Basic Math Examples

6 \frac{1}{1} - 4 \frac{1}{4}

$6 \frac{1}{1} - 4 \frac{1}{4}$

Step 1

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

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

$6 + \frac{1}{1} - 4 \frac{1}{4}$

Step 2

Convert

4 \frac{1}{4}

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

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Step 2.1

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

6 + \frac{1}{1} - (4 + \frac{1}{4})

$6 + \frac{1}{1} - (4 + \frac{1}{4})$

Step 2.2

Add

4

$4$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 2.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

6 + \frac{1}{1} - (4 \cdot \frac{4}{4} + \frac{1}{4})

$6 + \frac{1}{1} - (4 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.2.2

Combine

4

$4$ and

\frac{4}{4}

$\frac{4}{4}$ .

6 + \frac{1}{1} - (\frac{4 \cdot 4}{4} + \frac{1}{4})

$6 + \frac{1}{1} - (\frac{4 \cdot 4}{4} + \frac{1}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

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

$6 + \frac{1}{1} - \frac{4 \cdot 4 + 1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

4

$4$ by

4

$4$ .

6 + \frac{1}{1} - \frac{16 + 1}{4}

$6 + \frac{1}{1} - \frac{16 + 1}{4}$

Step 2.2.4.2

Add

16

$16$ and

1

$1$ .

6 + \frac{1}{1} - \frac{17}{4}

$6 + \frac{1}{1} - \frac{17}{4}$

6 + \frac{1}{1} - \frac{17}{4}

$6 + \frac{1}{1} - \frac{17}{4}$

6 + \frac{1}{1} - \frac{17}{4}

$6 + \frac{1}{1} - \frac{17}{4}$

6 + \frac{1}{1} - \frac{17}{4}

$6 + \frac{1}{1} - \frac{17}{4}$

Step 3

Find the common denominator.

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Step 3.1

Write

6

$6$ as a fraction with denominator

1

$1$ .

\frac{6}{1} + \frac{1}{1} - \frac{17}{4}

$\frac{6}{1} + \frac{1}{1} - \frac{17}{4}$

Step 3.2

Multiply

\frac{6}{1}

$\frac{6}{1}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{6}{1} \cdot \frac{4}{4} + \frac{1}{1} - \frac{17}{4}

$\frac{6}{1} \cdot \frac{4}{4} + \frac{1}{1} - \frac{17}{4}$

Step 3.3

Multiply

\frac{6}{1}

$\frac{6}{1}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{6 \cdot 4}{4} + \frac{1}{1} - \frac{17}{4}

$\frac{6 \cdot 4}{4} + \frac{1}{1} - \frac{17}{4}$

Step 3.4

Multiply

\frac{1}{1}

$\frac{1}{1}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{6 \cdot 4}{4} + \frac{1}{1} \cdot \frac{4}{4} - \frac{17}{4}

$\frac{6 \cdot 4}{4} + \frac{1}{1} \cdot \frac{4}{4} - \frac{17}{4}$

Step 3.5

Multiply

\frac{1}{1}

$\frac{1}{1}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{6 \cdot 4}{4} + \frac{4}{4} - \frac{17}{4}

$\frac{6 \cdot 4}{4} + \frac{4}{4} - \frac{17}{4}$

\frac{6 \cdot 4}{4} + \frac{4}{4} - \frac{17}{4}

$\frac{6 \cdot 4}{4} + \frac{4}{4} - \frac{17}{4}$

Step 4

Combine the numerators over the common denominator.

\frac{6 \cdot 4 + 4 - 17}{4}

$\frac{6 \cdot 4 + 4 - 17}{4}$

Step 5

Simplify the expression.

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Step 5.1

Multiply

6

$6$ by

4

$4$ .

\frac{24 + 4 - 17}{4}

$\frac{24 + 4 - 17}{4}$

Step 5.2

Add

24

$24$ and

4

$4$ .

\frac{28 - 17}{4}

$\frac{28 - 17}{4}$

Step 5.3

Subtract

17

$17$ from

28

$28$ .

\frac{11}{4}

$\frac{11}{4}$

\frac{11}{4}

$\frac{11}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{11}{4}

$\frac{11}{4}$

Decimal Form:

2.75

$2.75$

Mixed Number Form:

2 \frac{3}{4}

$2 \frac{3}{4}$