Basic Math Examples

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

Step 1

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $2$ and $\frac{1}{3}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.2.2

Combine $2$ and $\frac{3}{3}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $3$ .

$\frac{6 + 1}{3} - \frac{2}{3} + 1 \frac{4}{5}$

Step 1.2.4.2

Add $6$ and $1$ .

$\frac{7}{3} - \frac{2}{3} + 1 \frac{4}{5}$

Step 2

Convert $1 \frac{4}{5}$ to an improper fraction.

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Step 2.1

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

$\frac{7}{3} - \frac{2}{3} + 1 + \frac{4}{5}$

Step 2.2

Add $1$ and $\frac{4}{5}$ .

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Step 2.2.1

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

$\frac{7}{3} - \frac{2}{3} + \frac{5}{5} + \frac{4}{5}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{7}{3} - \frac{2}{3} + \frac{5 + 4}{5}$

Step 2.2.3

Add $5$ and $4$ .

$\frac{7}{3} - \frac{2}{3} + \frac{9}{5}$

Step 3

Combine the numerators over the common denominator.

$\frac{7 - 2}{3} + \frac{9}{5}$

Step 4

Subtract $2$ from $7$ .

$\frac{5}{3} + \frac{9}{5}$

Step 5

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5}{3} \cdot \frac{5}{5} + \frac{9}{5}$

Step 6

To write $\frac{9}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{3} \cdot \frac{5}{5} + \frac{9}{5} \cdot \frac{3}{3}$

Step 7

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{5}{3}$ by $\frac{5}{5}$ .

$\frac{5 \cdot 5}{3 \cdot 5} + \frac{9}{5} \cdot \frac{3}{3}$

Step 7.2

Multiply $3$ by $5$ .

$\frac{5 \cdot 5}{15} + \frac{9}{5} \cdot \frac{3}{3}$

Step 7.3

Multiply $\frac{9}{5}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 5}{15} + \frac{9 \cdot 3}{5 \cdot 3}$

Step 7.4

Multiply $5$ by $3$ .

$\frac{5 \cdot 5}{15} + \frac{9 \cdot 3}{15}$

Step 8

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 + 9 \cdot 3}{15}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $5$ by $5$ .

$\frac{25 + 9 \cdot 3}{15}$

Step 9.2

Multiply $9$ by $3$ .

$\frac{25 + 27}{15}$

Step 9.3

Add $25$ and $27$ .

$\frac{52}{15}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{52}{15}$

Decimal Form:

$3.4\overline{6}$

Mixed Number Form:

$3 \frac{7}{15}$