Evaluate ((5628)/(36-24))÷((147)/(24-16))

$\frac{56 \cdot 28}{36 \cdot - 24} \div \frac{14 \cdot 7}{24 \cdot - 16}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{56 \cdot 28}{36 \cdot - 24} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Step 2

Cancel the common factor of $56$ and $36$ .

Factor $4$ out of $56 \cdot 28$ .

$\frac{4 (14 \cdot 28)}{36 \cdot - 24} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Cancel the common factors.

Factor $4$ out of $36 \cdot - 24$ .

$\frac{4 (14 \cdot 28)}{4 (9 \cdot - 24)} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Cancel the common factor.

$\frac{4 (14 \cdot 28)}{4 (9 \cdot - 24)} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Rewrite the expression.

$\frac{14 \cdot 28}{9 \cdot - 24} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Step 3

Cancel the common factor of $14$ and $- 24$ .

Factor $2$ out of $14 \cdot 28$ .

$\frac{2 (7 \cdot 28)}{9 \cdot - 24} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Cancel the common factors.

Factor $2$ out of $9 \cdot - 24$ .

$\frac{2 (7 \cdot 28)}{2 (9 \cdot - 12)} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Cancel the common factor.

$\frac{2 (7 \cdot 28)}{2 (9 \cdot - 12)} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Rewrite the expression.

$\frac{7 \cdot 28}{9 \cdot - 12} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Step 4

Cancel the common factor of $28$ and $- 12$ .

Factor $4$ out of $7 \cdot 28$ .

$\frac{4 (7 \cdot 7)}{9 \cdot - 12} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Cancel the common factors.

Factor $4$ out of $9 \cdot - 12$ .

$\frac{4 (7 \cdot 7)}{4 (9 \cdot - 3)} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Cancel the common factor.

$\frac{4 (7 \cdot 7)}{4 (9 \cdot - 3)} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Rewrite the expression.

$\frac{7 \cdot 7}{9 \cdot - 3} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Step 5

Simplify the expression.

Multiply $7$ by $7$ .

$\frac{49}{9 \cdot - 3} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Multiply $9$ by $- 3$ .

$\frac{49}{- 27} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Move the negative in front of the fraction.

$- \frac{49}{27} \cdot \frac{24 \cdot - 16}{14 \cdot 7}$

Step 6

Cancel the common factor of $24$ and $14$ .

Factor $2$ out of $24 \cdot - 16$ .

$- \frac{49}{27} \cdot \frac{2 (12 \cdot - 16)}{14 \cdot 7}$

Cancel the common factors.

Factor $2$ out of $14 \cdot 7$ .

$- \frac{49}{27} \cdot \frac{2 (12 \cdot - 16)}{2 (7 \cdot 7)}$

Cancel the common factor.

$- \frac{49}{27} \cdot \frac{2 (12 \cdot - 16)}{2 (7 \cdot 7)}$

Rewrite the expression.

$- \frac{49}{27} \cdot \frac{12 \cdot - 16}{7 \cdot 7}$

Step 7

Multiply.

Multiply $12$ by $- 16$ .

$- \frac{49}{27} \cdot \frac{- 192}{7 \cdot 7}$

Multiply $7$ by $7$ .

$- \frac{49}{27} \cdot \frac{- 192}{49}$

Step 8

Cancel the common factor of $49$ .

Move the leading negative in $- \frac{49}{27}$ into the numerator.

$\frac{- 49}{27} \cdot \frac{- 192}{49}$

Factor $49$ out of $- 49$ .

$\frac{49 (- 1)}{27} \cdot \frac{- 192}{49}$

Cancel the common factor.

$\frac{49 \cdot - 1}{27} \cdot \frac{- 192}{49}$

Rewrite the expression.

$\frac{- 1}{27} \cdot - 192$

Step 9

Cancel the common factor of $3$ .

Factor $3$ out of $27$ .

$\frac{- 1}{3 (9)} \cdot - 192$

Factor $3$ out of $- 192$ .

$\frac{- 1}{3 \cdot 9} \cdot (3 \cdot - 64)$

Cancel the common factor.

$\frac{- 1}{3 \cdot 9} \cdot (3 \cdot - 64)$

Rewrite the expression.

$\frac{- 1}{9} \cdot - 64$

Step 10

Combine $\frac{- 1}{9}$ and $- 64$ .

$\frac{- - 64}{9}$

Step 11

Multiply $- 1$ by $- 64$ .

$\frac{64}{9}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{64}{9}$

Decimal Form:

$7.\overline{1}$

Mixed Number Form:

$7 \frac{1}{9}$

Evaluate ((56*28)/(36*-24))÷((14*7)/(24*-16))

Related Questions

Evaluate ((5628)/(36-24))÷((147)/(24-16))