Basic Math Examples

$3 \frac{7}{8} + 4 \frac{2}{3}$

Step 1

Convert

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

Tap for more steps...

Step 1.1

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

$3 + \frac{7}{8} + 4 \frac{2}{3}$

Step 1.2

Add

$3$ and

$\frac{7}{8}$ .

Tap for more steps...

Step 1.2.1

To write

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

$\frac{8}{8}$ .

$3 \cdot \frac{8}{8} + \frac{7}{8} + 4 \frac{2}{3}$

Step 1.2.2

Combine

$3$ and

$\frac{8}{8}$ .

$\frac{3 \cdot 8}{8} + \frac{7}{8} + 4 \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 8 + 7}{8} + 4 \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply

$3$ by

$8$ .

$\frac{24 + 7}{8} + 4 \frac{2}{3}$

Step 1.2.4.2

Add

$24$ and

$7$ .

$\frac{31}{8} + 4 \frac{2}{3}$

Step 2

Convert

$4 \frac{2}{3}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

$\frac{31}{8} + 4 + \frac{2}{3}$

Step 2.2

Add

$4$ and

$\frac{2}{3}$ .

Tap for more steps...

Step 2.2.1

To write

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

$\frac{3}{3}$ .

$\frac{31}{8} + 4 \cdot \frac{3}{3} + \frac{2}{3}$

Step 2.2.2

Combine

$4$ and

$\frac{3}{3}$ .

$\frac{31}{8} + \frac{4 \cdot 3}{3} + \frac{2}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{31}{8} + \frac{4 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply

$4$ by

$3$ .

$\frac{31}{8} + \frac{12 + 2}{3}$

Step 2.2.4.2

Add

$12$ and

$2$ .

$\frac{31}{8} + \frac{14}{3}$

Step 3

To write

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

$\frac{3}{3}$ .

$\frac{31}{8} \cdot \frac{3}{3} + \frac{14}{3}$

Step 4

To write

$\frac{14}{3}$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$\frac{31}{8} \cdot \frac{3}{3} + \frac{14}{3} \cdot \frac{8}{8}$

Step 5

Write each expression with a common denominator of

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

$1$ .

Tap for more steps...

Step 5.1

Multiply

$\frac{31}{8}$ by

$\frac{3}{3}$ .

$\frac{31 \cdot 3}{8 \cdot 3} + \frac{14}{3} \cdot \frac{8}{8}$

Step 5.2

Multiply

$8$ by

$3$ .

$\frac{31 \cdot 3}{24} + \frac{14}{3} \cdot \frac{8}{8}$

Step 5.3

Multiply

$\frac{14}{3}$ by

$\frac{8}{8}$ .

$\frac{31 \cdot 3}{24} + \frac{14 \cdot 8}{3 \cdot 8}$

Step 5.4

Multiply

$3$ by

$8$ .

$\frac{31 \cdot 3}{24} + \frac{14 \cdot 8}{24}$

Step 6

Combine the numerators over the common denominator.

$\frac{31 \cdot 3 + 14 \cdot 8}{24}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Multiply

$31$ by

$3$ .

$\frac{93 + 14 \cdot 8}{24}$

Step 7.2

Multiply

$14$ by

$8$ .

$\frac{93 + 112}{24}$

Step 7.3

Add

$93$ and

$112$ .

$\frac{205}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{205}{24}$

Decimal Form:

$8.541\overline{6}$

Mixed Number Form:

$8 \frac{13}{24}$