Basic Math Examples

$2 \frac{1}{2} \div 1 \frac{5}{7}$

Step 1

Convert

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

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Step 1.1

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

$(2 + \frac{1}{2}) \div 1 \frac{5}{7}$

Step 1.2

Add

$2$ and

$\frac{1}{2}$ .

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Step 1.2.1

To write

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

$\frac{2}{2}$ .

$(2 \cdot \frac{2}{2} + \frac{1}{2}) \div 1 \frac{5}{7}$

Step 1.2.2

Combine

$2$ and

$\frac{2}{2}$ .

$(\frac{2 \cdot 2}{2} + \frac{1}{2}) \div 1 \frac{5}{7}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 1}{2} \div 1 \frac{5}{7}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$2$ .

$\frac{4 + 1}{2} \div 1 \frac{5}{7}$

Step 1.2.4.2

Add

$4$ and

$1$ .

$\frac{5}{2} \div 1 \frac{5}{7}$

Step 2

Convert

$1 \frac{5}{7}$ to an improper fraction.

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Step 2.1

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

$\frac{5}{2} \div (1 + \frac{5}{7})$

Step 2.2

Add

$1$ and

$\frac{5}{7}$ .

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Step 2.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{5}{2} \div (\frac{7}{7} + \frac{5}{7})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{5}{2} \div \frac{7 + 5}{7}$

Step 2.2.3

Add

$7$ and

$5$ .

$\frac{5}{2} \div \frac{12}{7}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{2} \cdot \frac{7}{12}$

Step 4

Multiply

$\frac{5}{2} \cdot \frac{7}{12}$ .

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Step 4.1

Multiply

$\frac{5}{2}$ by

$\frac{7}{12}$ .

$\frac{5 \cdot 7}{2 \cdot 12}$

Step 4.2

Multiply

$5$ by

$7$ .

$\frac{35}{2 \cdot 12}$

Step 4.3

Multiply

$2$ by

$12$ .

$\frac{35}{24}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{24}$

Decimal Form:

$1.458\overline{3}$

Mixed Number Form:

$1 \frac{11}{24}$