Basic Math Examples

5 \frac{3}{7} - 2 \frac{6}{7}

$5 \frac{3}{7} - 2 \frac{6}{7}$

Step 1

Convert

5 \frac{3}{7}

$5 \frac{3}{7}$ 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{3}{7} - 2 \frac{6}{7}

$5 + \frac{3}{7} - 2 \frac{6}{7}$

Step 1.2

Add

5

$5$ and

\frac{3}{7}

$\frac{3}{7}$ .

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Step 1.2.1

To write

5

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

\frac{7}{7}

$\frac{7}{7}$ .

5 \cdot \frac{7}{7} + \frac{3}{7} - 2 \frac{6}{7}

$5 \cdot \frac{7}{7} + \frac{3}{7} - 2 \frac{6}{7}$

Step 1.2.2

Combine

5

$5$ and

\frac{7}{7}

$\frac{7}{7}$ .

\frac{5 \cdot 7}{7} + \frac{3}{7} - 2 \frac{6}{7}

$\frac{5 \cdot 7}{7} + \frac{3}{7} - 2 \frac{6}{7}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{5 \cdot 7 + 3}{7} - 2 \frac{6}{7}

$\frac{5 \cdot 7 + 3}{7} - 2 \frac{6}{7}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

7

$7$ .

\frac{35 + 3}{7} - 2 \frac{6}{7}

$\frac{35 + 3}{7} - 2 \frac{6}{7}$

Step 1.2.4.2

Add

35

$35$ and

3

$3$ .

\frac{38}{7} - 2 \frac{6}{7}

$\frac{38}{7} - 2 \frac{6}{7}$

\frac{38}{7} - 2 \frac{6}{7}

$\frac{38}{7} - 2 \frac{6}{7}$

\frac{38}{7} - 2 \frac{6}{7}

$\frac{38}{7} - 2 \frac{6}{7}$

\frac{38}{7} - 2 \frac{6}{7}

$\frac{38}{7} - 2 \frac{6}{7}$

Step 2

Convert

2 \frac{6}{7}

$2 \frac{6}{7}$ to an improper fraction.

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Step 2.1

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

\frac{38}{7} - (2 + \frac{6}{7})

$\frac{38}{7} - (2 + \frac{6}{7})$

Step 2.2

Add

2

$2$ and

\frac{6}{7}

$\frac{6}{7}$ .

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Step 2.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{38}{7} - (2 \cdot \frac{7}{7} + \frac{6}{7})

$\frac{38}{7} - (2 \cdot \frac{7}{7} + \frac{6}{7})$

Step 2.2.2

Combine

2

$2$ and

\frac{7}{7}

$\frac{7}{7}$ .

\frac{38}{7} - (\frac{2 \cdot 7}{7} + \frac{6}{7})

$\frac{38}{7} - (\frac{2 \cdot 7}{7} + \frac{6}{7})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{38}{7} - \frac{2 \cdot 7 + 6}{7}

$\frac{38}{7} - \frac{2 \cdot 7 + 6}{7}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

7

$7$ .

\frac{38}{7} - \frac{14 + 6}{7}

$\frac{38}{7} - \frac{14 + 6}{7}$

Step 2.2.4.2

Add

14

$14$ and

6

$6$ .

\frac{38}{7} - \frac{20}{7}

$\frac{38}{7} - \frac{20}{7}$

\frac{38}{7} - \frac{20}{7}

$\frac{38}{7} - \frac{20}{7}$

\frac{38}{7} - \frac{20}{7}

$\frac{38}{7} - \frac{20}{7}$

\frac{38}{7} - \frac{20}{7}

$\frac{38}{7} - \frac{20}{7}$

Step 3

Combine the numerators over the common denominator.

\frac{38 - 20}{7}

$\frac{38 - 20}{7}$

Step 4

Subtract

$20$ from

$38$ .

$\frac{18}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{18}{7}$

Decimal Form:

$2.\overline{571428}$

Mixed Number Form:

$2 \frac{4}{7}$