Basic Math Examples

$(\frac{5}{18} + \frac{7}{12}) \cdot 2 \frac{10}{31} + 1 \frac{13}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 1

Convert $2 \frac{10}{31}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

$(\frac{5}{18} + \frac{7}{12}) \cdot (2 + \frac{10}{31}) + 1 \frac{13}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 1.2

Add $2$ and $\frac{10}{31}$ .

Tap for more steps...

Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$(\frac{5}{18} + \frac{7}{12}) \cdot (2 \cdot \frac{31}{31} + \frac{10}{31}) + 1 \frac{13}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 1.2.2

Combine $2$ and $\frac{31}{31}$ .

$(\frac{5}{18} + \frac{7}{12}) \cdot (\frac{2 \cdot 31}{31} + \frac{10}{31}) + 1 \frac{13}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{5}{18} + \frac{7}{12}) \cdot \frac{2 \cdot 31 + 10}{31} + 1 \frac{13}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $2$ by $31$ .

$(\frac{5}{18} + \frac{7}{12}) \cdot \frac{62 + 10}{31} + 1 \frac{13}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 1.2.4.2

Add $62$ and $10$ .

$(\frac{5}{18} + \frac{7}{12}) \cdot \frac{72}{31} + 1 \frac{13}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 2

Convert $1 \frac{13}{51}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

$(\frac{5}{18} + \frac{7}{12}) \cdot \frac{72}{31} + (1 + \frac{13}{51}) \div (\frac{4}{17} - \frac{20}{51})$

Step 2.2

Add $1$ and $\frac{13}{51}$ .

Tap for more steps...

Step 2.2.1

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

$(\frac{5}{18} + \frac{7}{12}) \cdot \frac{72}{31} + (\frac{51}{51} + \frac{13}{51}) \div (\frac{4}{17} - \frac{20}{51})$

Step 2.2.2

Combine the numerators over the common denominator.

$(\frac{5}{18} + \frac{7}{12}) \cdot \frac{72}{31} + \frac{51 + 13}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 2.2.3

Add $51$ and $13$ .

$(\frac{5}{18} + \frac{7}{12}) \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

To write $\frac{5}{18}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{5}{18} \cdot \frac{2}{2} + \frac{7}{12}) \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.2

To write $\frac{7}{12}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{5}{18} \cdot \frac{2}{2} + \frac{7}{12} \cdot \frac{3}{3}) \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.3

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.3.1

Multiply $\frac{5}{18}$ by $\frac{2}{2}$ .

$(\frac{5 \cdot 2}{18 \cdot 2} + \frac{7}{12} \cdot \frac{3}{3}) \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.3.2

Multiply $18$ by $2$ .

$(\frac{5 \cdot 2}{36} + \frac{7}{12} \cdot \frac{3}{3}) \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.3.3

Multiply $\frac{7}{12}$ by $\frac{3}{3}$ .

$(\frac{5 \cdot 2}{36} + \frac{7 \cdot 3}{12 \cdot 3}) \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.3.4

Multiply $12$ by $3$ .

$(\frac{5 \cdot 2}{36} + \frac{7 \cdot 3}{36}) \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.4

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 + 7 \cdot 3}{36} \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Multiply $5$ by $2$ .

$\frac{10 + 7 \cdot 3}{36} \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.5.2

Multiply $7$ by $3$ .

$\frac{10 + 21}{36} \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.5.3

Add $10$ and $21$ .

$\frac{31}{36} \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.6

Cancel the common factor of $31$ .

Tap for more steps...

Step 3.6.1

Cancel the common factor.

$\frac{31}{36} \cdot \frac{72}{31} + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.6.2

Rewrite the expression.

$\frac{1}{36} \cdot 72 + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.7

Cancel the common factor of $36$ .

Tap for more steps...

Step 3.7.1

Factor $36$ out of $72$ .

$\frac{1}{36} \cdot (36 (2)) + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.7.2

Cancel the common factor.

