QuestionCalculate the result of the expression: $\frac{1}{8}+\frac{1}{18} \div \frac{1}{6}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\frac{1}{8}+\frac{1}{18} \div \frac{1}{6}$ . . We need to solve this expression following 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 perform the division operation in the expression, as per the order of operations.
$\frac{1}{18} \div \frac{1}{6}$

STEP 3

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{1}{18} \times \frac{6}{1}$

STEP 4

Multiply the fractions.
$\frac{1 \times6}{18 \times1} = \frac{6}{18}$

STEP 5

implify the fraction.
$\frac{}{18} = \frac{1}{3}$

STEP 6

Now, substitute the result back into the original expression and perform the addition operation.
$\frac{1}{8}+\frac{1}{3}$

STEP 7

To add fractions, we need to find a common denominator. The least common denominator (LCD) of and3 is24.
$\frac{1 \times3}{ \times3} + \frac{1 \times}{3 \times}$

STEP 8

Perform the multiplication in each fraction.
$\frac{3}{24} + \frac{8}{24}$

STEP 9

Now, add the fractions.
$\frac{3 +8}{24} = \frac{11}{24}$ So, the solution to the expression $\frac{}{8}+\frac{}{18} \div \frac{}{6}$ is $\frac{11}{24}$ .

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QuestionCalculate the result of the expression: $\frac{1}{8}+\frac{1}{18} \div \frac{1}{6}$ .

Studdy Solution

STEP 1

STEP 2

First, we need to perform the division operation in the expression, as per the order of operations.
$\frac{1}{18} \div \frac{1}{6}$

STEP 3

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{1}{18} \times \frac{6}{1}$

STEP 4

Multiply the fractions.
$\frac{1 \times6}{18 \times1} = \frac{6}{18}$

STEP 5

implify the fraction.
$\frac{}{18} = \frac{1}{3}$

STEP 6

Now, substitute the result back into the original expression and perform the addition operation.
$\frac{1}{8}+\frac{1}{3}$

STEP 7

To add fractions, we need to find a common denominator. The least common denominator (LCD) of and3 is24.
$\frac{1 \times3}{ \times3} + \frac{1 \times}{3 \times}$

STEP 8

Perform the multiplication in each fraction.
$\frac{3}{24} + \frac{8}{24}$

STEP 9

Now, add the fractions.
$\frac{3 +8}{24} = \frac{11}{24}$ So, the solution to the expression $\frac{}{8}+\frac{}{18} \div \frac{}{6}$ is $\frac{11}{24}$ .

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QuestionCalculate the result of the expression: 18+118÷16\frac{1}{8}+\frac{1}{18} \div \frac{1}{6}81​+181​÷61​.

Studdy Solution

STEP 1

STEP 2

First, we need to perform the division operation in the expression, as per the order of operations.118÷16\frac{1}{18} \div \frac{1}{6}181​÷61​

STEP 3

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.118×61\frac{1}{18} \times \frac{6}{1}181​×16​

STEP 4

Multiply the fractions.1×618×1=618\frac{1 \times6}{18 \times1} = \frac{6}{18}18×11×6​=186​

STEP 5

implify the fraction.18=13\frac{}{18} = \frac{1}{3}18​=31​

STEP 6

Now, substitute the result back into the original expression and perform the addition operation.18+13\frac{1}{8}+\frac{1}{3}81​+31​

STEP 7

To add fractions, we need to find a common denominator. The least common denominator (LCD) of and3 is24.1×3×3+1×3×\frac{1 \times3}{ \times3} + \frac{1 \times}{3 \times}×31×3​+3×1×​

STEP 8

Perform the multiplication in each fraction.324+824\frac{3}{24} + \frac{8}{24}243​+248​

STEP 9

Now, add the fractions.3+824=1124\frac{3 +8}{24} = \frac{11}{24}243+8​=2411​So, the solution to the expression 8+18÷6\frac{}{8}+\frac{}{18} \div \frac{}{6}8​+18​÷6​ is 1124\frac{11}{24}2411​.

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QuestionCalculate the result of the expression: $\frac{1}{8}+\frac{1}{18} \div \frac{1}{6}$ .

First, we need to perform the division operation in the expression, as per the order of operations.
$\frac{1}{18} \div \frac{1}{6}$

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{1}{18} \times \frac{6}{1}$

Multiply the fractions.
$\frac{1 \times6}{18 \times1} = \frac{6}{18}$

implify the fraction.
$\frac{}{18} = \frac{1}{3}$

Now, substitute the result back into the original expression and perform the addition operation.
$\frac{1}{8}+\frac{1}{3}$

To add fractions, we need to find a common denominator. The least common denominator (LCD) of and3 is24.
$\frac{1 \times3}{ \times3} + \frac{1 \times}{3 \times}$

Perform the multiplication in each fraction.
$\frac{3}{24} + \frac{8}{24}$

Now, add the fractions.
$\frac{3 +8}{24} = \frac{11}{24}$ So, the solution to the expression $\frac{}{8}+\frac{}{18} \div \frac{}{6}$ is $\frac{11}{24}$ .