Basic Math Examples

$\frac{93}{15} + \frac{14}{3} \div \frac{93}{15} - \frac{14}{3}$

Step 1

Find the common denominator.

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Step 1.1

Cancel the common factor of $93$ and $15$ .

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Step 1.1.1

Factor $3$ out of $93$ .

$\frac{93}{15} + \frac{14}{3} \div \frac{3 (31)}{15} - \frac{14}{3}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $15$ .

$\frac{93}{15} + \frac{14}{3} \div \frac{3 \cdot 31}{3 \cdot 5} - \frac{14}{3}$

Step 1.1.2.2

Cancel the common factor.

$\frac{93}{15} + \frac{14}{3} \div \frac{3 \cdot 31}{3 \cdot 5} - \frac{14}{3}$

Step 1.1.2.3

Rewrite the expression.

$\frac{93}{15} + \frac{14}{3} \div \frac{31}{5} - \frac{14}{3}$

Step 1.2

Multiply $\frac{93}{15}$ by $\frac{\frac{31}{5}}{\frac{31}{5}}$ .

$\frac{93}{15} \cdot \frac{\frac{31}{5}}{\frac{31}{5}} + \frac{14}{3} \div \frac{31}{5} - \frac{14}{3}$

Step 1.3

Multiply $\frac{93}{15}$ by $\frac{\frac{31}{5}}{\frac{31}{5}}$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{14}{3} \div \frac{31}{5} - \frac{14}{3}$

Step 1.4

Multiply $\frac{14}{3} \div \frac{31}{5}$ by $\frac{15}{15}$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{14}{3} \div \frac{31}{5} \cdot \frac{15}{15} - \frac{14}{3}$

Step 1.5

Multiply $\frac{14}{3} \div \frac{31}{5}$ by $\frac{15}{15}$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot 15}{\frac{31}{5} \cdot 15} - \frac{14}{3}$

Step 1.6

Multiply $\frac{14}{3}$ by $\frac{\frac{5 \cdot 31}{5}}{\frac{5 \cdot 31}{5}}$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot 15}{\frac{31}{5} \cdot 15} - (\frac{14}{3} \cdot \frac{\frac{5 \cdot 31}{5}}{\frac{5 \cdot 31}{5}})$

Step 1.7

Multiply $\frac{14}{3}$ by $\frac{\frac{5 \cdot 31}{5}}{\frac{5 \cdot 31}{5}}$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot 15}{\frac{31}{5} \cdot 15} - \frac{14 \frac{5 \cdot 31}{5}}{3 \frac{5 \cdot 31}{5}}$

Step 1.8

Reorder the factors of $\frac{31}{5} \cdot 15$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot 15}{15 (\frac{31}{5})} - \frac{14 \frac{5 \cdot 31}{5}}{3 \frac{5 \cdot 31}{5}}$

Step 1.9

Combine $15$ and $\frac{31}{5}$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot 15}{\frac{15 \cdot 31}{5}} - \frac{14 \frac{5 \cdot 31}{5}}{3 \frac{5 \cdot 31}{5}}$

Step 1.10

Multiply $15$ by $31$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot 15}{\frac{465}{5}} - \frac{14 \frac{5 \cdot 31}{5}}{3 \frac{5 \cdot 31}{5}}$

Step 1.11

Multiply $5$ by $31$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot 15}{\frac{465}{5}} - \frac{14 \frac{5 \cdot 31}{5}}{3 (\frac{155}{5})}$

Step 1.12

Combine $3$ and $\frac{155}{5}$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot 15}{\frac{465}{5}} - \frac{14 \frac{5 \cdot 31}{5}}{\frac{3 \cdot 155}{5}}$

Step 1.13

Multiply $3$ by $155$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot 15}{\frac{465}{5}} - \frac{14 \frac{5 \cdot 31}{5}}{\frac{465}{5}}$

Step 2

Combine the numerators over the common denominator.

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot 15 - 14 \frac{5 \cdot 31}{5}}{\frac{465}{5}}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Factor $3$ out of $15$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot (3 (5)) - 14 \frac{5 \cdot 31}{5}}{\frac{465}{5}}$

Step 3.1.2

Cancel the common factor.

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{\frac{14}{3} \cdot (3 \cdot 5) - 14 \frac{5 \cdot 31}{5}}{\frac{465}{5}}$

Step 3.1.3

Rewrite the expression.

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{14 \cdot 5 - 14 \frac{5 \cdot 31}{5}}{\frac{465}{5}}$

Step 3.2

Multiply $14$ by $5$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{70 - 14 \frac{5 \cdot 31}{5}}{\frac{465}{5}}$

Step 3.3

Cancel the common factor of $5$ .