$\frac{1}{36} \cdot (36 \cdot 2) + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.7.3

Rewrite the expression.

$2 + \frac{64}{51} \div (\frac{4}{17} - \frac{20}{51})$

Step 3.8

Rewrite the division as a fraction.

$2 + \frac{\frac{64}{51}}{\frac{4}{17} - \frac{20}{51}}$

Step 3.9

Multiply the numerator by the reciprocal of the denominator.

$2 + \frac{64}{51} \cdot \frac{1}{\frac{4}{17} - \frac{20}{51}}$

Step 3.10

Simplify the denominator.

Tap for more steps...

Step 3.10.1

To write $\frac{4}{17}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 + \frac{64}{51} \cdot \frac{1}{\frac{4}{17} \cdot \frac{3}{3} - \frac{20}{51}}$

Step 3.10.2

Write each expression with a common denominator of $51$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.10.2.1

Multiply $\frac{4}{17}$ by $\frac{3}{3}$ .

$2 + \frac{64}{51} \cdot \frac{1}{\frac{4 \cdot 3}{17 \cdot 3} - \frac{20}{51}}$

Step 3.10.2.2

Multiply $17$ by $3$ .

$2 + \frac{64}{51} \cdot \frac{1}{\frac{4 \cdot 3}{51} - \frac{20}{51}}$

Step 3.10.3

Combine the numerators over the common denominator.

$2 + \frac{64}{51} \cdot \frac{1}{\frac{4 \cdot 3 - 20}{51}}$

Step 3.10.4

Simplify the numerator.

Tap for more steps...

Step 3.10.4.1

Multiply $4$ by $3$ .

$2 + \frac{64}{51} \cdot \frac{1}{\frac{12 - 20}{51}}$

Step 3.10.4.2

Subtract $20$ from $12$ .

$2 + \frac{64}{51} \cdot \frac{1}{\frac{- 8}{51}}$

Step 3.10.5

Move the negative in front of the fraction.

$2 + \frac{64}{51} \cdot \frac{1}{- \frac{8}{51}}$

Step 3.11

Cancel the common factor of $1$ and $- 1$ .

Tap for more steps...

Step 3.11.1

Rewrite $1$ as $- 1 (- 1)$ .

$2 + \frac{64}{51} \cdot \frac{- 1 (- 1)}{- \frac{8}{51}}$

Step 3.11.2

Move the negative in front of the fraction.

$2 + \frac{64}{51} (- \frac{1}{\frac{8}{51}})$

Step 3.12

Multiply the numerator by the reciprocal of the denominator.

$2 + \frac{64}{51} (- (1 (\frac{51}{8})))$

Step 3.13

Multiply $\frac{51}{8}$ by $1$ .

$2 + \frac{64}{51} (- \frac{51}{8})$

Step 3.14

Cancel the common factor of $8$ .

Tap for more steps...

Step 3.14.1

Move the leading negative in $- \frac{51}{8}$ into the numerator.

$2 + \frac{64}{51} \cdot \frac{- 51}{8}$

Step 3.14.2

Factor $8$ out of $64$ .

$2 + \frac{8 (8)}{51} \cdot \frac{- 51}{8}$

Step 3.14.3

Cancel the common factor.

$2 + \frac{8 \cdot 8}{51} \cdot \frac{- 51}{8}$

Step 3.14.4

Rewrite the expression.

$2 + \frac{8}{51} \cdot - 51$

Step 3.15

Cancel the common factor of $51$ .

Tap for more steps...

Step 3.15.1

Factor $51$ out of $- 51$ .

$2 + \frac{8}{51} \cdot (51 (- 1))$

Step 3.15.2

Cancel the common factor.

$2 + \frac{8}{51} \cdot (51 \cdot - 1)$

Step 3.15.3

Rewrite the expression.

$2 + 8 \cdot - 1$

Step 3.16

Multiply $8$ by $- 1$ .

$2 - 8$

Step 4

Subtract $8$ from $2$ .

$- 6$