Basic Math Examples

$2 - \frac{5}{8} \cdot \frac{2}{3} + 2 \frac{1}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 1

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

Tap for more steps...

Step 1.1

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

$2 - \frac{5}{8} \cdot \frac{2}{3} + 2 + \frac{1}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

$2 - \frac{5}{8} \cdot \frac{2}{3} + 2 \cdot \frac{4}{4} + \frac{1}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 1.2.2

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

$2 - \frac{5}{8} \cdot \frac{2}{3} + \frac{2 \cdot 4}{4} + \frac{1}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$2 - \frac{5}{8} \cdot \frac{2}{3} + \frac{2 \cdot 4 + 1}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $2$ by $4$ .

$2 - \frac{5}{8} \cdot \frac{2}{3} + \frac{8 + 1}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 1.2.4.2

Add $8$ and $1$ .

$2 - \frac{5}{8} \cdot \frac{2}{3} + \frac{9}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1

Move the leading negative in $- \frac{5}{8}$ into the numerator.

$2 + \frac{- 5}{8} \cdot \frac{2}{3} + \frac{9}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 2.1.2

Factor $2$ out of $8$ .

$2 + \frac{- 5}{2 (4)} \cdot \frac{2}{3} + \frac{9}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 2.1.3

Cancel the common factor.

$2 + \frac{- 5}{2 \cdot 4} \cdot \frac{2}{3} + \frac{9}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 2.1.4

Rewrite the expression.

$2 + \frac{- 5}{4} \cdot \frac{1}{3} + \frac{9}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 2.2

Multiply $\frac{- 5}{4}$ by $\frac{1}{3}$ .

$2 + \frac{- 5}{4 \cdot 3} + \frac{9}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 2.3

Multiply $4$ by $3$ .

$2 + \frac{- 5}{12} + \frac{9}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 2.4

Move the negative in front of the fraction.

$2 - \frac{5}{12} + \frac{9}{4} - \frac{7}{10} \div \frac{14}{3}$

Step 2.5

To divide by a fraction, multiply by its reciprocal.

$2 - \frac{5}{12} + \frac{9}{4} - (\frac{7}{10} \cdot \frac{3}{14})$

Step 2.6

Cancel the common factor of $7$ .

Tap for more steps...

Step 2.6.1

Factor $7$ out of $14$ .

$2 - \frac{5}{12} + \frac{9}{4} - (\frac{7}{10} \cdot \frac{3}{7 (2)})$

Step 2.6.2

Cancel the common factor.

$2 - \frac{5}{12} + \frac{9}{4} - (\frac{7}{10} \cdot \frac{3}{7 \cdot 2})$

Step 2.6.3

Rewrite the expression.

$2 - \frac{5}{12} + \frac{9}{4} - (\frac{1}{10} \cdot \frac{3}{2})$

Step 2.7

Multiply $\frac{1}{10}$ by $\frac{3}{2}$ .

$2 - \frac{5}{12} + \frac{9}{4} - \frac{3}{10 \cdot 2}$

Step 2.8

Multiply $10$ by $2$ .

$2 - \frac{5}{12} + \frac{9}{4} - \frac{3}{20}$

Step 3

Find the common denominator.

Tap for more steps...

Step 3.1

Write $2$ as a fraction with denominator $1$ .

$\frac{2}{1} - \frac{5}{12} + \frac{9}{4} - \frac{3}{20}$

Step 3.2

Multiply $\frac{2}{1}$ by $\frac{60}{60}$ .

$\frac{2}{1} \cdot \frac{60}{60} - \frac{5}{12} + \frac{9}{4} - \frac{3}{20}$

Step 3.3

Multiply $\frac{2}{1}$ by $\frac{60}{60}$ .

