Algebra Examples

$2 \frac{1}{4} x + (4 \frac{1}{3} x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

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.

$(2 + \frac{1}{4}) x + (4 \frac{1}{3} x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

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 $\frac{4}{4}$ .

$(2 \cdot \frac{4}{4} + \frac{1}{4}) x + (4 \frac{1}{3} x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

Step 1.2.2

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

$(\frac{2 \cdot 4}{4} + \frac{1}{4}) x + (4 \frac{1}{3} x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 1}{4} x + (4 \frac{1}{3} x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $2$ by $4$ .

$\frac{8 + 1}{4} x + (4 \frac{1}{3} x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

Step 1.2.4.2

Add $8$ and $1$ .

$\frac{9}{4} x + (4 \frac{1}{3} x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

Step 2

Convert $4 \frac{1}{3}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

$\frac{9}{4} x + ((4 + \frac{1}{3}) x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

Step 2.2

Add $4$ and $\frac{1}{3}$ .

Tap for more steps...

Step 2.2.1

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

$\frac{9}{4} x + ((4 \cdot \frac{3}{3} + \frac{1}{3}) x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

Step 2.2.2

Combine $4$ and $\frac{3}{3}$ .

$\frac{9}{4} x + ((\frac{4 \cdot 3}{3} + \frac{1}{3}) x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{9}{4} x + (\frac{4 \cdot 3 + 1}{3} x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $4$ by $3$ .

$\frac{9}{4} x + (\frac{12 + 1}{3} x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

Step 2.2.4.2

Add $12$ and $1$ .

$\frac{9}{4} x + (\frac{13}{3} x - 7 \frac{4}{5}) \div 2 \frac{3}{5}$

Step 3

Convert $7 \frac{4}{5}$ to an improper fraction.

Tap for more steps...

Step 3.1

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

$\frac{9}{4} x + (\frac{13}{3} x - (7 + \frac{4}{5})) \div 2 \frac{3}{5}$

Step 3.2

Add $7$ and $\frac{4}{5}$ .

Tap for more steps...

Step 3.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9}{4} x + (\frac{13}{3} x - (7 \cdot \frac{5}{5} + \frac{4}{5})) \div 2 \frac{3}{5}$

Step 3.2.2

Combine $7$ and $\frac{5}{5}$ .

$\frac{9}{4} x + (\frac{13}{3} x - (\frac{7 \cdot 5}{5} + \frac{4}{5})) \div 2 \frac{3}{5}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{9}{4} x + (\frac{13}{3} x - \frac{7 \cdot 5 + 4}{5}) \div 2 \frac{3}{5}$

Step 3.2.4

Simplify the numerator.

Tap for more steps...

Step 3.2.4.1

Multiply $7$ by $5$ .

$\frac{9}{4} x + (\frac{13}{3} x - \frac{35 + 4}{5}) \div 2 \frac{3}{5}$

Step 3.2.4.2

Add $35$ and $4$ .

$\frac{9}{4} x + (\frac{13}{3} x - \frac{39}{5}) \div 2 \frac{3}{5}$

Step 4

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

Tap for more steps...

Step 4.1

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

$\frac{9}{4} x + (\frac{13}{3} x - \frac{39}{5}) \div (2 + \frac{3}{5})$

Step 4.2

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

Tap for more steps...

Step 4.2.1

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

$\frac{9}{4} x + (\frac{13}{3} x - \frac{39}{5}) \div (2 \cdot \frac{5}{5} + \frac{3}{5})$

Step 4.2.2

Combine $2$ and $\frac{5}{5}$ .

$\frac{9}{4} x + (\frac{13}{3} x - \frac{39}{5}) \div (\frac{2 \cdot 5}{5} + \frac{3}{5})$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{9}{4} x + (\frac{13}{3} x - \frac{39}{5}) \div \frac{2 \cdot 5 + 3}{5}$

Step 4.2.4

Simplify the numerator.

Tap for more steps...

Step 4.2.4.1

Multiply $2$ by $5$ .

$\frac{9}{4} x + (\frac{13}{3} x - \frac{39}{5}) \div \frac{10 + 3}{5}$

Step 4.2.4.2

Add $10$ and $3$ .

$\frac{9}{4} x + (\frac{13}{3} x - \frac{39}{5}) \div \frac{13}{5}$

Step 5

To write $\frac{13}{3} x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9}{4} x + (\frac{13}{3} x \cdot \frac{5}{5} - \frac{39}{5}) \div \frac{13}{5}$

Step 6

Simplify terms.

Tap for more steps...

Step 6.1

Combine $\frac{13}{3} x$ and $\frac{5}{5}$ .

$\frac{9}{4} x + (\frac{\frac{13}{3} x \cdot 5}{5} - \frac{39}{5}) \div \frac{13}{5}$

Step 6.2

Combine the numerators over the common denominator.

$\frac{9}{4} x + \frac{\frac{13}{3} x \cdot 5 - 39}{5} \div \frac{13}{5}$

Step 7

Simplify each term.

Tap for more steps...

Step 7.1

Combine $\frac{9}{4}$ and $x$ .

