Basic Math Examples

$5 \frac{7}{9} + (2 \frac{1}{3} - 1 \frac{1}{2})$

Step 1

Remove parentheses.

$5 \frac{7}{9} + 2 \frac{1}{3} - 1 \frac{1}{2}$

Step 2

Convert $5 \frac{7}{9}$ to an improper fraction.

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Step 2.1

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

$5 + \frac{7}{9} + 2 \frac{1}{3} - 1 \frac{1}{2}$

Step 2.2

Add $5$ and $\frac{7}{9}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$5 \cdot \frac{9}{9} + \frac{7}{9} + 2 \frac{1}{3} - 1 \frac{1}{2}$

Step 2.2.2

Combine $5$ and $\frac{9}{9}$ .

$\frac{5 \cdot 9}{9} + \frac{7}{9} + 2 \frac{1}{3} - 1 \frac{1}{2}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 9 + 7}{9} + 2 \frac{1}{3} - 1 \frac{1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $9$ .

$\frac{45 + 7}{9} + 2 \frac{1}{3} - 1 \frac{1}{2}$

Step 2.2.4.2

Add $45$ and $7$ .

$\frac{52}{9} + 2 \frac{1}{3} - 1 \frac{1}{2}$

Step 3

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 3.1

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

$\frac{52}{9} + 2 + \frac{1}{3} - 1 \frac{1}{2}$

Step 3.2

Add $2$ and $\frac{1}{3}$ .

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Step 3.2.1

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

$\frac{52}{9} + 2 \cdot \frac{3}{3} + \frac{1}{3} - 1 \frac{1}{2}$

Step 3.2.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{52}{9} + \frac{2 \cdot 3}{3} + \frac{1}{3} - 1 \frac{1}{2}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{52}{9} + \frac{2 \cdot 3 + 1}{3} - 1 \frac{1}{2}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $3$ .

$\frac{52}{9} + \frac{6 + 1}{3} - 1 \frac{1}{2}$

Step 3.2.4.2

Add $6$ and $1$ .

$\frac{52}{9} + \frac{7}{3} - 1 \frac{1}{2}$

Step 4

Convert $1 \frac{1}{2}$ to an improper fraction.

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Step 4.1

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

$\frac{52}{9} + \frac{7}{3} - (1 + \frac{1}{2})$

Step 4.2

Add $1$ and $\frac{1}{2}$ .

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Step 4.2.1

Write $1$ as a fraction with a common denominator.

$\frac{52}{9} + \frac{7}{3} - (\frac{2}{2} + \frac{1}{2})$

Step 4.2.2

Combine the numerators over the common denominator.

$\frac{52}{9} + \frac{7}{3} - \frac{2 + 1}{2}$

Step 4.2.3

Add $2$ and $1$ .

$\frac{52}{9} + \frac{7}{3} - \frac{3}{2}$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{52}{9}$ by $\frac{2}{2}$ .

$\frac{52}{9} \cdot \frac{2}{2} + \frac{7}{3} - \frac{3}{2}$

Step 5.2

Multiply $\frac{52}{9}$ by $\frac{2}{2}$ .

$\frac{52 \cdot 2}{9 \cdot 2} + \frac{7}{3} - \frac{3}{2}$

Step 5.3

Multiply $\frac{7}{3}$ by $\frac{6}{6}$ .

$\frac{52 \cdot 2}{9 \cdot 2} + \frac{7}{3} \cdot \frac{6}{6} - \frac{3}{2}$

Step 5.4

Multiply $\frac{7}{3}$ by $\frac{6}{6}$ .

$\frac{52 \cdot 2}{9 \cdot 2} + \frac{7 \cdot 6}{3 \cdot 6} - \frac{3}{2}$

Step 5.5

Multiply $\frac{3}{2}$ by $\frac{9}{9}$ .

$\frac{52 \cdot 2}{9 \cdot 2} + \frac{7 \cdot 6}{3 \cdot 6} - (\frac{3}{2} \cdot \frac{9}{9})$

Step 5.6

Multiply $\frac{3}{2}$ by $\frac{9}{9}$ .

$\frac{52 \cdot 2}{9 \cdot 2} + \frac{7 \cdot 6}{3 \cdot 6} - \frac{3 \cdot 9}{2 \cdot 9}$

Step 5.7

Reorder the factors of $9 \cdot 2$ .

$\frac{52 \cdot 2}{2 \cdot 9} + \frac{7 \cdot 6}{3 \cdot 6} - \frac{3 \cdot 9}{2 \cdot 9}$

Step 5.8

Multiply $2$ by $9$ .

$\frac{52 \cdot 2}{18} + \frac{7 \cdot 6}{3 \cdot 6} - \frac{3 \cdot 9}{2 \cdot 9}$

Step 5.9

Multiply $3$ by $6$ .

$\frac{52 \cdot 2}{18} + \frac{7 \cdot 6}{18} - \frac{3 \cdot 9}{2 \cdot 9}$

Step 5.10

Multiply $2$ by $9$ .

$\frac{52 \cdot 2}{18} + \frac{7 \cdot 6}{18} - \frac{3 \cdot 9}{18}$

Step 6

Combine the numerators over the common denominator.

$\frac{52 \cdot 2 + 7 \cdot 6 - 3 \cdot 9}{18}$

Step 7

Simplify each term.

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Step 7.1

Multiply $52$ by $2$ .

$\frac{104 + 7 \cdot 6 - 3 \cdot 9}{18}$

Step 7.2

Multiply $7$ by $6$ .

$\frac{104 + 42 - 3 \cdot 9}{18}$

Step 7.3

Multiply $- 3$ by $9$ .

$\frac{104 + 42 - 27}{18}$

Step 8

Simplify by adding and subtracting.

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Step 8.1

Add $104$ and $42$ .

$\frac{146 - 27}{18}$

Step 8.2

Subtract $27$ from $146$ .

$\frac{119}{18}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{119}{18}$

Decimal Form:

$6.6\overline{1}$

Mixed Number Form:

$6 \frac{11}{18}$