QuestionCalculate $\frac{1}{2}+\left(\frac{3}{8}-\frac{1}{8}\right)^{2}$ .

Studdy Solution

STEP 1

Assumptions1. We have the mathematical expression $\frac{1}{}+\left(\frac{3}{8}-\frac{1}{8}\right)^{}$ . . We need to follow the order of operations, also known as BIDMAS or PEMAS Brackets/parentheses, Indices/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

STEP 2

First, we need to solve the operation inside the parentheses.
$\frac{}{8}-\frac{1}{8}$

STEP 3

Subtract the fractions.
$\frac{3}{8}-\frac{1}{8} = \frac{2}{8}$

STEP 4

implify the fraction.
$\frac{2}{8} = \frac{1}{4}$

STEP 5

Now, we need to square the result from the operation inside the parentheses.
$\left(\frac{1}{4}\right)^{2}$

STEP 6

Square the fraction.
$\left(\frac{1}{4}\right)^{2} = \frac{1}{16}$

STEP 7

Now, we need to add the result from the squared operation to $\frac{1}{2}$ .
$\frac{1}{2} + \frac{1}{16}$

STEP 8

To add these fractions, we need to find a common denominator. The least common multiple of2 and16 is16.
$\frac{8}{16} + \frac{1}{16}$

STEP 9

Add the fractions.
$\frac{8}{16} + \frac{}{16} = \frac{9}{16}$ The solution to the given mathematical expression is $\frac{9}{16}$ .

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QuestionCalculate $\frac{1}{2}+\left(\frac{3}{8}-\frac{1}{8}\right)^{2}$ .

Studdy Solution

STEP 1

STEP 2

First, we need to solve the operation inside the parentheses.
$\frac{}{8}-\frac{1}{8}$

STEP 3

Subtract the fractions.
$\frac{3}{8}-\frac{1}{8} = \frac{2}{8}$

STEP 4

implify the fraction.
$\frac{2}{8} = \frac{1}{4}$

STEP 5

Now, we need to square the result from the operation inside the parentheses.
$\left(\frac{1}{4}\right)^{2}$

STEP 6

Square the fraction.
$\left(\frac{1}{4}\right)^{2} = \frac{1}{16}$

STEP 7

Now, we need to add the result from the squared operation to $\frac{1}{2}$ .
$\frac{1}{2} + \frac{1}{16}$

STEP 8

To add these fractions, we need to find a common denominator. The least common multiple of2 and16 is16.
$\frac{8}{16} + \frac{1}{16}$

STEP 9

Add the fractions.
$\frac{8}{16} + \frac{}{16} = \frac{9}{16}$ The solution to the given mathematical expression is $\frac{9}{16}$ .

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QuestionCalculate 12+(38−18)2\frac{1}{2}+\left(\frac{3}{8}-\frac{1}{8}\right)^{2}21​+(83​−81​)2.

Studdy Solution

STEP 1

STEP 2

First, we need to solve the operation inside the parentheses.8−18\frac{}{8}-\frac{1}{8}8​−81​

STEP 3

Subtract the fractions.38−18=28\frac{3}{8}-\frac{1}{8} = \frac{2}{8}83​−81​=82​

STEP 4

implify the fraction.28=14\frac{2}{8} = \frac{1}{4}82​=41​

STEP 5

Now, we need to square the result from the operation inside the parentheses.(14)2\left(\frac{1}{4}\right)^{2}(41​)2

STEP 6

Square the fraction.(14)2=116\left(\frac{1}{4}\right)^{2} = \frac{1}{16}(41​)2=161​

STEP 7

Now, we need to add the result from the squared operation to 12\frac{1}{2}21​.12+116\frac{1}{2} + \frac{1}{16}21​+161​

STEP 8

To add these fractions, we need to find a common denominator. The least common multiple of2 and16 is16.816+116\frac{8}{16} + \frac{1}{16}168​+161​

STEP 9

Add the fractions.816+16=916\frac{8}{16} + \frac{}{16} = \frac{9}{16}168​+16​=169​The solution to the given mathematical expression is 916\frac{9}{16}169​.

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QuestionCalculate $\frac{1}{2}+\left(\frac{3}{8}-\frac{1}{8}\right)^{2}$ .

First, we need to solve the operation inside the parentheses.
$\frac{}{8}-\frac{1}{8}$

Subtract the fractions.
$\frac{3}{8}-\frac{1}{8} = \frac{2}{8}$

implify the fraction.
$\frac{2}{8} = \frac{1}{4}$

Now, we need to square the result from the operation inside the parentheses.
$\left(\frac{1}{4}\right)^{2}$

Square the fraction.
$\left(\frac{1}{4}\right)^{2} = \frac{1}{16}$

Now, we need to add the result from the squared operation to $\frac{1}{2}$ .
$\frac{1}{2} + \frac{1}{16}$

To add these fractions, we need to find a common denominator. The least common multiple of2 and16 is16.
$\frac{8}{16} + \frac{1}{16}$

Add the fractions.
$\frac{8}{16} + \frac{}{16} = \frac{9}{16}$ The solution to the given mathematical expression is $\frac{9}{16}$ .