QuestionCalculate $\left(\frac{7}{9}-\frac{7}{12}\right) \div \frac{1}{6}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\left(\frac{7}{9}-\frac{7}{12}\right) \div \frac{1}{6}$ . . We follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often abbreviated as PEMAS.

STEP 2

First, we need to simplify the expression inside the parentheses. This involves subtracting the two fractions $\frac{7}{9}$ and $\frac{7}{12}$ .
$\frac{7}{9}-\frac{7}{12}$

STEP 3

To subtract fractions, we need a common denominator. The least common multiple of9 and12 is36. So, we convert both fractions to have this common denominator.
$\frac{7}{9} = \frac{7 \times}{9 \times} = \frac{28}{36}$ $\frac{7}{12} = \frac{7 \times3}{12 \times3} = \frac{21}{36}$

STEP 4

Now, subtract the two fractions.
$\frac{28}{36}-\frac{21}{36} = \frac{28 -21}{36} = \frac{7}{36}$

STEP 5

Now we have simplified the expression inside the parentheses to $\frac{7}{36}$ . The original expression now becomes $\frac{7}{36} \div \frac{1}{}$

STEP 6

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $\frac{1}{6}$ is $6$ .
$\frac{}{36} \div \frac{1}{6} = \frac{}{36} \times6$

STEP 7

Now, multiply the fraction $\frac{7}{36}$ by $6$ .
$\frac{7}{36} \times6 = \frac{7 \times6}{36} = \frac{42}{36}$

STEP 8

implify the fraction $\frac{42}{36}$ by dividing the numerator and the denominator by their greatest common divisor, which is6.
$\frac{42}{36} = \frac{42 \div6}{36 \div6} = \frac{7}{6}$ So, the solution to the given expression is $\frac{7}{6}$ .

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QuestionCalculate $\left(\frac{7}{9}-\frac{7}{12}\right) \div \frac{1}{6}$ .

Studdy Solution

STEP 1

STEP 2

First, we need to simplify the expression inside the parentheses. This involves subtracting the two fractions $\frac{7}{9}$ and $\frac{7}{12}$ .
$\frac{7}{9}-\frac{7}{12}$

STEP 3

To subtract fractions, we need a common denominator. The least common multiple of9 and12 is36. So, we convert both fractions to have this common denominator.
$\frac{7}{9} = \frac{7 \times}{9 \times} = \frac{28}{36}$ $\frac{7}{12} = \frac{7 \times3}{12 \times3} = \frac{21}{36}$

STEP 4

Now, subtract the two fractions.
$\frac{28}{36}-\frac{21}{36} = \frac{28 -21}{36} = \frac{7}{36}$

STEP 5

Now we have simplified the expression inside the parentheses to $\frac{7}{36}$ . The original expression now becomes $\frac{7}{36} \div \frac{1}{}$

STEP 6

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $\frac{1}{6}$ is $6$ .
$\frac{}{36} \div \frac{1}{6} = \frac{}{36} \times6$

STEP 7

Now, multiply the fraction $\frac{7}{36}$ by $6$ .
$\frac{7}{36} \times6 = \frac{7 \times6}{36} = \frac{42}{36}$

STEP 8

implify the fraction $\frac{42}{36}$ by dividing the numerator and the denominator by their greatest common divisor, which is6.
$\frac{42}{36} = \frac{42 \div6}{36 \div6} = \frac{7}{6}$ So, the solution to the given expression is $\frac{7}{6}$ .

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QuestionCalculate (79−712)÷16\left(\frac{7}{9}-\frac{7}{12}\right) \div \frac{1}{6}(97​−127​)÷61​.

Studdy Solution

STEP 1

STEP 2

First, we need to simplify the expression inside the parentheses. This involves subtracting the two fractions 79\frac{7}{9}97​ and 712\frac{7}{12}127​.79−712\frac{7}{9}-\frac{7}{12}97​−127​

STEP 3

STEP 4

Now, subtract the two fractions.2836−2136=28−2136=736\frac{28}{36}-\frac{21}{36} = \frac{28 -21}{36} = \frac{7}{36}3628​−3621​=3628−21​=367​

STEP 5

Now we have simplified the expression inside the parentheses to 736\frac{7}{36}367​. The original expression now becomes736÷1\frac{7}{36} \div \frac{1}{}367​÷1​

STEP 6

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 16\frac{1}{6}61​ is 666.36÷16=36×6\frac{}{36} \div \frac{1}{6} = \frac{}{36} \times636​÷61​=36​×6

STEP 7

Now, multiply the fraction 736\frac{7}{36}367​ by 666.736×6=7×636=4236\frac{7}{36} \times6 = \frac{7 \times6}{36} = \frac{42}{36}367​×6=367×6​=3642​

STEP 8

implify the fraction 4236\frac{42}{36}3642​ by dividing the numerator and the denominator by their greatest common divisor, which is6.4236=42÷636÷6=76\frac{42}{36} = \frac{42 \div6}{36 \div6} = \frac{7}{6}3642​=36÷642÷6​=67​So, the solution to the given expression is 76\frac{7}{6}67​.

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QuestionCalculate $\left(\frac{7}{9}-\frac{7}{12}\right) \div \frac{1}{6}$ .

First, we need to simplify the expression inside the parentheses. This involves subtracting the two fractions $\frac{7}{9}$ and $\frac{7}{12}$ .
$\frac{7}{9}-\frac{7}{12}$

Now, subtract the two fractions.
$\frac{28}{36}-\frac{21}{36} = \frac{28 -21}{36} = \frac{7}{36}$

Now we have simplified the expression inside the parentheses to $\frac{7}{36}$ . The original expression now becomes $\frac{7}{36} \div \frac{1}{}$

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $\frac{1}{6}$ is $6$ .
$\frac{}{36} \div \frac{1}{6} = \frac{}{36} \times6$

Now, multiply the fraction $\frac{7}{36}$ by $6$ .
$\frac{7}{36} \times6 = \frac{7 \times6}{36} = \frac{42}{36}$

implify the fraction $\frac{42}{36}$ by dividing the numerator and the denominator by their greatest common divisor, which is6.
$\frac{42}{36} = \frac{42 \div6}{36 \div6} = \frac{7}{6}$ So, the solution to the given expression is $\frac{7}{6}$ .