Basic Math Examples

$1 \frac{5}{6} + 3 \frac{7}{8}$

Step 1

Convert

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

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Step 1.1

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

$1 + \frac{5}{6} + 3 \frac{7}{8}$

Step 1.2

Add

$1$ and

$\frac{5}{6}$ .

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Step 1.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{6}{6} + \frac{5}{6} + 3 \frac{7}{8}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{6 + 5}{6} + 3 \frac{7}{8}$

Step 1.2.3

Add

$6$ and

$5$ .

$\frac{11}{6} + 3 \frac{7}{8}$

Step 2

Convert

$3 \frac{7}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{11}{6} + 3 + \frac{7}{8}$

Step 2.2

Add

$3$ and

$\frac{7}{8}$ .

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Step 2.2.1

To write

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

$\frac{8}{8}$ .

$\frac{11}{6} + 3 \cdot \frac{8}{8} + \frac{7}{8}$

Step 2.2.2

Combine

$3$ and

$\frac{8}{8}$ .

$\frac{11}{6} + \frac{3 \cdot 8}{8} + \frac{7}{8}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{11}{6} + \frac{3 \cdot 8 + 7}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$8$ .

$\frac{11}{6} + \frac{24 + 7}{8}$

Step 2.2.4.2

Add

$24$ and

$7$ .

$\frac{11}{6} + \frac{31}{8}$

Step 3

To write

$\frac{11}{6}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{11}{6} \cdot \frac{4}{4} + \frac{31}{8}$

Step 4

To write

$\frac{31}{8}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{11}{6} \cdot \frac{4}{4} + \frac{31}{8} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of

$24$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{11}{6}$ by

$\frac{4}{4}$ .

$\frac{11 \cdot 4}{6 \cdot 4} + \frac{31}{8} \cdot \frac{3}{3}$

Step 5.2

Multiply

$6$ by

$4$ .

$\frac{11 \cdot 4}{24} + \frac{31}{8} \cdot \frac{3}{3}$

Step 5.3

Multiply

$\frac{31}{8}$ by

$\frac{3}{3}$ .

$\frac{11 \cdot 4}{24} + \frac{31 \cdot 3}{8 \cdot 3}$

Step 5.4

Multiply

$8$ by

$3$ .

$\frac{11 \cdot 4}{24} + \frac{31 \cdot 3}{24}$

Step 6

Combine the numerators over the common denominator.

$\frac{11 \cdot 4 + 31 \cdot 3}{24}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$11$ by

$4$ .

$\frac{44 + 31 \cdot 3}{24}$

Step 7.2

Multiply

$31$ by

$3$ .

$\frac{44 + 93}{24}$

Step 7.3

Add

$44$ and

$93$ .

$\frac{137}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{137}{24}$

Decimal Form:

$5.708\overline{3}$

Mixed Number Form:

$5 \frac{17}{24}$