Basic Math Examples

$\frac{\frac{5}{6} - 2 (- 1 \frac{3}{4})}{5 \frac{1}{5}}$

Step 1

Convert $1 \frac{3}{4}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{\frac{5}{6} - 2 (- (1 + \frac{3}{4}))}{5 \frac{1}{5}}$

Step 1.2

Add $1$ and $\frac{3}{4}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{\frac{5}{6} - 2 (- (\frac{4}{4} + \frac{3}{4}))}{5 \frac{1}{5}}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{\frac{5}{6} - 2 (- \frac{4 + 3}{4})}{5 \frac{1}{5}}$

Step 1.2.3

Add $4$ and $3$ .

$\frac{\frac{5}{6} - 2 (- \frac{7}{4})}{5 \frac{1}{5}}$

Step 2

Convert $5 \frac{1}{5}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{\frac{5}{6} - 2 (- \frac{7}{4})}{5 + \frac{1}{5}}$

Step 2.2

Add $5$ and $\frac{1}{5}$ .

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Step 2.2.1

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

$\frac{\frac{5}{6} - 2 (- \frac{7}{4})}{5 \cdot \frac{5}{5} + \frac{1}{5}}$

Step 2.2.2

Combine $5$ and $\frac{5}{5}$ .

$\frac{\frac{5}{6} - 2 (- \frac{7}{4})}{\frac{5 \cdot 5}{5} + \frac{1}{5}}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{\frac{5}{6} - 2 (- \frac{7}{4})}{\frac{5 \cdot 5 + 1}{5}}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $5$ .

$\frac{\frac{5}{6} - 2 (- \frac{7}{4})}{\frac{25 + 1}{5}}$

Step 2.2.4.2

Add $25$ and $1$ .

$\frac{\frac{5}{6} - 2 (- \frac{7}{4})}{\frac{26}{5}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$(\frac{5}{6} - 2 (- \frac{7}{4})) \frac{5}{26}$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$(\frac{5}{6} - 2 (\frac{- 7}{4})) \frac{5}{26}$

Step 4.1.2

Factor $2$ out of $- 2$ .

$(\frac{5}{6} + 2 (- 1) \frac{- 7}{4}) \frac{5}{26}$

Step 4.1.3

Factor $2$ out of $4$ .

$(\frac{5}{6} + 2 \cdot - 1 \frac{- 7}{2 \cdot 2}) \frac{5}{26}$

Step 4.1.4

Cancel the common factor.

$(\frac{5}{6} + 2 \cdot - 1 \frac{- 7}{2 \cdot 2}) \frac{5}{26}$

Step 4.1.5

Rewrite the expression.

$(\frac{5}{6} - 1 (\frac{- 7}{2})) \frac{5}{26}$

Step 4.2

Move the negative in front of the fraction.

$(\frac{5}{6} - 1 (- \frac{7}{2})) \frac{5}{26}$

Step 4.3

Multiply $- 1 (- \frac{7}{2})$ .

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Step 4.3.1

Multiply $- 1$ by $- 1$ .

$(\frac{5}{6} + 1 (\frac{7}{2})) \frac{5}{26}$

Step 4.3.2

Multiply $\frac{7}{2}$ by $1$ .

$(\frac{5}{6} + \frac{7}{2}) \frac{5}{26}$

Step 5

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

$(\frac{5}{6} + \frac{7}{2} \cdot \frac{3}{3}) \frac{5}{26}$

Step 6

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

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

$(\frac{5}{6} + \frac{7 \cdot 3}{2 \cdot 3}) \frac{5}{26}$

Step 6.2

Multiply $2$ by $3$ .

$(\frac{5}{6} + \frac{7 \cdot 3}{6}) \frac{5}{26}$

Step 7

Combine the numerators over the common denominator.

$\frac{5 + 7 \cdot 3}{6} \cdot \frac{5}{26}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $7$ by $3$ .

$\frac{5 + 21}{6} \cdot \frac{5}{26}$

Step 8.2

Add $5$ and $21$ .

$\frac{26}{6} \cdot \frac{5}{26}$

Step 9

Cancel the common factor of $26$ .

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Step 9.1

Cancel the common factor.

$\frac{26}{6} \cdot \frac{5}{26}$

Step 9.2

Rewrite the expression.

$\frac{1}{6} \cdot 5$

Step 10

Combine $\frac{1}{6}$ and $5$ .

$\frac{5}{6}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{6}$

Decimal Form:

$0.8\overline{3}$