Basic Math Examples

$4 \frac{1}{2} - 3 \frac{1}{4} + (6 \frac{1}{5} - 5 \frac{1}{6})$

Step 1

Remove parentheses.

$4 \frac{1}{2} - 3 \frac{1}{4} + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 2

Convert $4 \frac{1}{2}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

$4 + \frac{1}{2} - 3 \frac{1}{4} + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 2.2

Add $4$ and $\frac{1}{2}$ .

Tap for more steps...

Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 \cdot \frac{2}{2} + \frac{1}{2} - 3 \frac{1}{4} + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 2.2.2

Combine $4$ and $\frac{2}{2}$ .

$\frac{4 \cdot 2}{2} + \frac{1}{2} - 3 \frac{1}{4} + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 + 1}{2} - 3 \frac{1}{4} + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $4$ by $2$ .

$\frac{8 + 1}{2} - 3 \frac{1}{4} + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 2.2.4.2

Add $8$ and $1$ .

$\frac{9}{2} - 3 \frac{1}{4} + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 3

Convert $3 \frac{1}{4}$ to an improper fraction.

Tap for more steps...

Step 3.1

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

$\frac{9}{2} - (3 + \frac{1}{4}) + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 3.2

Add $3$ and $\frac{1}{4}$ .

Tap for more steps...

Step 3.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{2} - (3 \cdot \frac{4}{4} + \frac{1}{4}) + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 3.2.2

Combine $3$ and $\frac{4}{4}$ .

$\frac{9}{2} - (\frac{3 \cdot 4}{4} + \frac{1}{4}) + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} - \frac{3 \cdot 4 + 1}{4} + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 3.2.4

Simplify the numerator.

Tap for more steps...

Step 3.2.4.1

Multiply $3$ by $4$ .

$\frac{9}{2} - \frac{12 + 1}{4} + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 3.2.4.2

Add $12$ and $1$ .

$\frac{9}{2} - \frac{13}{4} + 6 \frac{1}{5} - 5 \frac{1}{6}$

Step 4

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

Tap for more steps...

Step 4.1

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

$\frac{9}{2} - \frac{13}{4} + 6 + \frac{1}{5} - 5 \frac{1}{6}$

Step 4.2

Add $6$ and $\frac{1}{5}$ .

Tap for more steps...

Step 4.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9}{2} - \frac{13}{4} + 6 \cdot \frac{5}{5} + \frac{1}{5} - 5 \frac{1}{6}$

Step 4.2.2

Combine $6$ and $\frac{5}{5}$ .

$\frac{9}{2} - \frac{13}{4} + \frac{6 \cdot 5}{5} + \frac{1}{5} - 5 \frac{1}{6}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} - \frac{13}{4} + \frac{6 \cdot 5 + 1}{5} - 5 \frac{1}{6}$

Step 4.2.4

Simplify the numerator.

Tap for more steps...

Step 4.2.4.1

Multiply $6$ by $5$ .

$\frac{9}{2} - \frac{13}{4} + \frac{30 + 1}{5} - 5 \frac{1}{6}$

Step 4.2.4.2

Add $30$ and $1$ .

$\frac{9}{2} - \frac{13}{4} + \frac{31}{5} - 5 \frac{1}{6}$

Step 5

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

Tap for more steps...

Step 5.1

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

$\frac{9}{2} - \frac{13}{4} + \frac{31}{5} - (5 + \frac{1}{6})$

Step 5.2

Add $5$ and $\frac{1}{6}$ .

Tap for more steps...

Step 5.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{9}{2} - \frac{13}{4} + \frac{31}{5} - (5 \cdot \frac{6}{6} + \frac{1}{6})$

Step 5.2.2

Combine $5$ and $\frac{6}{6}$ .

$\frac{9}{2} - \frac{13}{4} + \frac{31}{5} - (\frac{5 \cdot 6}{6} + \frac{1}{6})$

Step 5.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} - \frac{13}{4} + \frac{31}{5} - \frac{5 \cdot 6 + 1}{6}$

Step 5.2.4

Simplify the numerator.

Tap for more steps...

Step 5.2.4.1

Multiply $5$ by $6$ .

$\frac{9}{2} - \frac{13}{4} + \frac{31}{5} - \frac{30 + 1}{6}$

Step 5.2.4.2

Add $30$ and $1$ .

$\frac{9}{2} - \frac{13}{4} + \frac{31}{5} - \frac{31}{6}$

Step 6

Find the common denominator.

Tap for more steps...

Step 6.1

Multiply $\frac{9}{2}$ by $\frac{30}{30}$ .

