Basic Math Examples

$\frac{15}{8} \cdot (- \frac{2}{5}) + (\frac{1}{7} - \frac{2}{5}) \div \sqrt{\frac{343}{7}}$

Step 1

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{15}{8} \cdot (- \frac{2}{5}) + (\frac{1}{7} \cdot \frac{5}{5} - \frac{2}{5}) \div \sqrt{\frac{343}{7}}$

Step 2

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{15}{8} \cdot (- \frac{2}{5}) + (\frac{1}{7} \cdot \frac{5}{5} - \frac{2}{5} \cdot \frac{7}{7}) \div \sqrt{\frac{343}{7}}$

Step 3

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{7}$ by $\frac{5}{5}$ .

$\frac{15}{8} \cdot (- \frac{2}{5}) + (\frac{5}{7 \cdot 5} - \frac{2}{5} \cdot \frac{7}{7}) \div \sqrt{\frac{343}{7}}$

Step 3.2

Multiply $7$ by $5$ .

$\frac{15}{8} \cdot (- \frac{2}{5}) + (\frac{5}{35} - \frac{2}{5} \cdot \frac{7}{7}) \div \sqrt{\frac{343}{7}}$

Step 3.3

Multiply $\frac{2}{5}$ by $\frac{7}{7}$ .

$\frac{15}{8} \cdot (- \frac{2}{5}) + (\frac{5}{35} - \frac{2 \cdot 7}{5 \cdot 7}) \div \sqrt{\frac{343}{7}}$

Step 3.4

Multiply $5$ by $7$ .

$\frac{15}{8} \cdot (- \frac{2}{5}) + (\frac{5}{35} - \frac{2 \cdot 7}{35}) \div \sqrt{\frac{343}{7}}$

Step 4

Combine the numerators over the common denominator.

$\frac{15}{8} \cdot (- \frac{2}{5}) + \frac{5 - 2 \cdot 7}{35} \div \sqrt{\frac{343}{7}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 2$ by $7$ .

$\frac{15}{8} \cdot (- \frac{2}{5}) + \frac{5 - 14}{35} \div \sqrt{\frac{343}{7}}$

Step 5.2

Subtract $14$ from $5$ .

$\frac{15}{8} \cdot (- \frac{2}{5}) + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6

Simplify each term.

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Step 6.1

Cancel the common factor of $5$ .

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Step 6.1.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{15}{8} \cdot \frac{- 2}{5} + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6.1.2

Factor $5$ out of $15$ .

$\frac{5 (3)}{8} \cdot \frac{- 2}{5} + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6.1.3

Cancel the common factor.

$\frac{5 \cdot 3}{8} \cdot \frac{- 2}{5} + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6.1.4

Rewrite the expression.

$\frac{3}{8} \cdot - 2 + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6.2

Cancel the common factor of $2$ .

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Step 6.2.1

Factor $2$ out of $8$ .

$\frac{3}{2 (4)} \cdot - 2 + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6.2.2

Factor $2$ out of $- 2$ .

$\frac{3}{2 \cdot 4} \cdot (2 \cdot - 1) + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6.2.3

Cancel the common factor.

$\frac{3}{2 \cdot 4} \cdot (2 \cdot - 1) + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6.2.4

Rewrite the expression.

$\frac{3}{4} \cdot - 1 + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6.3

Combine $\frac{3}{4}$ and $- 1$ .

$\frac{3 \cdot - 1}{4} + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6.4

Multiply $3$ by $- 1$ .

$\frac{- 3}{4} + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6.5

Move the negative in front of the fraction.

$- \frac{3}{4} + \frac{- 9}{35} \div \sqrt{\frac{343}{7}}$

Step 6.6

Rewrite the division as a fraction.

$- \frac{3}{4} + \frac{\frac{- 9}{35}}{\sqrt{\frac{343}{7}}}$

Step 6.7

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

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Step 6.7.1

Factor $7$ out of $343$ .

$- \frac{3}{4} + \frac{\frac{- 9}{35}}{\sqrt{\frac{7 \cdot 49}{7}}}$

Step 6.7.2

Cancel the common factors.

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Step 6.7.2.1

Factor $7$ out of $7$ .

$- \frac{3}{4} + \frac{\frac{- 9}{35}}{\sqrt{\frac{7 \cdot 49}{7 (1)}}}$

Step 6.7.2.2

Cancel the common factor.

$- \frac{3}{4} + \frac{\frac{- 9}{35}}{\sqrt{\frac{7 \cdot 49}{7 \cdot 1}}}$

Step 6.7.2.3

Rewrite the expression.

$- \frac{3}{4} + \frac{\frac{- 9}{35}}{\sqrt{\frac{49}{1}}}$

Step 6.7.2.4

Divide $49$ by $1$ .

$- \frac{3}{4} + \frac{\frac{- 9}{35}}{\sqrt{49}}$

Step 6.8

Multiply the numerator by the reciprocal of the denominator.

$- \frac{3}{4} + \frac{- 9}{35} \cdot \frac{1}{\sqrt{49}}$

Step 6.9

Move the negative in front of the fraction.

$- \frac{3}{4} - \frac{9}{35} \cdot \frac{1}{\sqrt{49}}$

Step 6.10

Simplify the denominator.

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Step 6.10.1

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

$- \frac{3}{4} - \frac{9}{35} \cdot \frac{1}{\sqrt{7^{2}}}$

Step 6.10.2

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

$- \frac{3}{4} - \frac{9}{35} \cdot \frac{1}{7}$

Step 6.11

Multiply $- \frac{9}{35} \cdot \frac{1}{7}$ .

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Step 6.11.1

Multiply $\frac{1}{7}$ by $\frac{9}{35}$ .

$- \frac{3}{4} - \frac{9}{7 \cdot 35}$

Step 6.11.2

Multiply $7$ by $35$ .

$- \frac{3}{4} - \frac{9}{245}$

Step 7

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{245}{245}$ .

$- \frac{3}{4} \cdot \frac{245}{245} - \frac{9}{245}$

Step 8

To write $- \frac{9}{245}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{3}{4} \cdot \frac{245}{245} - \frac{9}{245} \cdot \frac{4}{4}$

Step 9

Write each expression with a common denominator of $980$ , by multiplying each by an appropriate factor of $1$ .

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Step 9.1

Multiply $\frac{3}{4}$ by $\frac{245}{245}$ .

$- \frac{3 \cdot 245}{4 \cdot 245} - \frac{9}{245} \cdot \frac{4}{4}$

Step 9.2

Multiply $4$ by $245$ .

$- \frac{3 \cdot 245}{980} - \frac{9}{245} \cdot \frac{4}{4}$

Step 9.3

Multiply $\frac{9}{245}$ by $\frac{4}{4}$ .

$- \frac{3 \cdot 245}{980} - \frac{9 \cdot 4}{245 \cdot 4}$

Step 9.4

Multiply $245$ by $4$ .

$- \frac{3 \cdot 245}{980} - \frac{9 \cdot 4}{980}$

Step 10

Combine the numerators over the common denominator.

$\frac{- 3 \cdot 245 - 9 \cdot 4}{980}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply $- 3$ by $245$ .

$\frac{- 735 - 9 \cdot 4}{980}$

Step 11.2

Multiply $- 9$ by $4$ .

$\frac{- 735 - 36}{980}$

Step 11.3

Subtract $36$ from $- 735$ .

$\frac{- 771}{980}$

Step 12

Move the negative in front of the fraction.

$- \frac{771}{980}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$- \frac{771}{980}$

Decimal Form:

$- 0.78673469 \dots$