Basic Math Examples

2 \frac{1}{4} \div \frac{2}{7}

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

Step 1

Convert

2 \frac{1}{4}

$2 \frac{1}{4}$ 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}{4}) \div \frac{2}{7}

$(2 + \frac{1}{4}) \div \frac{2}{7}$

Step 1.2

Add

2

$2$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 1.2.1

To write

2

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

\frac{4}{4}

$\frac{4}{4}$ .

(2 \cdot \frac{4}{4} + \frac{1}{4}) \div \frac{2}{7}

$(2 \cdot \frac{4}{4} + \frac{1}{4}) \div \frac{2}{7}$

Step 1.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

(\frac{2 \cdot 4}{4} + \frac{1}{4}) \div \frac{2}{7}

$(\frac{2 \cdot 4}{4} + \frac{1}{4}) \div \frac{2}{7}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 4 + 1}{4} \div \frac{2}{7}

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{8 + 1}{4} \div \frac{2}{7}

$\frac{8 + 1}{4} \div \frac{2}{7}$

Step 1.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{9}{4} \div \frac{2}{7}

$\frac{9}{4} \div \frac{2}{7}$

\frac{9}{4} \div \frac{2}{7}

$\frac{9}{4} \div \frac{2}{7}$

\frac{9}{4} \div \frac{2}{7}

$\frac{9}{4} \div \frac{2}{7}$

\frac{9}{4} \div \frac{2}{7}

$\frac{9}{4} \div \frac{2}{7}$

Step 2

To divide by a fraction, multiply by its reciprocal.

\frac{9}{4} \cdot \frac{7}{2}

$\frac{9}{4} \cdot \frac{7}{2}$

Step 3

Multiply

\frac{9}{4} \cdot \frac{7}{2}

$\frac{9}{4} \cdot \frac{7}{2}$ .

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Step 3.1

Multiply

\frac{9}{4}

$\frac{9}{4}$ by

\frac{7}{2}

$\frac{7}{2}$ .

\frac{9 \cdot 7}{4 \cdot 2}

$\frac{9 \cdot 7}{4 \cdot 2}$

Step 3.2

Multiply

9

$9$ by

7

$7$ .

\frac{63}{4 \cdot 2}

$\frac{63}{4 \cdot 2}$

Step 3.3

Multiply

4

$4$ by

2

$2$ .

\frac{63}{8}

$\frac{63}{8}$

\frac{63}{8}

$\frac{63}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{63}{8}

$\frac{63}{8}$

Decimal Form:

7.875

$7.875$

Mixed Number Form:

7 \frac{7}{8}

$7 \frac{7}{8}$