Basic Math Examples

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

Step 1

Convert $5 \frac{4}{9}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $5$ and $\frac{4}{9}$ .

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $9$ .

$\frac{45 + 4}{9} - 3 \frac{1}{3} - (4 \frac{2}{5} - 4)$

Step 1.2.4.2

Add $45$ and $4$ .

$\frac{49}{9} - 3 \frac{1}{3} - (4 \frac{2}{5} - 4)$

Step 2

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

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Step 2.1

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

$\frac{49}{9} - (3 + \frac{1}{3}) - (4 \frac{2}{5} - 4)$

Step 2.2

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

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Step 2.2.1

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

$\frac{49}{9} - (3 \cdot \frac{3}{3} + \frac{1}{3}) - (4 \frac{2}{5} - 4)$

Step 2.2.2

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

$\frac{49}{9} - (\frac{3 \cdot 3}{3} + \frac{1}{3}) - (4 \frac{2}{5} - 4)$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{49}{9} - \frac{3 \cdot 3 + 1}{3} - (4 \frac{2}{5} - 4)$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $3$ .

$\frac{49}{9} - \frac{9 + 1}{3} - (4 \frac{2}{5} - 4)$

Step 2.2.4.2

Add $9$ and $1$ .

$\frac{49}{9} - \frac{10}{3} - (4 \frac{2}{5} - 4)$

Step 3

Convert $4 \frac{2}{5}$ to an improper fraction.

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Step 3.1

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

$\frac{49}{9} - \frac{10}{3} - (4 + \frac{2}{5} - 4)$

Step 3.2

Add $4$ and $\frac{2}{5}$ .

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Step 3.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{49}{9} - \frac{10}{3} - (4 \cdot \frac{5}{5} + \frac{2}{5} - 4)$

Step 3.2.2

Combine $4$ and $\frac{5}{5}$ .

$\frac{49}{9} - \frac{10}{3} - (\frac{4 \cdot 5}{5} + \frac{2}{5} - 4)$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{49}{9} - \frac{10}{3} - (\frac{4 \cdot 5 + 2}{5} - 4)$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $4$ by $5$ .

$\frac{49}{9} - \frac{10}{3} - (\frac{20 + 2}{5} - 4)$

Step 3.2.4.2

Add $20$ and $2$ .

$\frac{49}{9} - \frac{10}{3} - (\frac{22}{5} - 4)$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{10}{3}$ by $\frac{3}{3}$ .

$\frac{49}{9} - (\frac{10}{3} \cdot \frac{3}{3}) - (\frac{22}{5} - 4)$

Step 4.2

Multiply $\frac{10}{3}$ by $\frac{3}{3}$ .

$\frac{49}{9} - \frac{10 \cdot 3}{3 \cdot 3} - (\frac{22}{5} - 4)$

Step 4.3

Write $- (\frac{22}{5} - 4)$ as a fraction with denominator $1$ .

$\frac{49}{9} - \frac{10 \cdot 3}{3 \cdot 3} + \frac{- (\frac{22}{5} - 4)}{1}$

Step 4.4

Multiply $\frac{- (\frac{22}{5} - 4)}{1}$ by $\frac{9}{9}$ .

$\frac{49}{9} - \frac{10 \cdot 3}{3 \cdot 3} + \frac{- (\frac{22}{5} - 4)}{1} \cdot \frac{9}{9}$

Step 4.5

Multiply $\frac{- (\frac{22}{5} - 4)}{1}$ by $\frac{9}{9}$ .

$\frac{49}{9} - \frac{10 \cdot 3}{3 \cdot 3} + \frac{- (\frac{22}{5} - 4) \cdot 9}{9}$

Step 4.6

Multiply $3$ by $3$ .

$\frac{49}{9} - \frac{10 \cdot 3}{9} + \frac{- (\frac{22}{5} - 4) \cdot 9}{9}$

Step 5

Combine the numerators over the common denominator.

$\frac{49 - 10 \cdot 3 - (\frac{22}{5} - 4) \cdot 9}{9}$

Step 6

Simplify each term.