$\frac{9 x}{4} + \frac{\frac{13}{3} x \cdot 5 - 39}{5} \div \frac{13}{5}$

Step 7.2

To divide by a fraction, multiply by its reciprocal.

$\frac{9 x}{4} + \frac{\frac{13}{3} x \cdot 5 - 39}{5} \cdot \frac{5}{13}$

Step 7.3

Cancel the common factor of $5$ .

Tap for more steps...

Step 7.3.1

Cancel the common factor.

$\frac{9 x}{4} + \frac{\frac{13}{3} x \cdot 5 - 39}{5} \cdot \frac{5}{13}$

Step 7.3.2

Rewrite the expression.

$\frac{9 x}{4} + (\frac{13}{3} x \cdot 5 - 39) \frac{1}{13}$

Step 7.4

Combine $\frac{13}{3}$ and $x$ .

$\frac{9 x}{4} + (\frac{13 x}{3} \cdot 5 - 39) \frac{1}{13}$

Step 7.5

Combine $\frac{13 x}{3}$ and $5$ .

$\frac{9 x}{4} + (\frac{13 x \cdot 5}{3} - 39) \frac{1}{13}$

Step 7.6

Multiply $5$ by $13$ .

$\frac{9 x}{4} + (\frac{65 x}{3} - 39) \frac{1}{13}$

Step 7.7

To write $- 39$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9 x}{4} + (\frac{65 x}{3} - 39 \cdot \frac{3}{3}) \frac{1}{13}$

Step 7.8

Combine $- 39$ and $\frac{3}{3}$ .

$\frac{9 x}{4} + (\frac{65 x}{3} + \frac{- 39 \cdot 3}{3}) \frac{1}{13}$

Step 7.9

Combine the numerators over the common denominator.

$\frac{9 x}{4} + \frac{65 x - 39 \cdot 3}{3} \cdot \frac{1}{13}$

Step 7.10

Simplify the numerator.

Tap for more steps...

Step 7.10.1

Factor $13$ out of $65 x - 39 \cdot 3$ .

Tap for more steps...

Step 7.10.1.1

Factor $13$ out of $65 x$ .

$\frac{9 x}{4} + \frac{13 (5 x) - 39 \cdot 3}{3} \cdot \frac{1}{13}$

Step 7.10.1.2

Factor $13$ out of $- 39 \cdot 3$ .

$\frac{9 x}{4} + \frac{13 (5 x) + 13 (- 3 \cdot 3)}{3} \cdot \frac{1}{13}$

Step 7.10.1.3

Factor $13$ out of $13 (5 x) + 13 (- 3 \cdot 3)$ .

$\frac{9 x}{4} + \frac{13 (5 x - 3 \cdot 3)}{3} \cdot \frac{1}{13}$

Step 7.10.2

Multiply $- 3$ by $3$ .

$\frac{9 x}{4} + \frac{13 (5 x - 9)}{3} \cdot \frac{1}{13}$

Step 7.11

Cancel the common factor of $13$ .

Tap for more steps...

Step 7.11.1

Cancel the common factor.

$\frac{9 x}{4} + \frac{13 (5 x - 9)}{3} \cdot \frac{1}{13}$

Step 7.11.2

Rewrite the expression.

$\frac{9 x}{4} + \frac{5 x - 9}{3}$

Step 8

To write $\frac{9 x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9 x}{4} \cdot \frac{3}{3} + \frac{5 x - 9}{3}$

Step 9

To write $\frac{5 x - 9}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9 x}{4} \cdot \frac{3}{3} + \frac{5 x - 9}{3} \cdot \frac{4}{4}$

Step 10

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

Tap for more steps...

Step 10.1

Multiply $\frac{9 x}{4}$ by $\frac{3}{3}$ .

$\frac{9 x \cdot 3}{4 \cdot 3} + \frac{5 x - 9}{3} \cdot \frac{4}{4}$

Step 10.2

Multiply $4$ by $3$ .

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

Step 10.3

Multiply $\frac{5 x - 9}{3}$ by $\frac{4}{4}$ .

$\frac{9 x \cdot 3}{12} + \frac{(5 x - 9) \cdot 4}{3 \cdot 4}$

Step 10.4

Multiply $3$ by $4$ .

$\frac{9 x \cdot 3}{12} + \frac{(5 x - 9) \cdot 4}{12}$

Step 11

Combine the numerators over the common denominator.

$\frac{9 x \cdot 3 + (5 x - 9) \cdot 4}{12}$

Step 12

Simplify the numerator.

Tap for more steps...

Step 12.1

Multiply $3$ by $9$ .

$\frac{27 x + (5 x - 9) \cdot 4}{12}$

Step 12.2

Apply the distributive property.

$\frac{27 x + 5 x \cdot 4 - 9 \cdot 4}{12}$

Step 12.3

Multiply $4$ by $5$ .

$\frac{27 x + 20 x - 9 \cdot 4}{12}$

Step 12.4

Multiply $- 9$ by $4$ .

$\frac{27 x + 20 x - 36}{12}$

Step 12.5

Add $27 x$ and $20 x$ .

$\frac{47 x - 36}{12}$