$\frac{9}{2} \cdot \frac{30}{30} - \frac{13}{4} + \frac{31}{5} - \frac{31}{6}$

Step 6.2

Multiply $\frac{9}{2}$ by $\frac{30}{30}$ .

$\frac{9 \cdot 30}{2 \cdot 30} - \frac{13}{4} + \frac{31}{5} - \frac{31}{6}$

Step 6.3

Multiply $\frac{13}{4}$ by $\frac{15}{15}$ .

$\frac{9 \cdot 30}{2 \cdot 30} - (\frac{13}{4} \cdot \frac{15}{15}) + \frac{31}{5} - \frac{31}{6}$

Step 6.4

Multiply $\frac{13}{4}$ by $\frac{15}{15}$ .

$\frac{9 \cdot 30}{2 \cdot 30} - \frac{13 \cdot 15}{4 \cdot 15} + \frac{31}{5} - \frac{31}{6}$

Step 6.5

Multiply $\frac{31}{5}$ by $\frac{12}{12}$ .

$\frac{9 \cdot 30}{2 \cdot 30} - \frac{13 \cdot 15}{4 \cdot 15} + \frac{31}{5} \cdot \frac{12}{12} - \frac{31}{6}$

Step 6.6

Multiply $\frac{31}{5}$ by $\frac{12}{12}$ .

$\frac{9 \cdot 30}{2 \cdot 30} - \frac{13 \cdot 15}{4 \cdot 15} + \frac{31 \cdot 12}{5 \cdot 12} - \frac{31}{6}$

Step 6.7

Multiply $\frac{31}{6}$ by $\frac{10}{10}$ .

$\frac{9 \cdot 30}{2 \cdot 30} - \frac{13 \cdot 15}{4 \cdot 15} + \frac{31 \cdot 12}{5 \cdot 12} - (\frac{31}{6} \cdot \frac{10}{10})$

Step 6.8

Multiply $\frac{31}{6}$ by $\frac{10}{10}$ .

$\frac{9 \cdot 30}{2 \cdot 30} - \frac{13 \cdot 15}{4 \cdot 15} + \frac{31 \cdot 12}{5 \cdot 12} - \frac{31 \cdot 10}{6 \cdot 10}$

Step 6.9

Multiply $2$ by $30$ .

$\frac{9 \cdot 30}{60} - \frac{13 \cdot 15}{4 \cdot 15} + \frac{31 \cdot 12}{5 \cdot 12} - \frac{31 \cdot 10}{6 \cdot 10}$

Step 6.10

Multiply $4$ by $15$ .

$\frac{9 \cdot 30}{60} - \frac{13 \cdot 15}{60} + \frac{31 \cdot 12}{5 \cdot 12} - \frac{31 \cdot 10}{6 \cdot 10}$

Step 6.11

Multiply $5$ by $12$ .

$\frac{9 \cdot 30}{60} - \frac{13 \cdot 15}{60} + \frac{31 \cdot 12}{60} - \frac{31 \cdot 10}{6 \cdot 10}$

Step 6.12

Multiply $6$ by $10$ .

$\frac{9 \cdot 30}{60} - \frac{13 \cdot 15}{60} + \frac{31 \cdot 12}{60} - \frac{31 \cdot 10}{60}$

Step 7

Combine the numerators over the common denominator.

$\frac{9 \cdot 30 - 13 \cdot 15 + 31 \cdot 12 - 31 \cdot 10}{60}$

Step 8

Simplify each term.

Tap for more steps...

Step 8.1

Multiply $9$ by $30$ .

$\frac{270 - 13 \cdot 15 + 31 \cdot 12 - 31 \cdot 10}{60}$

Step 8.2

Multiply $- 13$ by $15$ .

$\frac{270 - 195 + 31 \cdot 12 - 31 \cdot 10}{60}$

Step 8.3

Multiply $31$ by $12$ .

$\frac{270 - 195 + 372 - 31 \cdot 10}{60}$

Step 8.4

Multiply $- 31$ by $10$ .

$\frac{270 - 195 + 372 - 310}{60}$

Step 9

Simplify by adding and subtracting.

Tap for more steps...

Step 9.1

Subtract $195$ from $270$ .

$\frac{75 + 372 - 310}{60}$

Step 9.2

Add $75$ and $372$ .

$\frac{447 - 310}{60}$

Step 9.3

Subtract $310$ from $447$ .

$\frac{137}{60}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{137}{60}$

Decimal Form:

$2.28\overline{3}$

Mixed Number Form:

$2 \frac{17}{60}$