Simplify 9/10*(-2/3)+(1/7-2/3)÷( square root of 343/7)

$\frac{9}{10} \cdot (- \frac{2}{3}) + (\frac{1}{7} - \frac{2}{3}) \div \sqrt{\frac{343}{7}}$

Step 1

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{10} \cdot (- \frac{2}{3}) + (\frac{1}{7} \cdot \frac{3}{3} - \frac{2}{3}) \div \sqrt{\frac{343}{7}}$

Step 2

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{9}{10} \cdot (- \frac{2}{3}) + (\frac{1}{7} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{7}{7}) \div \sqrt{\frac{343}{7}}$

Step 3

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

Multiply $\frac{1}{7}$ by $\frac{3}{3}$ .

$\frac{9}{10} \cdot (- \frac{2}{3}) + (\frac{3}{7 \cdot 3} - \frac{2}{3} \cdot \frac{7}{7}) \div \sqrt{\frac{343}{7}}$

Multiply $7$ by $3$ .

$\frac{9}{10} \cdot (- \frac{2}{3}) + (\frac{3}{21} - \frac{2}{3} \cdot \frac{7}{7}) \div \sqrt{\frac{343}{7}}$

Multiply $\frac{2}{3}$ by $\frac{7}{7}$ .

$\frac{9}{10} \cdot (- \frac{2}{3}) + (\frac{3}{21} - \frac{2 \cdot 7}{3 \cdot 7}) \div \sqrt{\frac{343}{7}}$

Multiply $3$ by $7$ .

$\frac{9}{10} \cdot (- \frac{2}{3}) + (\frac{3}{21} - \frac{2 \cdot 7}{21}) \div \sqrt{\frac{343}{7}}$

Step 4

Combine the numerators over the common denominator.

$\frac{9}{10} \cdot (- \frac{2}{3}) + \frac{3 - 2 \cdot 7}{21} \div \sqrt{\frac{343}{7}}$

Step 5

Simplify the numerator.

Multiply $- 2$ by $7$ .

$\frac{9}{10} \cdot (- \frac{2}{3}) + \frac{3 - 14}{21} \div \sqrt{\frac{343}{7}}$

Subtract $14$ from $3$ .

$\frac{9}{10} \cdot (- \frac{2}{3}) + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Step 6

Simplify each term.

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{9}{10} \cdot \frac{- 2}{3} + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Factor $3$ out of $9$ .

$\frac{3 (3)}{10} \cdot \frac{- 2}{3} + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Cancel the common factor.

$\frac{3 \cdot 3}{10} \cdot \frac{- 2}{3} + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Rewrite the expression.

$\frac{3}{10} \cdot - 2 + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$\frac{3}{2 (5)} \cdot - 2 + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Factor $2$ out of $- 2$ .

$\frac{3}{2 \cdot 5} \cdot (2 \cdot - 1) + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Cancel the common factor.

$\frac{3}{2 \cdot 5} \cdot (2 \cdot - 1) + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Rewrite the expression.

$\frac{3}{5} \cdot - 1 + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Combine $\frac{3}{5}$ and $- 1$ .

$\frac{3 \cdot - 1}{5} + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Multiply $3$ by $- 1$ .

$\frac{- 3}{5} + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Move the negative in front of the fraction.

$- \frac{3}{5} + \frac{- 11}{21} \div \sqrt{\frac{343}{7}}$

Rewrite the division as a fraction.

$- \frac{3}{5} + \frac{\frac{- 11}{21}}{\sqrt{\frac{343}{7}}}$

Cancel the common factor of $343$ and $7$ .

Factor $7$ out of $343$ .

$- \frac{3}{5} + \frac{\frac{- 11}{21}}{\sqrt{\frac{7 \cdot 49}{7}}}$

Cancel the common factors.

Factor $7$ out of $7$ .

$- \frac{3}{5} + \frac{\frac{- 11}{21}}{\sqrt{\frac{7 \cdot 49}{7 (1)}}}$

Cancel the common factor.

$- \frac{3}{5} + \frac{\frac{- 11}{21}}{\sqrt{\frac{7 \cdot 49}{7 \cdot 1}}}$

Rewrite the expression.

$- \frac{3}{5} + \frac{\frac{- 11}{21}}{\sqrt{\frac{49}{1}}}$

Divide $49$ by $1$ .

$- \frac{3}{5} + \frac{\frac{- 11}{21}}{\sqrt{49}}$

Multiply the numerator by the reciprocal of the denominator.

$- \frac{3}{5} + \frac{- 11}{21} \cdot \frac{1}{\sqrt{49}}$

Move the negative in front of the fraction.

$- \frac{3}{5} - \frac{11}{21} \cdot \frac{1}{\sqrt{49}}$

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

$- \frac{3}{5} - \frac{11}{21} \cdot \frac{1}{\sqrt{7^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$- \frac{3}{5} - \frac{11}{21} \cdot \frac{1}{7}$

Multiply $- \frac{11}{21} \cdot \frac{1}{7}$ .

Multiply $\frac{1}{7}$ by $\frac{11}{21}$ .

$- \frac{3}{5} - \frac{11}{7 \cdot 21}$

Multiply $7$ by $21$ .

$- \frac{3}{5} - \frac{11}{147}$

Step 7

To write $- \frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{147}{147}$ .

$- \frac{3}{5} \cdot \frac{147}{147} - \frac{11}{147}$

Step 8

To write $- \frac{11}{147}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{3}{5} \cdot \frac{147}{147} - \frac{11}{147} \cdot \frac{5}{5}$

Step 9

Write each expression with a common denominator of $735$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{5}$ by $\frac{147}{147}$ .

$- \frac{3 \cdot 147}{5 \cdot 147} - \frac{11}{147} \cdot \frac{5}{5}$

Multiply $5$ by $147$ .

$- \frac{3 \cdot 147}{735} - \frac{11}{147} \cdot \frac{5}{5}$

Multiply $\frac{11}{147}$ by $\frac{5}{5}$ .

$- \frac{3 \cdot 147}{735} - \frac{11 \cdot 5}{147 \cdot 5}$

Multiply $147$ by $5$ .

$- \frac{3 \cdot 147}{735} - \frac{11 \cdot 5}{735}$

Step 10

Combine the numerators over the common denominator.

$\frac{- 3 \cdot 147 - 11 \cdot 5}{735}$

Step 11

Simplify the numerator.

Multiply $- 3$ by $147$ .

$\frac{- 441 - 11 \cdot 5}{735}$

Multiply $- 11$ by $5$ .

$\frac{- 441 - 55}{735}$

Subtract $55$ from $- 441$ .

$\frac{- 496}{735}$

Step 12

Move the negative in front of the fraction.

$- \frac{496}{735}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$- \frac{496}{735}$

Decimal Form:

$- 0.67482993 \dots$

Simplify 9/10*(-2/3)+(1/7-2/3)÷( square root of 343/7)

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