Simplify (2.6÷1.2-4 1/2)÷(0.75-1/3)

$(2.6 \div 1.2 - 4 \frac{1}{2}) \div (0.75 - \frac{1}{3})$

Step 1

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

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

$(2.6 \div 1.2 - (4 + \frac{1}{2})) \div (0.75 - \frac{1}{3})$

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

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

$(2.6 \div 1.2 - (4 \cdot \frac{2}{2} + \frac{1}{2})) \div (0.75 - \frac{1}{3})$

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

$(2.6 \div 1.2 - (\frac{4 \cdot 2}{2} + \frac{1}{2})) \div (0.75 - \frac{1}{3})$

Combine the numerators over the common denominator.

$(2.6 \div 1.2 - \frac{4 \cdot 2 + 1}{2}) \div (0.75 - \frac{1}{3})$

Simplify the numerator.

Multiply $4$ by $2$ .

$(2.6 \div 1.2 - \frac{8 + 1}{2}) \div (0.75 - \frac{1}{3})$

Add $8$ and $1$ .

$(2.6 \div 1.2 - \frac{9}{2}) \div (0.75 - \frac{1}{3})$

Step 2

Rewrite the division as a fraction.

$\frac{2.6 \div 1.2 - \frac{9}{2}}{0.75 - \frac{1}{3}}$

Step 3

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

Multiply $\frac{2.6 \div 1.2 - \frac{9}{2}}{0.75 - \frac{1}{3}}$ by $\frac{6}{6}$ .

$\frac{6}{6} \cdot \frac{2.6 \div 1.2 - \frac{9}{2}}{0.75 - \frac{1}{3}}$

Combine.

$\frac{6 (2.6 \div 1.2 - \frac{9}{2})}{6 (0.75 - \frac{1}{3})}$

Step 4

Apply the distributive property.

$\frac{6 (2.6 \div 1.2) + 6 (- \frac{9}{2})}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Step 5

Simplify by cancelling.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$\frac{6 (2.6 \div 1.2) + 6 (\frac{- 9}{2})}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Factor $2$ out of $6$ .

$\frac{6 (2.6 \div 1.2) + 2 (3) \frac{- 9}{2}}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Cancel the common factor.

$\frac{6 (2.6 \div 1.2) + 2 \cdot 3 \frac{- 9}{2}}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Rewrite the expression.

$\frac{6 (2.6 \div 1.2) + 3 \cdot - 9}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Multiply $3$ by $- 9$ .

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 + 6 (\frac{- 1}{3})}$

Factor $3$ out of $6$ .

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 + 3 (2) \frac{- 1}{3}}$

Cancel the common factor.

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 + 3 \cdot 2 \frac{- 1}{3}}$

Rewrite the expression.

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 + 2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 - 2}$

Step 6

Simplify the numerator.

Divide $2.6$ by $1.2$ .

$\frac{6 \cdot 2.1\overline{6} - 27}{6 \cdot 0.75 - 2}$

Multiply $6$ by $2.1\overline{6}$ .

$\frac{13 - 27}{6 \cdot 0.75 - 2}$

Subtract $27$ from $13$ .

$\frac{- 14}{6 \cdot 0.75 - 2}$

Step 7

Simplify the denominator.

Multiply $6$ by $0.75$ .

$\frac{- 14}{4.5 - 2}$

Subtract $2$ from $4.5$ .

$\frac{- 14}{2.5}$

Step 8

Divide $- 14$ by $2.5$ .

$- 5.6$

Simplify (2.6÷1.2-4 1/2)÷(0.75-1/3)

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