numbers can be performed by multiplying the first number by the reciprocal of the second number.
26.95÷112=26.95×21126.95 \div -\frac{11}{2} =26.95 \times -\frac{2}{11}

STEP 6

Perform the multiplication operation.
26.95×211=4.926.95 \times -\frac{2}{11} = -4.9So, the value of the expression 26.95÷51226.95 \div -5 \frac{1}{2} is 4.9-4.9.

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