Basic Math Examples

5 \frac{3}{4} - 2 \frac{5}{6}

$5 \frac{3}{4} - 2 \frac{5}{6}$

Step 1

Convert

5 \frac{3}{4}

$5 \frac{3}{4}$ 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{3}{4} - 2 \frac{5}{6}

$5 + \frac{3}{4} - 2 \frac{5}{6}$

Step 1.2

Add

5

$5$ and

\frac{3}{4}

$\frac{3}{4}$ .

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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{3}{4} - 2 \frac{5}{6}

$5 \cdot \frac{4}{4} + \frac{3}{4} - 2 \frac{5}{6}$

Step 1.2.2

Combine

5

$5$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{5 \cdot 4}{4} + \frac{3}{4} - 2 \frac{5}{6}

$\frac{5 \cdot 4}{4} + \frac{3}{4} - 2 \frac{5}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{5 \cdot 4 + 3}{4} - 2 \frac{5}{6}

$\frac{5 \cdot 4 + 3}{4} - 2 \frac{5}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

4

$4$ .

\frac{20 + 3}{4} - 2 \frac{5}{6}

$\frac{20 + 3}{4} - 2 \frac{5}{6}$

Step 1.2.4.2

Add

20

$20$ and

3

$3$ .

\frac{23}{4} - 2 \frac{5}{6}

$\frac{23}{4} - 2 \frac{5}{6}$

\frac{23}{4} - 2 \frac{5}{6}

$\frac{23}{4} - 2 \frac{5}{6}$

\frac{23}{4} - 2 \frac{5}{6}

$\frac{23}{4} - 2 \frac{5}{6}$

\frac{23}{4} - 2 \frac{5}{6}

$\frac{23}{4} - 2 \frac{5}{6}$

Step 2

Convert

2 \frac{5}{6}

$2 \frac{5}{6}$ to an improper fraction.

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Step 2.1

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

\frac{23}{4} - (2 + \frac{5}{6})

$\frac{23}{4} - (2 + \frac{5}{6})$

Step 2.2

Add

2

$2$ and

\frac{5}{6}

$\frac{5}{6}$ .

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Step 2.2.1

To write

2

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

\frac{6}{6}

$\frac{6}{6}$ .

\frac{23}{4} - (2 \cdot \frac{6}{6} + \frac{5}{6})

$\frac{23}{4} - (2 \cdot \frac{6}{6} + \frac{5}{6})$

Step 2.2.2

Combine

2

$2$ and

\frac{6}{6}

$\frac{6}{6}$ .

\frac{23}{4} - (\frac{2 \cdot 6}{6} + \frac{5}{6})

$\frac{23}{4} - (\frac{2 \cdot 6}{6} + \frac{5}{6})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{23}{4} - \frac{2 \cdot 6 + 5}{6}

$\frac{23}{4} - \frac{2 \cdot 6 + 5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

6

$6$ .

\frac{23}{4} - \frac{12 + 5}{6}

$\frac{23}{4} - \frac{12 + 5}{6}$

Step 2.2.4.2

Add

12

$12$ and

5

$5$ .

\frac{23}{4} - \frac{17}{6}

$\frac{23}{4} - \frac{17}{6}$

\frac{23}{4} - \frac{17}{6}

$\frac{23}{4} - \frac{17}{6}$

\frac{23}{4} - \frac{17}{6}

$\frac{23}{4} - \frac{17}{6}$

\frac{23}{4} - \frac{17}{6}

$\frac{23}{4} - \frac{17}{6}$

Step 3

To write

\frac{23}{4}

$\frac{23}{4}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{23}{4} \cdot \frac{3}{3} - \frac{17}{6}

$\frac{23}{4} \cdot \frac{3}{3} - \frac{17}{6}$

Step 4

To write

- \frac{17}{6}

$- \frac{17}{6}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{23}{4} \cdot \frac{3}{3} - \frac{17}{6} \cdot \frac{2}{2}

$\frac{23}{4} \cdot \frac{3}{3} - \frac{17}{6} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of

12

$12$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.1

Multiply

\frac{23}{4}

$\frac{23}{4}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{23 \cdot 3}{4 \cdot 3} - \frac{17}{6} \cdot \frac{2}{2}

$\frac{23 \cdot 3}{4 \cdot 3} - \frac{17}{6} \cdot \frac{2}{2}$

Step 5.2

Multiply

4

$4$ by

3

$3$ .

\frac{23 \cdot 3}{12} - \frac{17}{6} \cdot \frac{2}{2}

$\frac{23 \cdot 3}{12} - \frac{17}{6} \cdot \frac{2}{2}$

Step 5.3

Multiply

\frac{17}{6}

$\frac{17}{6}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{23 \cdot 3}{12} - \frac{17 \cdot 2}{6 \cdot 2}

$\frac{23 \cdot 3}{12} - \frac{17 \cdot 2}{6 \cdot 2}$

Step 5.4

Multiply

6

$6$ by

2

$2$ .

\frac{23 \cdot 3}{12} - \frac{17 \cdot 2}{12}

$\frac{23 \cdot 3}{12} - \frac{17 \cdot 2}{12}$

\frac{23 \cdot 3}{12} - \frac{17 \cdot 2}{12}

$\frac{23 \cdot 3}{12} - \frac{17 \cdot 2}{12}$

Step 6

Combine the numerators over the common denominator.

\frac{23 \cdot 3 - 17 \cdot 2}{12}

$\frac{23 \cdot 3 - 17 \cdot 2}{12}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

23

$23$ by

3

$3$ .

\frac{69 - 17 \cdot 2}{12}

$\frac{69 - 17 \cdot 2}{12}$

Step 7.2

Multiply

- 17

$- 17$ by

2

$2$ .

\frac{69 - 34}{12}

$\frac{69 - 34}{12}$

Step 7.3

Subtract

34

$34$ from

69

$69$ .

\frac{35}{12}

$\frac{35}{12}$

\frac{35}{12}

$\frac{35}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{35}{12}

$\frac{35}{12}$

Decimal Form:

2.91\overline{6}

$2.91\overline{6}$

Mixed Number Form:

2 \frac{11}{12}

$2 \frac{11}{12}$