Basic Math Examples

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

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

Step 1

Convert

$4 \frac{3}{5}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add

$4$ and

$\frac{3}{5}$ .

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Step 1.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

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

Step 1.2.2

Combine

$4$ and

$\frac{5}{5}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$4$ by

$5$ .

$\frac{20 + 3}{5} - 2 \frac{1}{2}$

Step 1.2.4.2

Add

$20$ and

$3$ .

$\frac{23}{5} - 2 \frac{1}{2}$

Step 2

Convert

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

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Step 2.1

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

$\frac{23}{5} - (2 + \frac{1}{2})$

Step 2.2

Add

$2$ and

$\frac{1}{2}$ .

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Step 2.2.1

To write

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

$\frac{2}{2}$ .

$\frac{23}{5} - (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine

$2$ and

$\frac{2}{2}$ .

$\frac{23}{5} - (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{23}{5} - \frac{2 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$2$ .

$\frac{23}{5} - \frac{4 + 1}{2}$

Step 2.2.4.2

Add

$4$ and

$1$ .

$\frac{23}{5} - \frac{5}{2}$

Step 3

To write

$\frac{23}{5}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{23}{5} \cdot \frac{2}{2} - \frac{5}{2}$

Step 4

To write

$- \frac{5}{2}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{23}{5} \cdot \frac{2}{2} - \frac{5}{2} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of

$10$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{23}{5}$ by

$\frac{2}{2}$ .

$\frac{23 \cdot 2}{5 \cdot 2} - \frac{5}{2} \cdot \frac{5}{5}$

Step 5.2

Multiply

$5$ by

$2$ .

$\frac{23 \cdot 2}{10} - \frac{5}{2} \cdot \frac{5}{5}$

Step 5.3

Multiply

$\frac{5}{2}$ by

$\frac{5}{5}$ .

$\frac{23 \cdot 2}{10} - \frac{5 \cdot 5}{2 \cdot 5}$

Step 5.4

Multiply

$2$ by

$5$ .

$\frac{23 \cdot 2}{10} - \frac{5 \cdot 5}{10}$

Step 6

Combine the numerators over the common denominator.

$\frac{23 \cdot 2 - 5 \cdot 5}{10}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$23$ by

$2$ .

$\frac{46 - 5 \cdot 5}{10}$

Step 7.2

Multiply

$- 5$ by

$5$ .

$\frac{46 - 25}{10}$

Step 7.3

Subtract

$25$ from

$46$ .

$\frac{21}{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{21}{10}$

Decimal Form:

$2.1$

Mixed Number Form:

$2 \frac{1}{10}$