Basic Math Examples

$(\frac{3}{4} + \frac{2}{3} - \frac{1}{6}) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1

Simplify each term.

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Step 1.1

Find the common denominator.

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Step 1.1.1

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$(\frac{3}{4} \cdot \frac{3}{3} + \frac{2}{3} - \frac{1}{6}) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.1.2

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$(\frac{3 \cdot 3}{4 \cdot 3} + \frac{2}{3} - \frac{1}{6}) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.1.3

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$(\frac{3 \cdot 3}{4 \cdot 3} + \frac{2}{3} \cdot \frac{4}{4} - \frac{1}{6}) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.1.4

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$(\frac{3 \cdot 3}{4 \cdot 3} + \frac{2 \cdot 4}{3 \cdot 4} - \frac{1}{6}) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.1.5

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$(\frac{3 \cdot 3}{4 \cdot 3} + \frac{2 \cdot 4}{3 \cdot 4} - (\frac{1}{6} \cdot \frac{2}{2})) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.1.6

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$(\frac{3 \cdot 3}{4 \cdot 3} + \frac{2 \cdot 4}{3 \cdot 4} - \frac{2}{6 \cdot 2}) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.1.7

Reorder the factors of $4 \cdot 3$ .

$(\frac{3 \cdot 3}{3 \cdot 4} + \frac{2 \cdot 4}{3 \cdot 4} - \frac{2}{6 \cdot 2}) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.1.8

Multiply $3$ by $4$ .

$(\frac{3 \cdot 3}{12} + \frac{2 \cdot 4}{3 \cdot 4} - \frac{2}{6 \cdot 2}) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.1.9

Multiply $3$ by $4$ .

$(\frac{3 \cdot 3}{12} + \frac{2 \cdot 4}{12} - \frac{2}{6 \cdot 2}) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.1.10

Reorder the factors of $6 \cdot 2$ .

$(\frac{3 \cdot 3}{12} + \frac{2 \cdot 4}{12} - \frac{2}{2 \cdot 6}) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.1.11

Multiply $2$ by $6$ .

$(\frac{3 \cdot 3}{12} + \frac{2 \cdot 4}{12} - \frac{2}{12}) \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 2 \cdot 4 - 2}{12} \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $3$ by $3$ .

$\frac{9 + 2 \cdot 4 - 2}{12} \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.3.2

Multiply $2$ by $4$ .

$\frac{9 + 8 - 2}{12} \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.4

Add $9$ and $8$ .

$\frac{17 - 2}{12} \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.5

Subtract $2$ from $17$ .

$\frac{15}{12} \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.6

Cancel the common factor of $15$ and $12$ .

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Step 1.6.1

Factor $3$ out of $15$ .

$\frac{3 (5)}{12} \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $3$ out of $12$ .

$\frac{3 \cdot 5}{3 \cdot 4} \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.6.2.2

Cancel the common factor.

$\frac{3 \cdot 5}{3 \cdot 4} \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.6.2.3

Rewrite the expression.

$\frac{5}{4} \cdot \frac{1}{\frac{1}{2}} + \frac{4}{3}$

Step 1.7

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{4} \cdot (1 \cdot 2) + \frac{4}{3}$

Step 1.8

Cancel the common factor of $2$ .

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Step 1.8.1

Factor $2$ out of $4$ .

$\frac{5}{2 (2)} \cdot (1 \cdot 2) + \frac{4}{3}$

Step 1.8.2

Factor $2$ out of $1 \cdot 2$ .

$\frac{5}{2 (2)} \cdot (2 \cdot 1) + \frac{4}{3}$

Step 1.8.3

Cancel the common factor.

$\frac{5}{2 \cdot 2} \cdot (2 \cdot 1) + \frac{4}{3}$

Step 1.8.4

Rewrite the expression.

$\frac{5}{2} + \frac{4}{3}$

Step 2

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{2} \cdot \frac{3}{3} + \frac{4}{3}$

Step 3

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{2} \cdot \frac{3}{3} + \frac{4}{3} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{2}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{2 \cdot 3} + \frac{4}{3} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $3$ .

$\frac{5 \cdot 3}{6} + \frac{4}{3} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 3}{6} + \frac{4 \cdot 2}{3 \cdot 2}$

Step 4.4

Multiply $3$ by $2$ .

$\frac{5 \cdot 3}{6} + \frac{4 \cdot 2}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 4 \cdot 2}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $3$ .

$\frac{15 + 4 \cdot 2}{6}$

Step 6.2

Multiply $4$ by $2$ .

$\frac{15 + 8}{6}$

Step 6.3

Add $15$ and $8$ .

$\frac{23}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{6}$

Decimal Form:

$3.8\overline{3}$

Mixed Number Form:

$3 \frac{5}{6}$