Basic Math Examples

$- (\frac{\frac{31}{7}}{\frac{26}{10}} + \frac{5}{2}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $26$ and $10$ .

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Step 1.1.1.1

Factor $2$ out of $26$ .

$- (\frac{\frac{31}{7}}{\frac{2 (13)}{10}} + \frac{5}{2}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.1.1.2

Cancel the common factors.

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Step 1.1.1.2.1

Factor $2$ out of $10$ .

$- (\frac{\frac{31}{7}}{\frac{2 \cdot 13}{2 \cdot 5}} + \frac{5}{2}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.1.1.2.2

Cancel the common factor.

$- (\frac{\frac{31}{7}}{\frac{2 \cdot 13}{2 \cdot 5}} + \frac{5}{2}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.1.1.2.3

Rewrite the expression.

$- (\frac{\frac{31}{7}}{\frac{13}{5}} + \frac{5}{2}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.1.2

Multiply the numerator by the reciprocal of the denominator.

$- (\frac{31}{7} \cdot \frac{5}{13} + \frac{5}{2}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.1.3

Multiply $\frac{31}{7} \cdot \frac{5}{13}$ .

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Step 1.1.3.1

Multiply $\frac{31}{7}$ by $\frac{5}{13}$ .

$- (\frac{31 \cdot 5}{7 \cdot 13} + \frac{5}{2}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.1.3.2

Multiply $31$ by $5$ .

$- (\frac{155}{7 \cdot 13} + \frac{5}{2}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.1.3.3

Multiply $7$ by $13$ .

$- (\frac{155}{91} + \frac{5}{2}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.2

To write $\frac{155}{91}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- (\frac{155}{91} \cdot \frac{2}{2} + \frac{5}{2}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.3

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{91}{91}$ .

$- (\frac{155}{91} \cdot \frac{2}{2} + \frac{5}{2} \cdot \frac{91}{91}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.4

Write each expression with a common denominator of $182$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{155}{91}$ by $\frac{2}{2}$ .

$- (\frac{155 \cdot 2}{91 \cdot 2} + \frac{5}{2} \cdot \frac{91}{91}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.4.2

Multiply $91$ by $2$ .

$- (\frac{155 \cdot 2}{182} + \frac{5}{2} \cdot \frac{91}{91}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.4.3

Multiply $\frac{5}{2}$ by $\frac{91}{91}$ .

$- (\frac{155 \cdot 2}{182} + \frac{5 \cdot 91}{2 \cdot 91}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.4.4

Multiply $2$ by $91$ .

$- (\frac{155 \cdot 2}{182} + \frac{5 \cdot 91}{182}) \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.5

Combine the numerators over the common denominator.

$- \frac{155 \cdot 2 + 5 \cdot 91}{182} \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $155$ by $2$ .

$- \frac{310 + 5 \cdot 91}{182} \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.6.2

Multiply $5$ by $91$ .

$- \frac{310 + 455}{182} \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.6.3

Add $310$ and $455$ .

$- \frac{765}{182} \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.7

Cancel the common factor of $9$ .

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Step 1.7.1

Move the leading negative in $- \frac{765}{182}$ into the numerator.

$\frac{- 765}{182} \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.7.2

Factor $9$ out of $- 765$ .

$\frac{9 (- 85)}{182} \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.7.3

Cancel the common factor.

$\frac{9 \cdot - 85}{182} \cdot \frac{7}{9} - \frac{3}{7}$

Step 1.7.4

Rewrite the expression.

$\frac{- 85}{182} \cdot 7 - \frac{3}{7}$

Step 1.8

Cancel the common factor of $7$ .

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Step 1.8.1

Factor $7$ out of $182$ .

$\frac{- 85}{7 (26)} \cdot 7 - \frac{3}{7}$

Step 1.8.2

Cancel the common factor.

$\frac{- 85}{7 \cdot 26} \cdot 7 - \frac{3}{7}$

Step 1.8.3

Rewrite the expression.

$\frac{- 85}{26} - \frac{3}{7}$

Step 1.9

Move the negative in front of the fraction.

$- \frac{85}{26} - \frac{3}{7}$

Step 2

To write $- \frac{85}{26}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{85}{26} \cdot \frac{7}{7} - \frac{3}{7}$

Step 3

To write $- \frac{3}{7}$ as a fraction with a common denominator, multiply by $\frac{26}{26}$ .

$- \frac{85}{26} \cdot \frac{7}{7} - \frac{3}{7} \cdot \frac{26}{26}$

Step 4

Write each expression with a common denominator of $182$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{85}{26}$ by $\frac{7}{7}$ .

$- \frac{85 \cdot 7}{26 \cdot 7} - \frac{3}{7} \cdot \frac{26}{26}$

Step 4.2

Multiply $26$ by $7$ .

$- \frac{85 \cdot 7}{182} - \frac{3}{7} \cdot \frac{26}{26}$

Step 4.3

Multiply $\frac{3}{7}$ by $\frac{26}{26}$ .

$- \frac{85 \cdot 7}{182} - \frac{3 \cdot 26}{7 \cdot 26}$

Step 4.4

Multiply $7$ by $26$ .

$- \frac{85 \cdot 7}{182} - \frac{3 \cdot 26}{182}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 85 \cdot 7 - 3 \cdot 26}{182}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 85$ by $7$ .

$\frac{- 595 - 3 \cdot 26}{182}$

Step 6.2

Multiply $- 3$ by $26$ .

$\frac{- 595 - 78}{182}$

Step 6.3

Subtract $78$ from $- 595$ .

$\frac{- 673}{182}$

Step 7

Move the negative in front of the fraction.

$- \frac{673}{182}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{673}{182}$

Decimal Form:

$- 3.69780219 \dots$

Mixed Number Form:

$- 3 \frac{127}{182}$