Basic Math Examples

$8 \frac{2}{3} - 7 \frac{3}{5}$

Step 1

Convert $8 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$8 + \frac{2}{3} - 7 \frac{3}{5}$

Step 1.2

Add $8$ and $\frac{2}{3}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$8 \cdot \frac{3}{3} + \frac{2}{3} - 7 \frac{3}{5}$

Step 1.2.2

Combine $8$ and $\frac{3}{3}$ .

$\frac{8 \cdot 3}{3} + \frac{2}{3} - 7 \frac{3}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 3 + 2}{3} - 7 \frac{3}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $3$ .

$\frac{24 + 2}{3} - 7 \frac{3}{5}$

Step 1.2.4.2

Add $24$ and $2$ .

$\frac{26}{3} - 7 \frac{3}{5}$

Step 2

Convert $7 \frac{3}{5}$ to an improper fraction.

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Step 2.1

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

$\frac{26}{3} - (7 + \frac{3}{5})$

Step 2.2

Add $7$ and $\frac{3}{5}$ .

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Step 2.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{26}{3} - (7 \cdot \frac{5}{5} + \frac{3}{5})$

Step 2.2.2

Combine $7$ and $\frac{5}{5}$ .

$\frac{26}{3} - (\frac{7 \cdot 5}{5} + \frac{3}{5})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{26}{3} - \frac{7 \cdot 5 + 3}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $7$ by $5$ .

$\frac{26}{3} - \frac{35 + 3}{5}$

Step 2.2.4.2

Add $35$ and $3$ .

$\frac{26}{3} - \frac{38}{5}$

Step 3

To write $\frac{26}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{26}{3} \cdot \frac{5}{5} - \frac{38}{5}$

Step 4

To write $- \frac{38}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{26}{3} \cdot \frac{5}{5} - \frac{38}{5} \cdot \frac{3}{3}$

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 $\frac{26}{3}$ by $\frac{5}{5}$ .

$\frac{26 \cdot 5}{3 \cdot 5} - \frac{38}{5} \cdot \frac{3}{3}$

Step 5.2

Multiply $3$ by $5$ .

$\frac{26 \cdot 5}{15} - \frac{38}{5} \cdot \frac{3}{3}$

Step 5.3

Multiply $\frac{38}{5}$ by $\frac{3}{3}$ .

$\frac{26 \cdot 5}{15} - \frac{38 \cdot 3}{5 \cdot 3}$

Step 5.4

Multiply $5$ by $3$ .

$\frac{26 \cdot 5}{15} - \frac{38 \cdot 3}{15}$

Step 6

Combine the numerators over the common denominator.

$\frac{26 \cdot 5 - 38 \cdot 3}{15}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $26$ by $5$ .

$\frac{130 - 38 \cdot 3}{15}$

Step 7.2

Multiply $- 38$ by $3$ .

$\frac{130 - 114}{15}$

Step 7.3

Subtract $114$ from $130$ .

$\frac{16}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{15}$

Decimal Form:

$1.0\overline{6}$

Mixed Number Form:

$1 \frac{1}{15}$