Basic Math Examples

6 \frac{3}{5} - 3 \frac{1}{3}

$6 \frac{3}{5} - 3 \frac{1}{3}$

Step 1

Convert

6 \frac{3}{5}

$6 \frac{3}{5}$ 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{3}{5} - 3 \frac{1}{3}

$6 + \frac{3}{5} - 3 \frac{1}{3}$

Step 1.2

Add

6

$6$ and

\frac{3}{5}

$\frac{3}{5}$ .

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Step 1.2.1

To write

6

$6$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

6 \cdot \frac{5}{5} + \frac{3}{5} - 3 \frac{1}{3}

$6 \cdot \frac{5}{5} + \frac{3}{5} - 3 \frac{1}{3}$

Step 1.2.2

Combine

6

$6$ and

\frac{5}{5}

$\frac{5}{5}$ .

\frac{6 \cdot 5}{5} + \frac{3}{5} - 3 \frac{1}{3}

$\frac{6 \cdot 5}{5} + \frac{3}{5} - 3 \frac{1}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{6 \cdot 5 + 3}{5} - 3 \frac{1}{3}

$\frac{6 \cdot 5 + 3}{5} - 3 \frac{1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

6

$6$ by

5

$5$ .

\frac{30 + 3}{5} - 3 \frac{1}{3}

$\frac{30 + 3}{5} - 3 \frac{1}{3}$

Step 1.2.4.2

Add

30

$30$ and

3

$3$ .

\frac{33}{5} - 3 \frac{1}{3}

$\frac{33}{5} - 3 \frac{1}{3}$

\frac{33}{5} - 3 \frac{1}{3}

$\frac{33}{5} - 3 \frac{1}{3}$

\frac{33}{5} - 3 \frac{1}{3}

$\frac{33}{5} - 3 \frac{1}{3}$

\frac{33}{5} - 3 \frac{1}{3}

$\frac{33}{5} - 3 \frac{1}{3}$

Step 2

Convert

3 \frac{1}{3}

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

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Step 2.1

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

\frac{33}{5} - (3 + \frac{1}{3})

$\frac{33}{5} - (3 + \frac{1}{3})$

Step 2.2

Add

3

$3$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 2.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

$\frac{33}{5} - (3 \cdot \frac{3}{3} + \frac{1}{3})$

Step 2.2.2

Combine

$3$ and

$\frac{3}{3}$ .

$\frac{33}{5} - (\frac{3 \cdot 3}{3} + \frac{1}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{33}{5} - \frac{3 \cdot 3 + 1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$3$ .

$\frac{33}{5} - \frac{9 + 1}{3}$

Step 2.2.4.2

Add

$9$ and

$1$ .

$\frac{33}{5} - \frac{10}{3}$

Step 3

To write

$\frac{33}{5}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{33}{5} \cdot \frac{3}{3} - \frac{10}{3}$

Step 4

To write

$- \frac{10}{3}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{33}{5} \cdot \frac{3}{3} - \frac{10}{3} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of

$15$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{33}{5}$ by

$\frac{3}{3}$ .

$\frac{33 \cdot 3}{5 \cdot 3} - \frac{10}{3} \cdot \frac{5}{5}$

Step 5.2

Multiply

$5$ by

$3$ .

$\frac{33 \cdot 3}{15} - \frac{10}{3} \cdot \frac{5}{5}$

Step 5.3

Multiply

$\frac{10}{3}$ by

$\frac{5}{5}$ .

$\frac{33 \cdot 3}{15} - \frac{10 \cdot 5}{3 \cdot 5}$

Step 5.4

Multiply

$3$ by

$5$ .

$\frac{33 \cdot 3}{15} - \frac{10 \cdot 5}{15}$

Step 6

Combine the numerators over the common denominator.

$\frac{33 \cdot 3 - 10 \cdot 5}{15}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$33$ by

$3$ .

$\frac{99 - 10 \cdot 5}{15}$

Step 7.2

Multiply

$- 10$ by

$5$ .

$\frac{99 - 50}{15}$

Step 7.3

Subtract

$50$ from

$99$ .

$\frac{49}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{49}{15}$

Decimal Form:

$3.2\overline{6}$

Mixed Number Form:

$3 \frac{4}{15}$