Basic Math Examples

$(1 \div 3 + 1 \div 4) \div ((1) - (1 \div 5))$

Step 1

Rewrite the division as a fraction.

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

Step 2

Multiply the numerator and denominator of the fraction by $60$ .

Tap for more steps...

Step 2.1

Multiply $\frac{1 \div 3 + 1 \div 4}{1 - 1 \div 5}$ by $\frac{60}{60}$ .

$\frac{60}{60} \cdot \frac{1 \div 3 + 1 \div 4}{1 - 1 \div 5}$

Step 2.2

Combine.

$\frac{60 (1 \div 3 + 1 \div 4)}{60 (1 - 1 \div 5)}$

Step 3

Apply the distributive property.

$\frac{60 (1 \div 3) + 60 (1 \div 4)}{60 \cdot 1 + 60 (- 1 \div 5)}$

Step 4

Simplify by cancelling.

Tap for more steps...

Step 4.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.1.1

Move the leading negative in $- 1 \div 5$ into the numerator.

$\frac{60 (1 \div 3) + 60 (1 \div 4)}{60 \cdot 1 + 60 (- 1 \div 5)}$

Step 4.1.2

Factor $5$ out of $60$ .

$\frac{60 (1 \div 3) + 60 (1 \div 4)}{60 \cdot 1 + 5 (12) - 1 \div 5}$

Step 4.1.3

Cancel the common factor.

$\frac{60 (1 \div 3) + 60 (1 \div 4)}{60 \cdot 1 + 5 \cdot 12 - 1 \div 5}$

Step 4.1.4

Rewrite the expression.

$\frac{60 (1 \div 3) + 60 (1 \div 4)}{60 \cdot 1 + 12 \cdot - 1}$

Step 4.2

Multiply $12$ by $- 1$ .

$\frac{60 (1 \div 3) + 60 (1 \div 4)}{60 \cdot 1 - 12}$

Step 5

Cancel the common factor of $60 (1 \div 3) + 60 (1 \div 4)$ and $60 \cdot 1 - 12$ .

Tap for more steps...

Step 5.1

Factor $12$ out of $60 (1 \div 3)$ .

$\frac{12 (5 (1 \div 3)) + 60 (1 \div 4)}{60 \cdot 1 - 12}$

Step 5.2

Factor $12$ out of $60 (1 \div 4)$ .

$\frac{12 (5 (1 \div 3)) + 12 (5 (1 \div 4))}{60 \cdot 1 - 12}$

Step 5.3

Factor $12$ out of $12 (5 (1 \div 3)) + 12 (5 (1 \div 4))$ .

$\frac{12 (5 (1 \div 3) + 5 (1 \div 4))}{60 \cdot 1 - 12}$

Step 5.4

Cancel the common factors.

Tap for more steps...

Step 5.4.1

Factor $12$ out of $60 \cdot 1$ .

$\frac{12 (5 (1 \div 3) + 5 (1 \div 4))}{12 (5 \cdot 1) - 12}$

Step 5.4.2

Factor $12$ out of $- 12$ .

$\frac{12 (5 (1 \div 3) + 5 (1 \div 4))}{12 (5 \cdot 1) + 12 (- 1)}$

Step 5.4.3

Factor $12$ out of $12 (5 \cdot 1) + 12 (- 1)$ .

$\frac{12 (5 (1 \div 3) + 5 (1 \div 4))}{12 (5 \cdot 1 - 1)}$

Step 5.4.4

Cancel the common factor.

$\frac{12 (5 (1 \div 3) + 5 (1 \div 4))}{12 (5 \cdot 1 - 1)}$

Step 5.4.5

Rewrite the expression.

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

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Rewrite the division as a fraction.

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

Step 6.2

Combine $5$ and $\frac{1}{3}$ .

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

Step 6.3

Rewrite the division as a fraction.

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

Step 6.4

Combine $5$ and $\frac{1}{4}$ .

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

Step 6.5

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

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

Step 6.6

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

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

Step 6.7

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 6.7.1

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

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

Step 6.7.2

Multiply $3$ by $4$ .

$\frac{\frac{5 \cdot 4}{12} + \frac{5}{4} \cdot \frac{3}{3}}{5 \cdot 1 - 1}$

Step 6.7.3

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

$\frac{\frac{5 \cdot 4}{12} + \frac{5 \cdot 3}{4 \cdot 3}}{5 \cdot 1 - 1}$

Step 6.7.4

Multiply $4$ by $3$ .

$\frac{\frac{5 \cdot 4}{12} + \frac{5 \cdot 3}{12}}{5 \cdot 1 - 1}$

Step 6.8

Combine the numerators over the common denominator.

$\frac{\frac{5 \cdot 4 + 5 \cdot 3}{12}}{5 \cdot 1 - 1}$

Step 6.9

Simplify the numerator.

Tap for more steps...

Step 6.9.1

Multiply $5$ by $4$ .

$\frac{\frac{20 + 5 \cdot 3}{12}}{5 \cdot 1 - 1}$

Step 6.9.2

Multiply $5$ by $3$ .

$\frac{\frac{20 + 15}{12}}{5 \cdot 1 - 1}$

Step 6.9.3

Add $20$ and $15$ .

$\frac{\frac{35}{12}}{5 \cdot 1 - 1}$

Step 7

Simplify the denominator.

Tap for more steps...

Step 7.1

Multiply $5$ by $1$ .

$\frac{\frac{35}{12}}{5 - 1}$

Step 7.2

Subtract $1$ from $5$ .

$\frac{\frac{35}{12}}{4}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{35}{12} \cdot \frac{1}{4}$

Step 9

Multiply $\frac{35}{12} \cdot \frac{1}{4}$ .

Tap for more steps...

Step 9.1

Multiply $\frac{35}{12}$ by $\frac{1}{4}$ .

$\frac{35}{12 \cdot 4}$

Step 9.2

Multiply $12$ by $4$ .

$\frac{35}{48}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{48}$

Decimal Form:

$0.7291\overline{6}$