Basic Math Examples

$(6 \frac{3}{4} \cdot (2 \frac{2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4}) \cdot \frac{8}{9} \div \frac{3}{2}$

Step 1

Convert $6 \frac{3}{4}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

$(6 + \frac{3}{4}) \cdot (2 \frac{2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 1.2

Add $6$ and $\frac{3}{4}$ .

Tap for more steps...

Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(6 \cdot \frac{4}{4} + \frac{3}{4}) \cdot (2 \frac{2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 1.2.2

Combine $6$ and $\frac{4}{4}$ .

$(\frac{6 \cdot 4}{4} + \frac{3}{4}) \cdot (2 \frac{2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{6 \cdot 4 + 3}{4} \cdot (2 \frac{2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $6$ by $4$ .

$\frac{24 + 3}{4} \cdot (2 \frac{2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 1.2.4.2

Add $24$ and $3$ .

$\frac{27}{4} \cdot (2 \frac{2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 2

Convert $2 \frac{2}{7}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

$\frac{27}{4} \cdot (2 + \frac{2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 2.2

Add $2$ and $\frac{2}{7}$ .

Tap for more steps...

Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{27}{4} \cdot (2 \cdot \frac{7}{7} + \frac{2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 2.2.2

Combine $2$ and $\frac{7}{7}$ .

$\frac{27}{4} \cdot (\frac{2 \cdot 7}{7} + \frac{2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{27}{4} \cdot (\frac{2 \cdot 7 + 2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $2$ by $7$ .

$\frac{27}{4} \cdot (\frac{14 + 2}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 2.2.4.2

Add $14$ and $2$ .

$\frac{27}{4} \cdot (\frac{16}{7} - 1 \frac{1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 3

Convert $1 \frac{1}{21}$ to an improper fraction.

Tap for more steps...

Step 3.1

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

$\frac{27}{4} \cdot (\frac{16}{7} - (1 + \frac{1}{21})) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 3.2

Add $1$ and $\frac{1}{21}$ .

Tap for more steps...

Step 3.2.1

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

$\frac{27}{4} \cdot (\frac{16}{7} - (\frac{21}{21} + \frac{1}{21})) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{27}{4} \cdot (\frac{16}{7} - \frac{21 + 1}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 3.2.3

Add $21$ and $1$ .

$\frac{27}{4} \cdot (\frac{16}{7} - \frac{22}{21}) \div 2 \frac{1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 4

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

Tap for more steps...

Step 4.1

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

$\frac{27}{4} \cdot (\frac{16}{7} - \frac{22}{21}) \div (2 + \frac{1}{4}) \cdot \frac{8}{9} \div \frac{3}{2}$

Step 4.2

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

Tap for more steps...

Step 4.2.1

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

$\frac{27}{4} \cdot (\frac{16}{7} - \frac{22}{21}) \div (2 \cdot \frac{4}{4} + \frac{1}{4}) \cdot \frac{8}{9} \div \frac{3}{2}$

Step 4.2.2

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

$\frac{27}{4} \cdot (\frac{16}{7} - \frac{22}{21}) \div (\frac{2 \cdot 4}{4} + \frac{1}{4}) \cdot \frac{8}{9} \div \frac{3}{2}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{27}{4} \cdot (\frac{16}{7} - \frac{22}{21}) \div \frac{2 \cdot 4 + 1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 4.2.4

Simplify the numerator.

Tap for more steps...

Step 4.2.4.1

Multiply $2$ by $4$ .

$\frac{27}{4} \cdot (\frac{16}{7} - \frac{22}{21}) \div \frac{8 + 1}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 4.2.4.2

Add $8$ and $1$ .

$\frac{27}{4} \cdot (\frac{16}{7} - \frac{22}{21}) \div \frac{9}{4} \cdot \frac{8}{9} \div \frac{3}{2}$

Step 5

To divide by a fraction, multiply by its reciprocal.

$\frac{27}{4} \cdot (\frac{16}{7} - \frac{22}{21}) \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

To write $\frac{16}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{27}{4} (\frac{16}{7} \cdot \frac{3}{3} - \frac{22}{21}) \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 6.2

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 6.2.1

Multiply $\frac{16}{7}$ by $\frac{3}{3}$ .

$\frac{27}{4} (\frac{16 \cdot 3}{7 \cdot 3} - \frac{22}{21}) \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 6.2.2

Multiply $7$ by $3$ .

