Basic Math Examples

$3 \frac{1}{2} - \frac{2}{3}$

Step 1

Convert

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

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Step 1.1

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

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

Step 1.2

Add

$3$ and

$\frac{1}{2}$ .

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Step 1.2.1

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

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

Step 1.2.2

Combine

$3$ and

$\frac{2}{2}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$3$ by

$2$ .

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

Step 1.2.4.2

Add

$6$ and

$1$ .

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

Step 2

To write

$\frac{7}{2}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{7}{2} \cdot \frac{3}{3} - \frac{2}{3}$

Step 3

To write

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

$\frac{2}{2}$ .

$\frac{7}{2} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of

$6$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.1

Multiply

$\frac{7}{2}$ by

$\frac{3}{3}$ .

$\frac{7 \cdot 3}{2 \cdot 3} - \frac{2}{3} \cdot \frac{2}{2}$

Step 4.2

Multiply

$2$ by

$3$ .

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

Step 4.3

Multiply

$\frac{2}{3}$ by

$\frac{2}{2}$ .

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

Step 4.4

Multiply

$3$ by

$2$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$7$ by

$3$ .

$\frac{21 - 2 \cdot 2}{6}$

Step 6.2

Multiply

$- 2$ by

$2$ .

$\frac{21 - 4}{6}$

Step 6.3

Subtract

$4$ from

$21$ .

$\frac{17}{6}$