Basic Math Examples

5 \frac{1}{4} \div 3

$5 \frac{1}{4} \div 3$

Step 1

Convert

5 \frac{1}{4}

$5 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

(5 + \frac{1}{4}) \div 3

$(5 + \frac{1}{4}) \div 3$

Step 1.2

Add

5

$5$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 1.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

(5 \cdot \frac{4}{4} + \frac{1}{4}) \div 3

$(5 \cdot \frac{4}{4} + \frac{1}{4}) \div 3$

Step 1.2.2

Combine

5

$5$ and

\frac{4}{4}

$\frac{4}{4}$ .

(\frac{5 \cdot 4}{4} + \frac{1}{4}) \div 3

$(\frac{5 \cdot 4}{4} + \frac{1}{4}) \div 3$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{5 \cdot 4 + 1}{4} \div 3

$\frac{5 \cdot 4 + 1}{4} \div 3$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

4

$4$ .

\frac{20 + 1}{4} \div 3

$\frac{20 + 1}{4} \div 3$

Step 1.2.4.2

Add

20

$20$ and

1

$1$ .

\frac{21}{4} \div 3

$\frac{21}{4} \div 3$

\frac{21}{4} \div 3

$\frac{21}{4} \div 3$

\frac{21}{4} \div 3

$\frac{21}{4} \div 3$

\frac{21}{4} \div 3

$\frac{21}{4} \div 3$

Step 2

Rewrite the division as a fraction.

\frac{\frac{21}{4}}{3}

$\frac{\frac{21}{4}}{3}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

\frac{21}{4} \cdot \frac{1}{3}

$\frac{21}{4} \cdot \frac{1}{3}$

Step 4

Cancel the common factor of

3

$3$ .

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Step 4.1

Factor

3

$3$ out of

21

$21$ .

\frac{3 (7)}{4} \cdot \frac{1}{3}

$\frac{3 (7)}{4} \cdot \frac{1}{3}$

Step 4.2

Cancel the common factor.

$\frac{3 \cdot 7}{4} \cdot \frac{1}{3}$

Step 4.3

Rewrite the expression.

$\frac{7}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{4}$

Decimal Form:

$1.75$

Mixed Number Form:

$1 \frac{3}{4}$