$\frac{27}{4} (\frac{16 \cdot 3}{21} - \frac{22}{21}) \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 6.3

Combine the numerators over the common denominator.

$\frac{27}{4} \cdot \frac{16 \cdot 3 - 22}{21} \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 6.4

Simplify the numerator.

Tap for more steps...

Step 6.4.1

Multiply $16$ by $3$ .

$\frac{27}{4} \cdot \frac{48 - 22}{21} \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 6.4.2

Subtract $22$ from $48$ .

$\frac{27}{4} \cdot \frac{26}{21} \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 7

Simplify terms.

Tap for more steps...

Step 7.1

Multiply $\frac{27}{4}$ by $\frac{26}{21}$ .

$\frac{27 \cdot 26}{4 \cdot 21} \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 7.2

Multiply.

Tap for more steps...

Step 7.2.1

Multiply $27$ by $26$ .

$\frac{702}{4 \cdot 21} \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 7.2.2

Multiply $4$ by $21$ .

$\frac{702}{84} \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 7.3

Cancel the common factor of $702$ and $84$ .

Tap for more steps...

Step 7.3.1

Factor $6$ out of $702$ .

$\frac{6 (117)}{84} \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 7.3.2

Cancel the common factors.

Tap for more steps...

Step 7.3.2.1

Factor $6$ out of $84$ .

$\frac{6 \cdot 117}{6 \cdot 14} \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 7.3.2.2

Cancel the common factor.

$\frac{6 \cdot 117}{6 \cdot 14} \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 7.3.2.3

Rewrite the expression.

$\frac{117}{14} \div \frac{9}{4} \cdot \frac{8}{9} \frac{2}{3}$

Step 8

To divide by a fraction, multiply by its reciprocal.

$\frac{117}{14} \cdot \frac{4}{9} \cdot \frac{8}{9} \frac{2}{3}$

Step 9

Cancel the common factor of $9$ .

Tap for more steps...

Step 9.1

Factor $9$ out of $117$ .

$\frac{9 (13)}{14} \cdot \frac{4}{9} \cdot \frac{8}{9} \frac{2}{3}$

Step 9.2

Cancel the common factor.

$\frac{9 \cdot 13}{14} \cdot \frac{4}{9} \cdot \frac{8}{9} \frac{2}{3}$

Step 9.3

Rewrite the expression.

$\frac{13}{14} \cdot 4 \cdot \frac{8}{9} \frac{2}{3}$

Step 10

Cancel the common factor of $2$ .

Tap for more steps...

Step 10.1

Factor $2$ out of $14$ .

$\frac{13}{2 (7)} \cdot 4 \cdot \frac{8}{9} \frac{2}{3}$

Step 10.2

Factor $2$ out of $4$ .

$\frac{13}{2 \cdot 7} \cdot (2 \cdot 2) \cdot \frac{8}{9} \frac{2}{3}$

Step 10.3

Cancel the common factor.

$\frac{13}{2 \cdot 7} \cdot (2 \cdot 2) \cdot \frac{8}{9} \frac{2}{3}$

Step 10.4

Rewrite the expression.

$\frac{13}{7} \cdot 2 \cdot \frac{8}{9} \frac{2}{3}$

Step 11

Combine $\frac{13}{7}$ and $2$ .

$\frac{13 \cdot 2}{7} \cdot \frac{8}{9} \frac{2}{3}$

Step 12

Multiply $13$ by $2$ .

$\frac{26}{7} \cdot \frac{8}{9} \frac{2}{3}$

Step 13

Multiply $\frac{26}{7} \cdot \frac{8}{9}$ .

Tap for more steps...

Step 13.1

Multiply $\frac{26}{7}$ by $\frac{8}{9}$ .

$\frac{26 \cdot 8}{7 \cdot 9} \cdot \frac{2}{3}$

Step 13.2

Multiply $26$ by $8$ .

$\frac{208}{7 \cdot 9} \cdot \frac{2}{3}$

Step 13.3

Multiply $7$ by $9$ .

$\frac{208}{63} \cdot \frac{2}{3}$

Step 14

Multiply $\frac{208}{63} \cdot \frac{2}{3}$ .

Tap for more steps...

Step 14.1

Multiply $\frac{208}{63}$ by $\frac{2}{3}$ .

$\frac{208 \cdot 2}{63 \cdot 3}$

Step 14.2

Multiply $208$ by $2$ .

$\frac{416}{63 \cdot 3}$

Step 14.3

Multiply $63$ by $3$ .

$\frac{416}{189}$