Basic Math Examples

10 - 5 \frac{2}{3}

$10 - 5 \frac{2}{3}$

Step 1

Convert

5 \frac{2}{3}

$5 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

10 - (5 + \frac{2}{3})

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

Step 1.2

Add

5

$5$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 1.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

10 - (5 \cdot \frac{3}{3} + \frac{2}{3})

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

Step 1.2.2

Combine

5

$5$ and

\frac{3}{3}

$\frac{3}{3}$ .

10 - (\frac{5 \cdot 3}{3} + \frac{2}{3})

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

Step 1.2.3

Combine the numerators over the common denominator.

10 - \frac{5 \cdot 3 + 2}{3}

$10 - \frac{5 \cdot 3 + 2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

3

$3$ .

10 - \frac{15 + 2}{3}

$10 - \frac{15 + 2}{3}$

Step 1.2.4.2

Add

15

$15$ and

2

$2$ .

10 - \frac{17}{3}

$10 - \frac{17}{3}$

10 - \frac{17}{3}

$10 - \frac{17}{3}$

10 - \frac{17}{3}

$10 - \frac{17}{3}$

10 - \frac{17}{3}

$10 - \frac{17}{3}$

Step 2

To write

10

$10$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

10 \cdot \frac{3}{3} - \frac{17}{3}

$10 \cdot \frac{3}{3} - \frac{17}{3}$

Step 3

Combine

10

$10$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{10 \cdot 3}{3} - \frac{17}{3}

$\frac{10 \cdot 3}{3} - \frac{17}{3}$

Step 4

Combine the numerators over the common denominator.

\frac{10 \cdot 3 - 17}{3}

$\frac{10 \cdot 3 - 17}{3}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

10

$10$ by

3

$3$ .

\frac{30 - 17}{3}

$\frac{30 - 17}{3}$

Step 5.2

Subtract

17

$17$ from

30

$30$ .

\frac{13}{3}

$\frac{13}{3}$

\frac{13}{3}

$\frac{13}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{13}{3}

$\frac{13}{3}$

Decimal Form:

4.\overline{3}

$4.\overline{3}$

Mixed Number Form:

4 \frac{1}{3}

$4 \frac{1}{3}$