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QuestionCalculate: 712÷(412−518)=?7 \frac{1}{2} \div (4 \frac{1}{2} - 5 \frac{1}{8}) = ? Options: −41116,12,−12,41116-4 \frac{11}{16}, 12, -12, 4 \frac{11}{16}.

Studdy Solution

STEP 1

Assumptions1. We are dealing with mixed numbers (a whole number and a fraction combined) in the problem. . We need to convert these mixed numbers into improper fractions before performing the operations.
3. The order of operations is followed, which means we perform operations in parentheses first.

STEP 2

First, let's convert the mixed numbers into improper fractions. The formula to convert a mixed number into an improper fraction isImproper fraction=Whole number×Denominator+umerator\text{Improper fraction} = \text{Whole number} \times \text{Denominator} + \text{umerator}Let's convert 7127 \frac{1}{2} into an improper fraction.

STEP 3

Substitute the values into the formulaImproper fraction=7×2+1=15/2\text{Improper fraction} =7 \times2 +1 =15/2So, 7127 \frac{1}{2} is equivalent to 152\frac{15}{2}.

STEP 4

Now, let's convert 4124 \frac{1}{2} into an improper fraction.

STEP 5

Substitute the values into the formulaImproper fraction=4×2+1=9/2\text{Improper fraction} =4 \times2 +1 =9/2So, 4124 \frac{1}{2} is equivalent to 92\frac{9}{2}.

STEP 6

Next, convert 5185 \frac{1}{8} into an improper fraction.

STEP 7

Substitute the values into the formulaImproper fraction=5×+1=41/\text{Improper fraction} =5 \times +1 =41/So, 515 \frac{1}{} is equivalent to 41\frac{41}{}.

STEP 8

Now, we can rewrite the original problem using these improper fractions152÷(2−418)\frac{15}{2} \div \left(\frac{}{2} - \frac{41}{8}\right)

STEP 9

We need to perform the operation in the parentheses first. So, let's subtract 418\frac{41}{8} from 92\frac{9}{2}.To subtract fractions, they must have the same denominator. We can convert 92\frac{9}{2} to have a denominator of8 by multiplying both the numerator and denominator by4.

STEP 10

Convert 92\frac{9}{2} to a fraction with a denominator of892=9×42×4=368\frac{9}{2} = \frac{9 \times4}{2 \times4} = \frac{36}{8}

STEP 11

Now, subtract 418\frac{41}{8} from 368\frac{36}{8}368−418=−58\frac{36}{8} - \frac{41}{8} = -\frac{5}{8}

STEP 12

Now, we can rewrite the problem as152÷−58\frac{15}{2} \div -\frac{5}{8}

STEP 13

To divide fractions, we multiply by the reciprocal of the divisor. The reciprocal of −58-\frac{5}{8} is −85-\frac{8}{5}.

STEP 14

Multiply 2\frac{}{2} by −8-\frac{8}{}2×−8=−×82×\frac{}{2} \times -\frac{8}{} = -\frac{ \times8}{2 \times}

STEP 15

implify the fraction−15×82×5=−12010=−12-\frac{15 \times8}{2 \times5} = -\frac{120}{10} = -12The solution to the problem is −12-12.

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