QuestionSimplify the expression: $\frac{1}{2} + 5\left(\frac{1}{5} + \frac{2}{5}\right)$

Studdy Solution

STEP 1

Assumptions1. We are given the mathematical expression $\frac{1}{}+5\left(\frac{1}{5}+\frac{}{5}\right)$ . Our task is to simplify this expression following the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right).

STEP 2

First, we need to simplify the expression inside the parentheses. This is according to the order of operations (PEMDAS/BODMAS) which states that operations inside parentheses should be performed first.
$5\left(\frac{1}{5}+\frac{2}{5}\right)$

STEP 3

Add the fractions inside the parentheses.
$5\left(\frac{1}{5}+\frac{2}{5}\right) =5\left(\frac{3}{5}\right)$

STEP 4

Next, we need to multiply the result inside the parentheses by.
$\left(\frac{3}{}\right) =3$

STEP 5

Now, substitute the result back into the original expression.
$\frac{1}{2}+5\left(\frac{1}{5}+\frac{2}{5}\right) = \frac{1}{2} +3$

STEP 6

Finally, add the two numbers to simplify the expression.
$\frac{1}{2} +3 =3.5$ The simplified expression is3.5.

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QuestionSimplify the expression: $\frac{1}{2} + 5\left(\frac{1}{5} + \frac{2}{5}\right)$

Studdy Solution

STEP 1

STEP 2

First, we need to simplify the expression inside the parentheses. This is according to the order of operations (PEMDAS/BODMAS) which states that operations inside parentheses should be performed first.
$5\left(\frac{1}{5}+\frac{2}{5}\right)$

STEP 3

Add the fractions inside the parentheses.
$5\left(\frac{1}{5}+\frac{2}{5}\right) =5\left(\frac{3}{5}\right)$

STEP 4

Next, we need to multiply the result inside the parentheses by.
$\left(\frac{3}{}\right) =3$

STEP 5

Now, substitute the result back into the original expression.
$\frac{1}{2}+5\left(\frac{1}{5}+\frac{2}{5}\right) = \frac{1}{2} +3$

STEP 6

Finally, add the two numbers to simplify the expression.
$\frac{1}{2} +3 =3.5$ The simplified expression is3.5.

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QuestionSimplify the expression: 12+5(15+25) \frac{1}{2} + 5\left(\frac{1}{5} + \frac{2}{5}\right) 21​+5(51​+52​)

Studdy Solution

STEP 1

STEP 2

First, we need to simplify the expression inside the parentheses. This is according to the order of operations (PEMDAS/BODMAS) which states that operations inside parentheses should be performed first.5(15+25)5\left(\frac{1}{5}+\frac{2}{5}\right)5(51​+52​)

STEP 3

Add the fractions inside the parentheses.5(15+25)=5(35)5\left(\frac{1}{5}+\frac{2}{5}\right) =5\left(\frac{3}{5}\right)5(51​+52​)=5(53​)

STEP 4

Next, we need to multiply the result inside the parentheses by.(3)=3\left(\frac{3}{}\right) =3(3​)=3

STEP 5

Now, substitute the result back into the original expression.12+5(15+25)=12+3\frac{1}{2}+5\left(\frac{1}{5}+\frac{2}{5}\right) = \frac{1}{2} +321​+5(51​+52​)=21​+3

STEP 6

Finally, add the two numbers to simplify the expression.12+3=3.5\frac{1}{2} +3 =3.521​+3=3.5The simplified expression is3.5.

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QuestionSimplify the expression: $\frac{1}{2} + 5\left(\frac{1}{5} + \frac{2}{5}\right)$

First, we need to simplify the expression inside the parentheses. This is according to the order of operations (PEMDAS/BODMAS) which states that operations inside parentheses should be performed first.
$5\left(\frac{1}{5}+\frac{2}{5}\right)$

Add the fractions inside the parentheses.
$5\left(\frac{1}{5}+\frac{2}{5}\right) =5\left(\frac{3}{5}\right)$

Next, we need to multiply the result inside the parentheses by.
$\left(\frac{3}{}\right) =3$

Now, substitute the result back into the original expression.
$\frac{1}{2}+5\left(\frac{1}{5}+\frac{2}{5}\right) = \frac{1}{2} +3$

Finally, add the two numbers to simplify the expression.
$\frac{1}{2} +3 =3.5$ The simplified expression is3.5.