Basic Math Examples

2 \frac{3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}

$2 \frac{3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}$

Step 1

Convert

2 \frac{3}{8}

$2 \frac{3}{8}$ to an improper fraction.

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Step 1.1

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

2 + \frac{3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}

$2 + \frac{3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}$

Step 1.2

Add

2

$2$ and

\frac{3}{8}

$\frac{3}{8}$ .

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Step 1.2.1

To write

2

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

\frac{8}{8}

$\frac{8}{8}$ .

2 \cdot \frac{8}{8} + \frac{3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}

$2 \cdot \frac{8}{8} + \frac{3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}$

Step 1.2.2

Combine

2

$2$ and

\frac{8}{8}

$\frac{8}{8}$ .

\frac{2 \cdot 8}{8} + \frac{3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}

$\frac{2 \cdot 8}{8} + \frac{3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 8 + 3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}

$\frac{2 \cdot 8 + 3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

8

$8$ .

\frac{16 + 3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}

$\frac{16 + 3}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}$

Step 1.2.4.2

Add

16

$16$ and

3

$3$ .

\frac{19}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}

$\frac{19}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}$

\frac{19}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}

$\frac{19}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}$

\frac{19}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}

$\frac{19}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}$

\frac{19}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}

$\frac{19}{8} + 3 \frac{2}{3} - 1 \frac{5}{6}$

Step 2

Convert

3 \frac{2}{3}

$3 \frac{2}{3}$ to an improper fraction.

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Step 2.1

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

\frac{19}{8} + 3 + \frac{2}{3} - 1 \frac{5}{6}

$\frac{19}{8} + 3 + \frac{2}{3} - 1 \frac{5}{6}$

Step 2.2

Add

3

$3$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 2.2.1

To write

3

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

\frac{3}{3}

$\frac{3}{3}$ .

\frac{19}{8} + 3 \cdot \frac{3}{3} + \frac{2}{3} - 1 \frac{5}{6}

$\frac{19}{8} + 3 \cdot \frac{3}{3} + \frac{2}{3} - 1 \frac{5}{6}$

Step 2.2.2

Combine

3

$3$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{19}{8} + \frac{3 \cdot 3}{3} + \frac{2}{3} - 1 \frac{5}{6}

$\frac{19}{8} + \frac{3 \cdot 3}{3} + \frac{2}{3} - 1 \frac{5}{6}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{19}{8} + \frac{3 \cdot 3 + 2}{3} - 1 \frac{5}{6}

$\frac{19}{8} + \frac{3 \cdot 3 + 2}{3} - 1 \frac{5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

3

$3$ .

\frac{19}{8} + \frac{9 + 2}{3} - 1 \frac{5}{6}

$\frac{19}{8} + \frac{9 + 2}{3} - 1 \frac{5}{6}$

Step 2.2.4.2

Add

9

$9$ and

2

$2$ .

\frac{19}{8} + \frac{11}{3} - 1 \frac{5}{6}

$\frac{19}{8} + \frac{11}{3} - 1 \frac{5}{6}$

\frac{19}{8} + \frac{11}{3} - 1 \frac{5}{6}

$\frac{19}{8} + \frac{11}{3} - 1 \frac{5}{6}$

\frac{19}{8} + \frac{11}{3} - 1 \frac{5}{6}

$\frac{19}{8} + \frac{11}{3} - 1 \frac{5}{6}$

\frac{19}{8} + \frac{11}{3} - 1 \frac{5}{6}

$\frac{19}{8} + \frac{11}{3} - 1 \frac{5}{6}$

Step 3

Convert

1 \frac{5}{6}

$1 \frac{5}{6}$ to an improper fraction.

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Step 3.1

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

\frac{19}{8} + \frac{11}{3} - (1 + \frac{5}{6})

$\frac{19}{8} + \frac{11}{3} - (1 + \frac{5}{6})$

Step 3.2

Add

1

$1$ and

\frac{5}{6}

$\frac{5}{6}$ .

