Basic Math Examples

$\frac{\frac{10}{21} + \frac{1}{14}}{\frac{10}{3} - \frac{7}{9}}$

Step 1

Multiply the numerator and denominator of the fraction by $126$ .

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Step 1.1

Multiply $\frac{\frac{10}{21} + \frac{1}{14}}{\frac{10}{3} - \frac{7}{9}}$ by $\frac{126}{126}$ .

$\frac{126}{126} \cdot \frac{\frac{10}{21} + \frac{1}{14}}{\frac{10}{3} - \frac{7}{9}}$

Step 1.2

Combine.

$\frac{126 (\frac{10}{21} + \frac{1}{14})}{126 (\frac{10}{3} - \frac{7}{9})}$

Step 2

Apply the distributive property.

$\frac{126 (\frac{10}{21}) + 126 (\frac{1}{14})}{126 (\frac{10}{3}) + 126 (- \frac{7}{9})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $21$ .

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Step 3.1.1

Factor $21$ out of $126$ .

$\frac{21 (6) \frac{10}{21} + 126 (\frac{1}{14})}{126 (\frac{10}{3}) + 126 (- \frac{7}{9})}$

Step 3.1.2

Cancel the common factor.

$\frac{21 \cdot 6 \frac{10}{21} + 126 (\frac{1}{14})}{126 (\frac{10}{3}) + 126 (- \frac{7}{9})}$

Step 3.1.3

Rewrite the expression.

$\frac{6 \cdot 10 + 126 (\frac{1}{14})}{126 (\frac{10}{3}) + 126 (- \frac{7}{9})}$

Step 3.2

Multiply $6$ by $10$ .

$\frac{60 + 126 (\frac{1}{14})}{126 (\frac{10}{3}) + 126 (- \frac{7}{9})}$

Step 3.3

Cancel the common factor of $14$ .

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Step 3.3.1

Factor $14$ out of $126$ .

$\frac{60 + 14 (9) \frac{1}{14}}{126 (\frac{10}{3}) + 126 (- \frac{7}{9})}$

Step 3.3.2

Cancel the common factor.

$\frac{60 + 14 \cdot 9 \frac{1}{14}}{126 (\frac{10}{3}) + 126 (- \frac{7}{9})}$

Step 3.3.3

Rewrite the expression.

$\frac{60 + 9}{126 (\frac{10}{3}) + 126 (- \frac{7}{9})}$

Step 3.4

Cancel the common factor of $3$ .

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Step 3.4.1

Factor $3$ out of $126$ .

$\frac{60 + 9}{3 (42) \frac{10}{3} + 126 (- \frac{7}{9})}$

Step 3.4.2

Cancel the common factor.

$\frac{60 + 9}{3 \cdot 42 \frac{10}{3} + 126 (- \frac{7}{9})}$

Step 3.4.3

Rewrite the expression.

$\frac{60 + 9}{42 \cdot 10 + 126 (- \frac{7}{9})}$

Step 3.5

Multiply $42$ by $10$ .

$\frac{60 + 9}{420 + 126 (- \frac{7}{9})}$

Step 3.6

Cancel the common factor of $9$ .

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Step 3.6.1

Move the leading negative in $- \frac{7}{9}$ into the numerator.

$\frac{60 + 9}{420 + 126 (\frac{- 7}{9})}$

Step 3.6.2

Factor $9$ out of $126$ .

$\frac{60 + 9}{420 + 9 (14) \frac{- 7}{9}}$

Step 3.6.3

Cancel the common factor.

$\frac{60 + 9}{420 + 9 \cdot 14 \frac{- 7}{9}}$

Step 3.6.4

Rewrite the expression.

$\frac{60 + 9}{420 + 14 \cdot - 7}$

Step 3.7

Multiply $14$ by $- 7$ .

$\frac{60 + 9}{420 - 98}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Add $60$ and $9$ .

$\frac{69}{420 - 98}$

Step 4.2

Subtract $98$ from $420$ .

$\frac{69}{322}$

Step 4.3

Cancel the common factor of $69$ and $322$ .

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Step 4.3.1

Factor $23$ out of $69$ .

$\frac{23 (3)}{322}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $23$ out of $322$ .

$\frac{23 \cdot 3}{23 \cdot 14}$

Step 4.3.2.2

Cancel the common factor.

$\frac{23 \cdot 3}{23 \cdot 14}$

Step 4.3.2.3

Rewrite the expression.

$\frac{3}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{14}$

Decimal Form:

$0.2\overline{142857}$