Algebra Examples

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

Step 1

Convert $5 \frac{1}{3}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $5$ by $3$ .

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

Step 1.2.4.2

Add $15$ and $1$ .

$(\frac{16}{3} - 4 \frac{1}{3}) \div (4 - 3 \frac{1}{2})$

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.

$(\frac{16}{3} - (4 + \frac{1}{3})) \div (4 - 3 \frac{1}{2})$

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 $\frac{3}{3}$ .

$(\frac{16}{3} - (4 \cdot \frac{3}{3} + \frac{1}{3})) \div (4 - 3 \frac{1}{2})$

Step 2.2.2

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

$(\frac{16}{3} - (\frac{4 \cdot 3}{3} + \frac{1}{3})) \div (4 - 3 \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

$(\frac{16}{3} - \frac{4 \cdot 3 + 1}{3}) \div (4 - 3 \frac{1}{2})$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $4$ by $3$ .

$(\frac{16}{3} - \frac{12 + 1}{3}) \div (4 - 3 \frac{1}{2})$

Step 2.2.4.2

Add $12$ and $1$ .

$(\frac{16}{3} - \frac{13}{3}) \div (4 - 3 \frac{1}{2})$

Step 3

Convert $3 \frac{1}{2}$ to an improper fraction.

Tap for more steps...

Step 3.1

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

$(\frac{16}{3} - \frac{13}{3}) \div (4 - (3 + \frac{1}{2}))$

Step 3.2

Add $3$ and $\frac{1}{2}$ .

Tap for more steps...

Step 3.2.1

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

$(\frac{16}{3} - \frac{13}{3}) \div (4 - (3 \cdot \frac{2}{2} + \frac{1}{2}))$

Step 3.2.2

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

$(\frac{16}{3} - \frac{13}{3}) \div (4 - (\frac{3 \cdot 2}{2} + \frac{1}{2}))$

Step 3.2.3

Combine the numerators over the common denominator.

$(\frac{16}{3} - \frac{13}{3}) \div (4 - \frac{3 \cdot 2 + 1}{2})$

Step 3.2.4

Simplify the numerator.

Tap for more steps...

Step 3.2.4.1

Multiply $3$ by $2$ .

$(\frac{16}{3} - \frac{13}{3}) \div (4 - \frac{6 + 1}{2})$

Step 3.2.4.2

Add $6$ and $1$ .

$(\frac{16}{3} - \frac{13}{3}) \div (4 - \frac{7}{2})$

Step 4

Rewrite the division as a fraction.

$\frac{\frac{16}{3} - \frac{13}{3}}{4 - \frac{7}{2}}$

Step 5

Multiply the numerator and denominator of the fraction by $6$ .

Tap for more steps...

Step 5.1

Multiply $\frac{\frac{16}{3} - \frac{13}{3}}{4 - \frac{7}{2}}$ by $\frac{6}{6}$ .

$\frac{6}{6} \cdot \frac{\frac{16}{3} - \frac{13}{3}}{4 - \frac{7}{2}}$

Step 5.2

Combine.

$\frac{6 (\frac{16}{3} - \frac{13}{3})}{6 (4 - \frac{7}{2})}$

Step 6

Apply the distributive property.

$\frac{6 (\frac{16}{3}) + 6 (- \frac{13}{3})}{6 \cdot 4 + 6 (- \frac{7}{2})}$

Step 7

Simplify by cancelling.

Tap for more steps...

Step 7.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 7.1.1

Factor $3$ out of $6$ .

$\frac{3 (2) \frac{16}{3} + 6 (- \frac{13}{3})}{6 \cdot 4 + 6 (- \frac{7}{2})}$

Step 7.1.2

Cancel the common factor.

$\frac{3 \cdot 2 \frac{16}{3} + 6 (- \frac{13}{3})}{6 \cdot 4 + 6 (- \frac{7}{2})}$

Step 7.1.3

Rewrite the expression.

$\frac{2 \cdot 16 + 6 (- \frac{13}{3})}{6 \cdot 4 + 6 (- \frac{7}{2})}$

Step 7.2

Multiply $2$ by $16$ .

$\frac{32 + 6 (- \frac{13}{3})}{6 \cdot 4 + 6 (- \frac{7}{2})}$

Step 7.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 7.3.1

Move the leading negative in $- \frac{13}{3}$ into the numerator.

$\frac{32 + 6 (\frac{- 13}{3})}{6 \cdot 4 + 6 (- \frac{7}{2})}$

Step 7.3.2

Factor $3$ out of $6$ .

$\frac{32 + 3 (2) \frac{- 13}{3}}{6 \cdot 4 + 6 (- \frac{7}{2})}$

Step 7.3.3

Cancel the common factor.

$\frac{32 + 3 \cdot 2 \frac{- 13}{3}}{6 \cdot 4 + 6 (- \frac{7}{2})}$

Step 7.3.4

Rewrite the expression.

$\frac{32 + 2 \cdot - 13}{6 \cdot 4 + 6 (- \frac{7}{2})}$

Step 7.4

Multiply $2$ by $- 13$ .

$\frac{32 - 26}{6 \cdot 4 + 6 (- \frac{7}{2})}$

Step 7.5

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.5.1

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$\frac{32 - 26}{6 \cdot 4 + 6 (\frac{- 7}{2})}$

Step 7.5.2

Factor $2$ out of $6$ .

$\frac{32 - 26}{6 \cdot 4 + 2 (3) \frac{- 7}{2}}$

Step 7.5.3

Cancel the common factor.

$\frac{32 - 26}{6 \cdot 4 + 2 \cdot 3 \frac{- 7}{2}}$

Step 7.5.4

Rewrite the expression.

$\frac{32 - 26}{6 \cdot 4 + 3 \cdot - 7}$

Step 7.6

Multiply $3$ by $- 7$ .

$\frac{32 - 26}{6 \cdot 4 - 21}$

Step 8

Subtract $26$ from $32$ .

$\frac{6}{6 \cdot 4 - 21}$

Step 9

Simplify the denominator.

Tap for more steps...

Step 9.1

Multiply $6$ by $4$ .

$\frac{6}{24 - 21}$

Step 9.2

Subtract $21$ from $24$ .

$\frac{6}{3}$

Step 10

Divide $6$ by $3$ .

$2$