Simplify 4(1/2+1/5)+4

$4 (\frac{1}{2} + \frac{1}{5}) + 4$

Step 1

Simplify each term.

To write

$\frac{1}{2}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$4 (\frac{1}{2} \cdot \frac{5}{5} + \frac{1}{5}) + 4$

To write

$\frac{1}{5}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$4 (\frac{1}{2} \cdot \frac{5}{5} + \frac{1}{5} \cdot \frac{2}{2}) + 4$

Write each expression with a common denominator of

$10$ , by multiplying each by an appropriate factor of

$1$ .

Multiply

$\frac{1}{2}$ by

$\frac{5}{5}$ .

$4 (\frac{5}{2 \cdot 5} + \frac{1}{5} \cdot \frac{2}{2}) + 4$

Multiply

$2$ by

$5$ .

$4 (\frac{5}{10} + \frac{1}{5} \cdot \frac{2}{2}) + 4$

Multiply

$\frac{1}{5}$ by

$\frac{2}{2}$ .

$4 (\frac{5}{10} + \frac{2}{5 \cdot 2}) + 4$

Multiply

$5$ by

$2$ .

$4 (\frac{5}{10} + \frac{2}{10}) + 4$

Combine the numerators over the common denominator.

$4 \frac{5 + 2}{10} + 4$

Add

$5$ and

$2$ .

$4 (\frac{7}{10}) + 4$

Cancel the common factor of

$2$ .

Factor

$2$ out of

$4$ .

$2 (2) \frac{7}{10} + 4$

Factor

$2$ out of

$10$ .

$2 \cdot 2 \frac{7}{2 \cdot 5} + 4$

Cancel the common factor.

$2 \cdot 2 \frac{7}{2 \cdot 5} + 4$

Rewrite the expression.

$2 (\frac{7}{5}) + 4$

Combine

$2$ and

$\frac{7}{5}$ .

$\frac{2 \cdot 7}{5} + 4$

Multiply

$2$ by

$7$ .

$\frac{14}{5} + 4$

Step 2

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{14}{5} + 4 \cdot \frac{5}{5}$

Step 3

Combine

$4$ and

$\frac{5}{5}$ .

$\frac{14}{5} + \frac{4 \cdot 5}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{14 + 4 \cdot 5}{5}$

Step 5

Simplify the numerator.

Multiply

$4$ by

$5$ .

$\frac{14 + 20}{5}$

Add

$14$ and

$20$ .

$\frac{34}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{34}{5}$

Decimal Form:

$6.8$

Mixed Number Form:

$6 \frac{4}{5}$

Simplify 4(1/2+1/5)+4

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