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Step 3.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{19}{8} + \frac{11}{3} - (\frac{6}{6} + \frac{5}{6})

$\frac{19}{8} + \frac{11}{3} - (\frac{6}{6} + \frac{5}{6})$

Step 3.2.2

Combine the numerators over the common denominator.

\frac{19}{8} + \frac{11}{3} - \frac{6 + 5}{6}

$\frac{19}{8} + \frac{11}{3} - \frac{6 + 5}{6}$

Step 3.2.3

Add

6

$6$ and

$5$ .

$\frac{19}{8} + \frac{11}{3} - \frac{11}{6}$

Step 4

Find the common denominator.

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Step 4.1

Multiply

$\frac{19}{8}$ by

$\frac{3}{3}$ .

$\frac{19}{8} \cdot \frac{3}{3} + \frac{11}{3} - \frac{11}{6}$

Step 4.2

Multiply

$\frac{19}{8}$ by

$\frac{3}{3}$ .

$\frac{19 \cdot 3}{8 \cdot 3} + \frac{11}{3} - \frac{11}{6}$

Step 4.3

Multiply

$\frac{11}{3}$ by

$\frac{8}{8}$ .

$\frac{19 \cdot 3}{8 \cdot 3} + \frac{11}{3} \cdot \frac{8}{8} - \frac{11}{6}$

Step 4.4

Multiply

$\frac{11}{3}$ by

$\frac{8}{8}$ .

$\frac{19 \cdot 3}{8 \cdot 3} + \frac{11 \cdot 8}{3 \cdot 8} - \frac{11}{6}$

Step 4.5

Multiply

$\frac{11}{6}$ by

$\frac{4}{4}$ .

$\frac{19 \cdot 3}{8 \cdot 3} + \frac{11 \cdot 8}{3 \cdot 8} - (\frac{11}{6} \cdot \frac{4}{4})$

Step 4.6

Multiply

$\frac{11}{6}$ by

$\frac{4}{4}$ .

$\frac{19 \cdot 3}{8 \cdot 3} + \frac{11 \cdot 8}{3 \cdot 8} - \frac{11 \cdot 4}{6 \cdot 4}$

Step 4.7

Reorder the factors of

$8 \cdot 3$ .

$\frac{19 \cdot 3}{3 \cdot 8} + \frac{11 \cdot 8}{3 \cdot 8} - \frac{11 \cdot 4}{6 \cdot 4}$

Step 4.8

Multiply

$3$ by

$8$ .

$\frac{19 \cdot 3}{24} + \frac{11 \cdot 8}{3 \cdot 8} - \frac{11 \cdot 4}{6 \cdot 4}$

Step 4.9

Multiply

$3$ by

$8$ .

$\frac{19 \cdot 3}{24} + \frac{11 \cdot 8}{24} - \frac{11 \cdot 4}{6 \cdot 4}$

Step 4.10

Reorder the factors of

$6 \cdot 4$ .

$\frac{19 \cdot 3}{24} + \frac{11 \cdot 8}{24} - \frac{11 \cdot 4}{4 \cdot 6}$

Step 4.11

Multiply

$4$ by

$6$ .

$\frac{19 \cdot 3}{24} + \frac{11 \cdot 8}{24} - \frac{11 \cdot 4}{24}$

Step 5

Combine the numerators over the common denominator.

$\frac{19 \cdot 3 + 11 \cdot 8 - 11 \cdot 4}{24}$

Step 6

Simplify each term.

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Step 6.1

Multiply

$19$ by

$3$ .

$\frac{57 + 11 \cdot 8 - 11 \cdot 4}{24}$

Step 6.2

Multiply

$11$ by

$8$ .

$\frac{57 + 88 - 11 \cdot 4}{24}$

Step 6.3

Multiply

$- 11$ by

$4$ .

$\frac{57 + 88 - 44}{24}$

Step 7

Simplify by adding and subtracting.

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Step 7.1

Add

$57$ and

$88$ .

$\frac{145 - 44}{24}$

Step 7.2

Subtract

$44$ from

$145$ .

$\frac{101}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{101}{24}$

Decimal Form:

$4.208\overline{3}$

Mixed Number Form:

$4 \frac{5}{24}$