Basic Math Examples

$(6 \frac{2}{3} - 1 \frac{7}{9}) - (5 \frac{4}{7} - 2)$

Step 1

Convert $6 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$6 + \frac{2}{3} - 1 \frac{7}{9} - (5 \frac{4}{7} - 2)$

Step 1.2

Add $6$ and $\frac{2}{3}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$6 \cdot \frac{3}{3} + \frac{2}{3} - 1 \frac{7}{9} - (5 \frac{4}{7} - 2)$

Step 1.2.2

Combine $6$ and $\frac{3}{3}$ .

$\frac{6 \cdot 3}{3} + \frac{2}{3} - 1 \frac{7}{9} - (5 \frac{4}{7} - 2)$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{6 \cdot 3 + 2}{3} - 1 \frac{7}{9} - (5 \frac{4}{7} - 2)$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $3$ .

$\frac{18 + 2}{3} - 1 \frac{7}{9} - (5 \frac{4}{7} - 2)$

Step 1.2.4.2

Add $18$ and $2$ .

$\frac{20}{3} - 1 \frac{7}{9} - (5 \frac{4}{7} - 2)$

Step 2

Convert $1 \frac{7}{9}$ to an improper fraction.

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Step 2.1

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

$\frac{20}{3} - (1 + \frac{7}{9}) - (5 \frac{4}{7} - 2)$

Step 2.2

Add $1$ and $\frac{7}{9}$ .

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Step 2.2.1

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

$\frac{20}{3} - (\frac{9}{9} + \frac{7}{9}) - (5 \frac{4}{7} - 2)$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{20}{3} - \frac{9 + 7}{9} - (5 \frac{4}{7} - 2)$

Step 2.2.3

Add $9$ and $7$ .

$\frac{20}{3} - \frac{16}{9} - (5 \frac{4}{7} - 2)$

Step 3

Convert $5 \frac{4}{7}$ to an improper fraction.

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Step 3.1

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

$\frac{20}{3} - \frac{16}{9} - (5 + \frac{4}{7} - 2)$

Step 3.2

Add $5$ and $\frac{4}{7}$ .

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Step 3.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{20}{3} - \frac{16}{9} - (5 \cdot \frac{7}{7} + \frac{4}{7} - 2)$

Step 3.2.2

Combine $5$ and $\frac{7}{7}$ .

$\frac{20}{3} - \frac{16}{9} - (\frac{5 \cdot 7}{7} + \frac{4}{7} - 2)$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{20}{3} - \frac{16}{9} - (\frac{5 \cdot 7 + 4}{7} - 2)$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $5$ by $7$ .

$\frac{20}{3} - \frac{16}{9} - (\frac{35 + 4}{7} - 2)$

Step 3.2.4.2

Add $35$ and $4$ .

$\frac{20}{3} - \frac{16}{9} - (\frac{39}{7} - 2)$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{20}{3}$ by $\frac{3}{3}$ .

$\frac{20}{3} \cdot \frac{3}{3} - \frac{16}{9} - (\frac{39}{7} - 2)$

Step 4.2

Multiply $\frac{20}{3}$ by $\frac{3}{3}$ .

$\frac{20 \cdot 3}{3 \cdot 3} - \frac{16}{9} - (\frac{39}{7} - 2)$

Step 4.3

Write $- (\frac{39}{7} - 2)$ as a fraction with denominator $1$ .

$\frac{20 \cdot 3}{3 \cdot 3} - \frac{16}{9} + \frac{- (\frac{39}{7} - 2)}{1}$

Step 4.4

Multiply $\frac{- (\frac{39}{7} - 2)}{1}$ by $\frac{9}{9}$ .

$\frac{20 \cdot 3}{3 \cdot 3} - \frac{16}{9} + \frac{- (\frac{39}{7} - 2)}{1} \cdot \frac{9}{9}$

Step 4.5

Multiply $\frac{- (\frac{39}{7} - 2)}{1}$ by $\frac{9}{9}$ .

$\frac{20 \cdot 3}{3 \cdot 3} - \frac{16}{9} + \frac{- (\frac{39}{7} - 2) \cdot 9}{9}$

Step 4.6

Multiply $3$ by $3$ .

$\frac{20 \cdot 3}{9} - \frac{16}{9} + \frac{- (\frac{39}{7} - 2) \cdot 9}{9}$

Step 5

Combine the numerators over the common denominator.

