Basic Math Examples

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

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

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} - 3 \frac{3}{4}

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

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} - 3 \frac{3}{4}

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

Step 1.2.2

Combine

5

$5$ and

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

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} - 3 \frac{3}{4}

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

Step 1.2.4.2

Add

20

$20$ and

1

$1$ .

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

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

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

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

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

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

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

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

Step 2

Convert

3 \frac{3}{4}

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

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Step 2.1

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

\frac{21}{4} - (3 + \frac{3}{4})

$\frac{21}{4} - (3 + \frac{3}{4})$

Step 2.2

Add

3

$3$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 2.2.1

To write

3

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

\frac{4}{4}

$\frac{4}{4}$ .

\frac{21}{4} - (3 \cdot \frac{4}{4} + \frac{3}{4})

$\frac{21}{4} - (3 \cdot \frac{4}{4} + \frac{3}{4})$

Step 2.2.2

Combine

3

$3$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{21}{4} - (\frac{3 \cdot 4}{4} + \frac{3}{4})

$\frac{21}{4} - (\frac{3 \cdot 4}{4} + \frac{3}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{21}{4} - \frac{3 \cdot 4 + 3}{4}

$\frac{21}{4} - \frac{3 \cdot 4 + 3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

4

$4$ .

\frac{21}{4} - \frac{12 + 3}{4}

$\frac{21}{4} - \frac{12 + 3}{4}$

Step 2.2.4.2

Add

12

$12$ and

3

$3$ .

\frac{21}{4} - \frac{15}{4}

$\frac{21}{4} - \frac{15}{4}$

\frac{21}{4} - \frac{15}{4}

$\frac{21}{4} - \frac{15}{4}$

\frac{21}{4} - \frac{15}{4}

$\frac{21}{4} - \frac{15}{4}$

\frac{21}{4} - \frac{15}{4}

$\frac{21}{4} - \frac{15}{4}$

Step 3

Combine the numerators over the common denominator.

\frac{21 - 15}{4}

$\frac{21 - 15}{4}$

Step 4

Subtract

15

$15$ from

21

$21$ .

\frac{6}{4}

$\frac{6}{4}$

Step 5

Cancel the common factor of

6

$6$ and

4

$4$ .

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Step 5.1

Factor

2

$2$ out of

6

$6$ .

\frac{2 (3)}{4}

$\frac{2 (3)}{4}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor

2

$2$ out of

4

$4$ .

\frac{2 \cdot 3}{2 \cdot 2}

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

Step 5.2.2

Cancel the common factor.

\frac{2 \cdot 3}{2 \cdot 2}

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

Step 5.2.3

Rewrite the expression.

\frac{3}{2}

$\frac{3}{2}$

\frac{3}{2}

$\frac{3}{2}$

\frac{3}{2}

$\frac{3}{2}$