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Step 3.3.1

Cancel the common factor.

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{70 - 14 \frac{5 \cdot 31}{5}}{\frac{465}{5}}$

Step 3.3.2

Divide $31$ by $1$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{70 - 14 \cdot 31}{\frac{465}{5}}$

Step 3.4

Multiply $- 14$ by $31$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{70 - 434}{\frac{465}{5}}$

Step 4

Subtract $434$ from $70$ .

$\frac{93 (\frac{31}{5})}{15 (\frac{31}{5})} + \frac{- 364}{\frac{465}{5}}$

Step 5

Simplify each term.

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Step 5.1

Cancel the common factor of $93$ and $15$ .

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Step 5.1.1

Factor $3$ out of $93 (\frac{31}{5})$ .

$\frac{3 (31 (\frac{31}{5}))}{15 (\frac{31}{5})} + \frac{- 364}{\frac{465}{5}}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $3$ out of $15 (\frac{31}{5})$ .

$\frac{3 (31 (\frac{31}{5}))}{3 (5 (\frac{31}{5}))} + \frac{- 364}{\frac{465}{5}}$

Step 5.1.2.2

Cancel the common factor.

$\frac{3 (31 (\frac{31}{5}))}{3 (5 (\frac{31}{5}))} + \frac{- 364}{\frac{465}{5}}$

Step 5.1.2.3

Rewrite the expression.

$\frac{31 (\frac{31}{5})}{5 (\frac{31}{5})} + \frac{- 364}{\frac{465}{5}}$

Step 5.2

Cancel the common factor of $\frac{31}{5}$ .

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Step 5.2.1

Cancel the common factor.

$\frac{31 (\frac{31}{5})}{5 (\frac{31}{5})} + \frac{- 364}{\frac{465}{5}}$

Step 5.2.2

Rewrite the expression.

$\frac{31}{5} + \frac{- 364}{\frac{465}{5}}$

Step 5.3

Cancel the common factor of $465$ and $5$ .

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Step 5.3.1

Factor $5$ out of $465$ .

$\frac{31}{5} + \frac{- 364}{\frac{5 \cdot 93}{5}}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $5$ out of $5$ .

$\frac{31}{5} + \frac{- 364}{\frac{5 \cdot 93}{5 (1)}}$

Step 5.3.2.2

Cancel the common factor.

$\frac{31}{5} + \frac{- 364}{\frac{5 \cdot 93}{5 \cdot 1}}$

Step 5.3.2.3

Rewrite the expression.

$\frac{31}{5} + \frac{- 364}{\frac{93}{1}}$

Step 5.3.2.4

Divide $93$ by $1$ .

$\frac{31}{5} + \frac{- 364}{93}$

Step 5.4

Move the negative in front of the fraction.

$\frac{31}{5} - \frac{364}{93}$

Step 6

To write $\frac{31}{5}$ as a fraction with a common denominator, multiply by $\frac{93}{93}$ .

$\frac{31}{5} \cdot \frac{93}{93} - \frac{364}{93}$

Step 7

To write $- \frac{364}{93}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{31}{5} \cdot \frac{93}{93} - \frac{364}{93} \cdot \frac{5}{5}$

Step 8

Write each expression with a common denominator of $465$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{31}{5}$ by $\frac{93}{93}$ .

$\frac{31 \cdot 93}{5 \cdot 93} - \frac{364}{93} \cdot \frac{5}{5}$

Step 8.2

Multiply $5$ by $93$ .

$\frac{31 \cdot 93}{465} - \frac{364}{93} \cdot \frac{5}{5}$

Step 8.3

Multiply $\frac{364}{93}$ by $\frac{5}{5}$ .

$\frac{31 \cdot 93}{465} - \frac{364 \cdot 5}{93 \cdot 5}$

Step 8.4

Multiply $93$ by $5$ .

$\frac{31 \cdot 93}{465} - \frac{364 \cdot 5}{465}$

Step 9

Combine the numerators over the common denominator.

$\frac{31 \cdot 93 - 364 \cdot 5}{465}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $31$ by $93$ .

$\frac{2883 - 364 \cdot 5}{465}$

Step 10.2

Multiply $- 364$ by $5$ .

$\frac{2883 - 1820}{465}$

Step 10.3

Subtract $1820$ from $2883$ .

$\frac{1063}{465}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{1063}{465}$

Decimal Form:

$2.28602150 \dots$

Mixed Number Form:

$2 \frac{133}{465}$