Basic Math Examples

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

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

Step 1

Convert

3 \frac{1}{4}

$3 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

3

$3$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 1.2.1

To write

3

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

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.2

Combine

3

$3$ and

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

4

$4$ .

\frac{12 + 1}{4} - 1 \frac{3}{4}

$\frac{12 + 1}{4} - 1 \frac{3}{4}$

Step 1.2.4.2

Add

12

$12$ and

1

$1$ .

\frac{13}{4} - 1 \frac{3}{4}

$\frac{13}{4} - 1 \frac{3}{4}$

\frac{13}{4} - 1 \frac{3}{4}

$\frac{13}{4} - 1 \frac{3}{4}$

\frac{13}{4} - 1 \frac{3}{4}

$\frac{13}{4} - 1 \frac{3}{4}$

\frac{13}{4} - 1 \frac{3}{4}

$\frac{13}{4} - 1 \frac{3}{4}$

Step 2

Convert

1 \frac{3}{4}

$1 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

\frac{13}{4} - (1 + \frac{3}{4})

$\frac{13}{4} - (1 + \frac{3}{4})$

Step 2.2

Add

1

$1$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{13}{4} - (\frac{4}{4} + \frac{3}{4})

$\frac{13}{4} - (\frac{4}{4} + \frac{3}{4})$

Step 2.2.2

Combine the numerators over the common denominator.

\frac{13}{4} - \frac{4 + 3}{4}

$\frac{13}{4} - \frac{4 + 3}{4}$

Step 2.2.3

Add

4

$4$ and

3

$3$ .

\frac{13}{4} - \frac{7}{4}

$\frac{13}{4} - \frac{7}{4}$

\frac{13}{4} - \frac{7}{4}

$\frac{13}{4} - \frac{7}{4}$

\frac{13}{4} - \frac{7}{4}

$\frac{13}{4} - \frac{7}{4}$

Step 3

Combine the numerators over the common denominator.

\frac{13 - 7}{4}

$\frac{13 - 7}{4}$

Step 4

Subtract

7

$7$ from

13

$13$ .

\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.

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

Step 5.2.3

Rewrite the expression.

$\frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$