Basic Math Examples

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

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.

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

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

$\frac{3}{3}$ .

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

Step 1.2.2

Combine

$6$ and

$\frac{3}{3}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$6$ by

$3$ .

$\frac{18 + 2}{3} - 2 \frac{3}{5}$

Step 1.2.4.2

Add

$18$ and

$2$ .

$\frac{20}{3} - 2 \frac{3}{5}$

Step 2

Convert

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

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Step 2.1

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

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

Step 2.2

Add

$2$ and

$\frac{3}{5}$ .

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Step 2.2.1

To write

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

$\frac{5}{5}$ .

$\frac{20}{3} - (2 \cdot \frac{5}{5} + \frac{3}{5})$

Step 2.2.2

Combine

$2$ and

$\frac{5}{5}$ .

$\frac{20}{3} - (\frac{2 \cdot 5}{5} + \frac{3}{5})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{20}{3} - \frac{2 \cdot 5 + 3}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$5$ .

$\frac{20}{3} - \frac{10 + 3}{5}$

Step 2.2.4.2

Add

$10$ and

$3$ .

$\frac{20}{3} - \frac{13}{5}$

Step 3

To write

$\frac{20}{3}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{20}{3} \cdot \frac{5}{5} - \frac{13}{5}$

Step 4

To write

$- \frac{13}{5}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{20}{3} \cdot \frac{5}{5} - \frac{13}{5} \cdot \frac{3}{3}$

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

$\frac{20}{3}$ by

$\frac{5}{5}$ .

$\frac{20 \cdot 5}{3 \cdot 5} - \frac{13}{5} \cdot \frac{3}{3}$

Step 5.2

Multiply

$3$ by

$5$ .

$\frac{20 \cdot 5}{15} - \frac{13}{5} \cdot \frac{3}{3}$

Step 5.3

Multiply

$\frac{13}{5}$ by

$\frac{3}{3}$ .

$\frac{20 \cdot 5}{15} - \frac{13 \cdot 3}{5 \cdot 3}$

Step 5.4

Multiply

$5$ by

$3$ .

$\frac{20 \cdot 5}{15} - \frac{13 \cdot 3}{15}$

Step 6

Combine the numerators over the common denominator.

$\frac{20 \cdot 5 - 13 \cdot 3}{15}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$20$ by

$5$ .

$\frac{100 - 13 \cdot 3}{15}$

Step 7.2

Multiply

$- 13$ by

$3$ .

$\frac{100 - 39}{15}$

Step 7.3

Subtract

$39$ from

$100$ .

$\frac{61}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{61}{15}$

Decimal Form:

$4.0\overline{6}$

Mixed Number Form:

$4 \frac{1}{15}$