Basic Math Examples

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

Step 1

Convert $3 \frac{2}{5}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

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

Step 1.2

Add $3$ and $\frac{2}{5}$ .

Tap for more steps...

Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 1.2.2

Combine $3$ and $\frac{5}{5}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $3$ by $5$ .

$10 (\frac{3}{4} - \frac{15 + 2}{5}) - 2 (\frac{1}{3} + 3)$

Step 1.2.4.2

Add $15$ and $2$ .

$10 (\frac{3}{4} - \frac{17}{5}) - 2 (\frac{1}{3} + 3)$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$10 (\frac{3}{4} \cdot \frac{5}{5} - \frac{17}{5}) - 2 (\frac{1}{3} + 3)$

Step 2.2

To write $- \frac{17}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$10 (\frac{3}{4} \cdot \frac{5}{5} - \frac{17}{5} \cdot \frac{4}{4}) - 2 (\frac{1}{3} + 3)$

Step 2.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.3.1

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

$10 (\frac{3 \cdot 5}{4 \cdot 5} - \frac{17}{5} \cdot \frac{4}{4}) - 2 (\frac{1}{3} + 3)$

Step 2.3.2

Multiply $4$ by $5$ .

$10 (\frac{3 \cdot 5}{20} - \frac{17}{5} \cdot \frac{4}{4}) - 2 (\frac{1}{3} + 3)$

Step 2.3.3

Multiply $\frac{17}{5}$ by $\frac{4}{4}$ .

$10 (\frac{3 \cdot 5}{20} - \frac{17 \cdot 4}{5 \cdot 4}) - 2 (\frac{1}{3} + 3)$

Step 2.3.4

Multiply $5$ by $4$ .

$10 (\frac{3 \cdot 5}{20} - \frac{17 \cdot 4}{20}) - 2 (\frac{1}{3} + 3)$

Step 2.4

Combine the numerators over the common denominator.

$10 \frac{3 \cdot 5 - 17 \cdot 4}{20} - 2 (\frac{1}{3} + 3)$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $3$ by $5$ .

$10 \frac{15 - 17 \cdot 4}{20} - 2 (\frac{1}{3} + 3)$

Step 2.5.2

Multiply $- 17$ by $4$ .

$10 \frac{15 - 68}{20} - 2 (\frac{1}{3} + 3)$

Step 2.5.3

Subtract $68$ from $15$ .

$10 (\frac{- 53}{20}) - 2 (\frac{1}{3} + 3)$

Step 2.6

Cancel the common factor of $10$ .

Tap for more steps...

Step 2.6.1

Factor $10$ out of $20$ .

$10 \frac{- 53}{10 (2)} - 2 (\frac{1}{3} + 3)$

Step 2.6.2

Cancel the common factor.

$10 \frac{- 53}{10 \cdot 2} - 2 (\frac{1}{3} + 3)$

Step 2.6.3

Rewrite the expression.

$\frac{- 53}{2} - 2 (\frac{1}{3} + 3)$

Step 2.7

Move the negative in front of the fraction.

$- \frac{53}{2} - 2 (\frac{1}{3} + 3)$

Step 2.8

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

$- \frac{53}{2} - 2 (\frac{1}{3} + 3 \cdot \frac{3}{3})$

Step 2.9

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

$- \frac{53}{2} - 2 (\frac{1}{3} + \frac{3 \cdot 3}{3})$

Step 2.10

Combine the numerators over the common denominator.

$- \frac{53}{2} - 2 \frac{1 + 3 \cdot 3}{3}$

Step 2.11

Simplify the numerator.

Tap for more steps...

Step 2.11.1

Multiply $3$ by $3$ .

$- \frac{53}{2} - 2 \frac{1 + 9}{3}$

Step 2.11.2

Add $1$ and $9$ .

$- \frac{53}{2} - 2 (\frac{10}{3})$

Step 2.12

Multiply $- 2 (\frac{10}{3})$ .

Tap for more steps...

Step 2.12.1

Combine $- 2$ and $\frac{10}{3}$ .

$- \frac{53}{2} + \frac{- 2 \cdot 10}{3}$

Step 2.12.2

Multiply $- 2$ by $10$ .

$- \frac{53}{2} + \frac{- 20}{3}$

Step 2.13

Move the negative in front of the fraction.

$- \frac{53}{2} - \frac{20}{3}$

Step 3

To write $- \frac{53}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{53}{2} \cdot \frac{3}{3} - \frac{20}{3}$

Step 4

To write $- \frac{20}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{53}{2} \cdot \frac{3}{3} - \frac{20}{3} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 5.1

Multiply $\frac{53}{2}$ by $\frac{3}{3}$ .

$- \frac{53 \cdot 3}{2 \cdot 3} - \frac{20}{3} \cdot \frac{2}{2}$

Step 5.2

Multiply $2$ by $3$ .

$- \frac{53 \cdot 3}{6} - \frac{20}{3} \cdot \frac{2}{2}$

Step 5.3

Multiply $\frac{20}{3}$ by $\frac{2}{2}$ .

$- \frac{53 \cdot 3}{6} - \frac{20 \cdot 2}{3 \cdot 2}$

Step 5.4

Multiply $3$ by $2$ .

$- \frac{53 \cdot 3}{6} - \frac{20 \cdot 2}{6}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 53 \cdot 3 - 20 \cdot 2}{6}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Multiply $- 53$ by $3$ .

$\frac{- 159 - 20 \cdot 2}{6}$

Step 7.2

Multiply $- 20$ by $2$ .

$\frac{- 159 - 40}{6}$

Step 7.3

Subtract $40$ from $- 159$ .

$\frac{- 199}{6}$

Step 8

Move the negative in front of the fraction.

$- \frac{199}{6}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{199}{6}$

Decimal Form:

$- 33.1\overline{6}$

Mixed Number Form:

$- 33 \frac{1}{6}$