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Step 6.1

Multiply $- 10$ by $3$ .

$\frac{49 - 30 - (\frac{22}{5} - 4) \cdot 9}{9}$

Step 6.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{49 - 30 - (\frac{22}{5} - 4 \cdot \frac{5}{5}) \cdot 9}{9}$

Step 6.3

Combine $- 4$ and $\frac{5}{5}$ .

$\frac{49 - 30 - (\frac{22}{5} + \frac{- 4 \cdot 5}{5}) \cdot 9}{9}$

Step 6.4

Combine the numerators over the common denominator.

$\frac{49 - 30 - \frac{22 - 4 \cdot 5}{5} \cdot 9}{9}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $- 4$ by $5$ .

$\frac{49 - 30 - \frac{22 - 20}{5} \cdot 9}{9}$

Step 6.5.2

Subtract $20$ from $22$ .

$\frac{49 - 30 - \frac{2}{5} \cdot 9}{9}$

Step 6.6

Multiply $- \frac{2}{5} \cdot 9$ .

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Step 6.6.1

Multiply $9$ by $- 1$ .

$\frac{49 - 30 - 9 (\frac{2}{5})}{9}$

Step 6.6.2

Combine $- 9$ and $\frac{2}{5}$ .

$\frac{49 - 30 + \frac{- 9 \cdot 2}{5}}{9}$

Step 6.6.3

Multiply $- 9$ by $2$ .

$\frac{49 - 30 + \frac{- 18}{5}}{9}$

Step 6.7

Move the negative in front of the fraction.

$\frac{49 - 30 - \frac{18}{5}}{9}$

Step 7

Find the common denominator.

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Step 7.1

Write $49$ as a fraction with denominator $1$ .

$\frac{\frac{49}{1} - 30 - \frac{18}{5}}{9}$

Step 7.2

Multiply $\frac{49}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{49}{1} \cdot \frac{5}{5} - 30 - \frac{18}{5}}{9}$

Step 7.3

Multiply $\frac{49}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{49 \cdot 5}{5} - 30 - \frac{18}{5}}{9}$

Step 7.4

Write $- 30$ as a fraction with denominator $1$ .

$\frac{\frac{49 \cdot 5}{5} + \frac{- 30}{1} - \frac{18}{5}}{9}$

Step 7.5

Multiply $\frac{- 30}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{49 \cdot 5}{5} + \frac{- 30}{1} \cdot \frac{5}{5} - \frac{18}{5}}{9}$

Step 7.6

Multiply $\frac{- 30}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{49 \cdot 5}{5} + \frac{- 30 \cdot 5}{5} - \frac{18}{5}}{9}$

Step 8

Combine the numerators over the common denominator.

$\frac{\frac{49 \cdot 5 - 30 \cdot 5 - 18}{5}}{9}$

Step 9

Simplify each term.

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Step 9.1

Multiply $49$ by $5$ .

$\frac{\frac{245 - 30 \cdot 5 - 18}{5}}{9}$

Step 9.2

Multiply $- 30$ by $5$ .

$\frac{\frac{245 - 150 - 18}{5}}{9}$

Step 10

Simplify by subtracting numbers.

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Step 10.1

Subtract $150$ from $245$ .

$\frac{\frac{95 - 18}{5}}{9}$

Step 10.2

Subtract $18$ from $95$ .

$\frac{\frac{77}{5}}{9}$

Step 11

Multiply the numerator by the reciprocal of the denominator.

$\frac{77}{5} \cdot \frac{1}{9}$

Step 12

Multiply $\frac{77}{5} \cdot \frac{1}{9}$ .

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Step 12.1

Multiply $\frac{77}{5}$ by $\frac{1}{9}$ .

$\frac{77}{5 \cdot 9}$

Step 12.2

Multiply $5$ by $9$ .

$\frac{77}{45}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{77}{45}$

Decimal Form:

$1.7\overline{1}$

Mixed Number Form:

$1 \frac{32}{45}$