$\frac{2 \cdot 60}{60} - \frac{5}{12} + \frac{9}{4} - \frac{3}{20}$

Step 3.4

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

$\frac{2 \cdot 60}{60} - (\frac{5}{12} \cdot \frac{5}{5}) + \frac{9}{4} - \frac{3}{20}$

Step 3.5

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

$\frac{2 \cdot 60}{60} - \frac{5 \cdot 5}{12 \cdot 5} + \frac{9}{4} - \frac{3}{20}$

Step 3.6

Multiply $\frac{9}{4}$ by $\frac{15}{15}$ .

$\frac{2 \cdot 60}{60} - \frac{5 \cdot 5}{12 \cdot 5} + \frac{9}{4} \cdot \frac{15}{15} - \frac{3}{20}$

Step 3.7

Multiply $\frac{9}{4}$ by $\frac{15}{15}$ .

$\frac{2 \cdot 60}{60} - \frac{5 \cdot 5}{12 \cdot 5} + \frac{9 \cdot 15}{4 \cdot 15} - \frac{3}{20}$

Step 3.8

Multiply $\frac{3}{20}$ by $\frac{3}{3}$ .

$\frac{2 \cdot 60}{60} - \frac{5 \cdot 5}{12 \cdot 5} + \frac{9 \cdot 15}{4 \cdot 15} - (\frac{3}{20} \cdot \frac{3}{3})$

Step 3.9

Multiply $\frac{3}{20}$ by $\frac{3}{3}$ .

$\frac{2 \cdot 60}{60} - \frac{5 \cdot 5}{12 \cdot 5} + \frac{9 \cdot 15}{4 \cdot 15} - \frac{3 \cdot 3}{20 \cdot 3}$

Step 3.10

Reorder the factors of $12 \cdot 5$ .

$\frac{2 \cdot 60}{60} - \frac{5 \cdot 5}{5 \cdot 12} + \frac{9 \cdot 15}{4 \cdot 15} - \frac{3 \cdot 3}{20 \cdot 3}$

Step 3.11

Multiply $5$ by $12$ .

$\frac{2 \cdot 60}{60} - \frac{5 \cdot 5}{60} + \frac{9 \cdot 15}{4 \cdot 15} - \frac{3 \cdot 3}{20 \cdot 3}$

Step 3.12

Multiply $4$ by $15$ .

$\frac{2 \cdot 60}{60} - \frac{5 \cdot 5}{60} + \frac{9 \cdot 15}{60} - \frac{3 \cdot 3}{20 \cdot 3}$

Step 3.13

Reorder the factors of $20 \cdot 3$ .

$\frac{2 \cdot 60}{60} - \frac{5 \cdot 5}{60} + \frac{9 \cdot 15}{60} - \frac{3 \cdot 3}{3 \cdot 20}$

Step 3.14

Multiply $3$ by $20$ .

$\frac{2 \cdot 60}{60} - \frac{5 \cdot 5}{60} + \frac{9 \cdot 15}{60} - \frac{3 \cdot 3}{60}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 \cdot 60 - 5 \cdot 5 + 9 \cdot 15 - 3 \cdot 3}{60}$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Multiply $2$ by $60$ .

$\frac{120 - 5 \cdot 5 + 9 \cdot 15 - 3 \cdot 3}{60}$

Step 5.2

Multiply $- 5$ by $5$ .

$\frac{120 - 25 + 9 \cdot 15 - 3 \cdot 3}{60}$

Step 5.3

Multiply $9$ by $15$ .

$\frac{120 - 25 + 135 - 3 \cdot 3}{60}$

Step 5.4

Multiply $- 3$ by $3$ .

$\frac{120 - 25 + 135 - 9}{60}$

Step 6

Simplify by adding and subtracting.

Tap for more steps...

Step 6.1

Subtract $25$ from $120$ .

$\frac{95 + 135 - 9}{60}$

Step 6.2

Add $95$ and $135$ .

$\frac{230 - 9}{60}$

Step 6.3

Subtract $9$ from $230$ .

$\frac{221}{60}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{221}{60}$

Decimal Form:

$3.68\overline{3}$

Mixed Number Form:

$3 \frac{41}{60}$