$\frac{20 \cdot 3 - 16 - (\frac{39}{7} - 2) \cdot 9}{9}$

Step 6

Simplify each term.

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Step 6.1

Multiply $20$ by $3$ .

$\frac{60 - 16 - (\frac{39}{7} - 2) \cdot 9}{9}$

Step 6.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{60 - 16 - (\frac{39}{7} - 2 \cdot \frac{7}{7}) \cdot 9}{9}$

Step 6.3

Combine $- 2$ and $\frac{7}{7}$ .

$\frac{60 - 16 - (\frac{39}{7} + \frac{- 2 \cdot 7}{7}) \cdot 9}{9}$

Step 6.4

Combine the numerators over the common denominator.

$\frac{60 - 16 - \frac{39 - 2 \cdot 7}{7} \cdot 9}{9}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $- 2$ by $7$ .

$\frac{60 - 16 - \frac{39 - 14}{7} \cdot 9}{9}$

Step 6.5.2

Subtract $14$ from $39$ .

$\frac{60 - 16 - \frac{25}{7} \cdot 9}{9}$

Step 6.6

Multiply $- \frac{25}{7} \cdot 9$ .

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Step 6.6.1

Multiply $9$ by $- 1$ .

$\frac{60 - 16 - 9 (\frac{25}{7})}{9}$

Step 6.6.2

Combine $- 9$ and $\frac{25}{7}$ .

$\frac{60 - 16 + \frac{- 9 \cdot 25}{7}}{9}$

Step 6.6.3

Multiply $- 9$ by $25$ .

$\frac{60 - 16 + \frac{- 225}{7}}{9}$

Step 6.7

Move the negative in front of the fraction.

$\frac{60 - 16 - \frac{225}{7}}{9}$

Step 7

Find the common denominator.

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Step 7.1

Write $60$ as a fraction with denominator $1$ .

$\frac{\frac{60}{1} - 16 - \frac{225}{7}}{9}$

Step 7.2

Multiply $\frac{60}{1}$ by $\frac{7}{7}$ .

$\frac{\frac{60}{1} \cdot \frac{7}{7} - 16 - \frac{225}{7}}{9}$

Step 7.3

Multiply $\frac{60}{1}$ by $\frac{7}{7}$ .

$\frac{\frac{60 \cdot 7}{7} - 16 - \frac{225}{7}}{9}$

Step 7.4

Write $- 16$ as a fraction with denominator $1$ .

$\frac{\frac{60 \cdot 7}{7} + \frac{- 16}{1} - \frac{225}{7}}{9}$

Step 7.5

Multiply $\frac{- 16}{1}$ by $\frac{7}{7}$ .

$\frac{\frac{60 \cdot 7}{7} + \frac{- 16}{1} \cdot \frac{7}{7} - \frac{225}{7}}{9}$

Step 7.6

Multiply $\frac{- 16}{1}$ by $\frac{7}{7}$ .

$\frac{\frac{60 \cdot 7}{7} + \frac{- 16 \cdot 7}{7} - \frac{225}{7}}{9}$

Step 8

Combine the numerators over the common denominator.

$\frac{\frac{60 \cdot 7 - 16 \cdot 7 - 225}{7}}{9}$

Step 9

Simplify each term.

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Step 9.1

Multiply $60$ by $7$ .

$\frac{\frac{420 - 16 \cdot 7 - 225}{7}}{9}$

Step 9.2

Multiply $- 16$ by $7$ .

$\frac{\frac{420 - 112 - 225}{7}}{9}$

Step 10

Simplify by subtracting numbers.

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Step 10.1

Subtract $112$ from $420$ .

$\frac{\frac{308 - 225}{7}}{9}$

Step 10.2

Subtract $225$ from $308$ .

$\frac{\frac{83}{7}}{9}$

Step 11

Multiply the numerator by the reciprocal of the denominator.

$\frac{83}{7} \cdot \frac{1}{9}$

Step 12

Multiply $\frac{83}{7} \cdot \frac{1}{9}$ .

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Step 12.1

Multiply $\frac{83}{7}$ by $\frac{1}{9}$ .

$\frac{83}{7 \cdot 9}$

Step 12.2

Multiply $7$ by $9$ .

$\frac{83}{63}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{83}{63}$

Decimal Form:

$1.\overline{317460}$

Mixed Number Form:

$1 \frac{20}{63}$