Basic Math Examples

$(5 \frac{4}{8} - 2 \frac{5}{6}) \cdot \frac{4}{12}$

Step 1

Convert $5 \frac{4}{8}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$(5 + \frac{4}{8} - 2 \frac{5}{6}) \cdot \frac{4}{12}$

Step 1.2

Add $5$ and $\frac{4}{8}$ .

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Step 1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(5 \cdot \frac{8}{8} + \frac{4}{8} - 2 \frac{5}{6}) \cdot \frac{4}{12}$

Step 1.2.2

Combine $5$ and $\frac{8}{8}$ .

$(\frac{5 \cdot 8}{8} + \frac{4}{8} - 2 \frac{5}{6}) \cdot \frac{4}{12}$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{5 \cdot 8 + 4}{8} - 2 \frac{5}{6}) \cdot \frac{4}{12}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $8$ .

$(\frac{40 + 4}{8} - 2 \frac{5}{6}) \cdot \frac{4}{12}$

Step 1.2.4.2

Add $40$ and $4$ .

$(\frac{44}{8} - 2 \frac{5}{6}) \cdot \frac{4}{12}$

Step 2

Convert $2 \frac{5}{6}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$(\frac{44}{8} - (2 + \frac{5}{6})) \cdot \frac{4}{12}$

Step 2.2

Add $2$ and $\frac{5}{6}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(\frac{44}{8} - (2 \cdot \frac{6}{6} + \frac{5}{6})) \cdot \frac{4}{12}$

Step 2.2.2

Combine $2$ and $\frac{6}{6}$ .

$(\frac{44}{8} - (\frac{2 \cdot 6}{6} + \frac{5}{6})) \cdot \frac{4}{12}$

Step 2.2.3

Combine the numerators over the common denominator.

$(\frac{44}{8} - \frac{2 \cdot 6 + 5}{6}) \cdot \frac{4}{12}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $6$ .

$(\frac{44}{8} - \frac{12 + 5}{6}) \cdot \frac{4}{12}$

Step 2.2.4.2

Add $12$ and $5$ .

$(\frac{44}{8} - \frac{17}{6}) \cdot \frac{4}{12}$

Step 3

Cancel the common factor of $44$ and $8$ .

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Step 3.1

Factor $4$ out of $44$ .

$(\frac{4 (11)}{8} - \frac{17}{6}) \cdot \frac{4}{12}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $8$ .

$(\frac{4 \cdot 11}{4 \cdot 2} - \frac{17}{6}) \cdot \frac{4}{12}$

Step 3.2.2

Cancel the common factor.

$(\frac{4 \cdot 11}{4 \cdot 2} - \frac{17}{6}) \cdot \frac{4}{12}$

Step 3.2.3

Rewrite the expression.

$(\frac{11}{2} - \frac{17}{6}) \cdot \frac{4}{12}$

Step 4

To write $\frac{11}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{11}{2} \cdot \frac{3}{3} - \frac{17}{6}) \cdot \frac{4}{12}$

Step 5

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

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Step 5.1

Multiply $\frac{11}{2}$ by $\frac{3}{3}$ .

$(\frac{11 \cdot 3}{2 \cdot 3} - \frac{17}{6}) \cdot \frac{4}{12}$

Step 5.2

Multiply $2$ by $3$ .

$(\frac{11 \cdot 3}{6} - \frac{17}{6}) \cdot \frac{4}{12}$

Step 6

Combine the numerators over the common denominator.

$\frac{11 \cdot 3 - 17}{6} \cdot \frac{4}{12}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $11$ by $3$ .

$\frac{33 - 17}{6} \cdot \frac{4}{12}$

Step 7.2

Subtract $17$ from $33$ .

$\frac{16}{6} \cdot \frac{4}{12}$

Step 8

Cancel the common factor of $4$ .

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Step 8.1

Factor $4$ out of $16$ .

$\frac{4 (4)}{6} \cdot \frac{4}{12}$

Step 8.2

Factor $4$ out of $12$ .

$\frac{4 \cdot 4}{6} \cdot \frac{4}{4 \cdot 3}$

Step 8.3

Cancel the common factor.

$\frac{4 \cdot 4}{6} \cdot \frac{4}{4 \cdot 3}$

Step 8.4

Rewrite the expression.

$\frac{4}{6} \cdot \frac{4}{3}$

Step 9

Cancel the common factor of $2$ .

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Step 9.1

Factor $2$ out of $6$ .

$\frac{4}{2 (3)} \cdot \frac{4}{3}$

Step 9.2

Factor $2$ out of $4$ .

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

Step 9.3

Cancel the common factor.

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

Step 9.4

Rewrite the expression.

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

Step 10

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

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

Step 11

Multiply.

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Step 11.1

Multiply $4$ by $2$ .

$\frac{8}{3 \cdot 3}$

Step 11.2

Multiply $3$ by $3$ .

$\frac{8}{9}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{9}$

Decimal Form:

$0.\overline{8}$