Basic Math Examples

$(\frac{864}{9 \div 897 - 21}) - (64 - 22 \div 5)$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $9$ and $897$ .

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Step 1.1.1

Factor $3$ out of $9$ .

$\frac{864}{3 (3) \div 897 - 21} - (64 - 22 \div 5)$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $897$ .

$\frac{864}{3 \cdot 3 \div 3 \cdot 299 - 21} - (64 - 22 \div 5)$

Step 1.1.2.2

Cancel the common factor.

$\frac{864}{3 \cdot 3 \div 3 \cdot 299 - 21} - (64 - 22 \div 5)$

Step 1.1.2.3

Rewrite the expression.

$\frac{864}{\frac{3}{299} - 21} - (64 - 22 \div 5)$

Step 1.2

Cancel the common factor of $864$ and $\frac{3}{299} - 21$ .

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Step 1.2.1

Factor $3$ out of $864$ .

$\frac{3 \cdot 288}{\frac{3}{299} - 21} - (64 - 22 \div 5)$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $\frac{3}{299}$ .

$\frac{3 \cdot 288}{3 (\frac{1}{299}) - 21} - (64 - 22 \div 5)$

Step 1.2.2.2

Factor $3$ out of $- 21$ .

$\frac{3 \cdot 288}{3 (\frac{1}{299}) + 3 \cdot - 7} - (64 - 22 \div 5)$

Step 1.2.2.3

Factor $3$ out of $3 (\frac{1}{299}) + 3 \cdot - 7$ .

$\frac{3 \cdot 288}{3 (\frac{1}{299} - 7)} - (64 - 22 \div 5)$

Step 1.2.2.4

Cancel the common factor.

$\frac{3 \cdot 288}{3 (\frac{1}{299} - 7)} - (64 - 22 \div 5)$

Step 1.2.2.5

Rewrite the expression.

$\frac{288}{\frac{1}{299} - 7} - (64 - 22 \div 5)$

Step 1.3

Simplify the denominator.

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Step 1.3.1

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{299}{299}$ .

$\frac{288}{\frac{1}{299} - 7 \cdot \frac{299}{299}} - (64 - 22 \div 5)$

Step 1.3.2

Combine $- 7$ and $\frac{299}{299}$ .

$\frac{288}{\frac{1}{299} + \frac{- 7 \cdot 299}{299}} - (64 - 22 \div 5)$

Step 1.3.3

Combine the numerators over the common denominator.

$\frac{288}{\frac{1 - 7 \cdot 299}{299}} - (64 - 22 \div 5)$

Step 1.3.4

Simplify the numerator.

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Step 1.3.4.1

Multiply $- 7$ by $299$ .

$\frac{288}{\frac{1 - 2093}{299}} - (64 - 22 \div 5)$

Step 1.3.4.2

Subtract $2093$ from $1$ .

$\frac{288}{\frac{- 2092}{299}} - (64 - 22 \div 5)$

Step 1.3.5

Move the negative in front of the fraction.

$\frac{288}{- \frac{2092}{299}} - (64 - 22 \div 5)$

Step 1.4

Multiply the numerator by the reciprocal of the denominator.

$288 (- \frac{299}{2092}) - (64 - 22 \div 5)$

Step 1.5

Cancel the common factor of $4$ .

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Step 1.5.1

Move the leading negative in $- \frac{299}{2092}$ into the numerator.

$288 (\frac{- 299}{2092}) - (64 - 22 \div 5)$

Step 1.5.2

Factor $4$ out of $288$ .

$4 (72) \frac{- 299}{2092} - (64 - 22 \div 5)$

Step 1.5.3

Factor $4$ out of $2092$ .

$4 \cdot 72 \frac{- 299}{4 \cdot 523} - (64 - 22 \div 5)$

Step 1.5.4

Cancel the common factor.

$4 \cdot 72 \frac{- 299}{4 \cdot 523} - (64 - 22 \div 5)$

Step 1.5.5

Rewrite the expression.

$72 (\frac{- 299}{523}) - (64 - 22 \div 5)$

Step 1.6

Combine $72$ and $\frac{- 299}{523}$ .

$\frac{72 \cdot - 299}{523} - (64 - 22 \div 5)$

Step 1.7

Multiply $72$ by $- 299$ .

$\frac{- 21528}{523} - (64 - 22 \div 5)$

Step 1.8

Move the negative in front of the fraction.

$- \frac{21528}{523} - (64 - 22 \div 5)$

Step 1.9

Rewrite the division as a fraction.

$- \frac{21528}{523} - (64 - \frac{22}{5})$

Step 1.10

To write $64$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{21528}{523} - (64 \cdot \frac{5}{5} - \frac{22}{5})$

Step 1.11

Combine $64$ and $\frac{5}{5}$ .

$- \frac{21528}{523} - (\frac{64 \cdot 5}{5} - \frac{22}{5})$

Step 1.12

Combine the numerators over the common denominator.

$- \frac{21528}{523} - \frac{64 \cdot 5 - 22}{5}$

Step 1.13

Simplify the numerator.

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Step 1.13.1

Multiply $64$ by $5$ .

$- \frac{21528}{523} - \frac{320 - 22}{5}$

Step 1.13.2

Subtract $22$ from $320$ .

$- \frac{21528}{523} - \frac{298}{5}$

Step 2

To write $- \frac{21528}{523}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{21528}{523} \cdot \frac{5}{5} - \frac{298}{5}$

Step 3

To write $- \frac{298}{5}$ as a fraction with a common denominator, multiply by $\frac{523}{523}$ .

$- \frac{21528}{523} \cdot \frac{5}{5} - \frac{298}{5} \cdot \frac{523}{523}$

Step 4

Write each expression with a common denominator of $2615$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{21528}{523}$ by $\frac{5}{5}$ .

$- \frac{21528 \cdot 5}{523 \cdot 5} - \frac{298}{5} \cdot \frac{523}{523}$

Step 4.2

Multiply $523$ by $5$ .

$- \frac{21528 \cdot 5}{2615} - \frac{298}{5} \cdot \frac{523}{523}$

Step 4.3

Multiply $\frac{298}{5}$ by $\frac{523}{523}$ .

$- \frac{21528 \cdot 5}{2615} - \frac{298 \cdot 523}{5 \cdot 523}$

Step 4.4

Multiply $5$ by $523$ .

$- \frac{21528 \cdot 5}{2615} - \frac{298 \cdot 523}{2615}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 21528 \cdot 5 - 298 \cdot 523}{2615}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 21528$ by $5$ .

$\frac{- 107640 - 298 \cdot 523}{2615}$

Step 6.2

Multiply $- 298$ by $523$ .

$\frac{- 107640 - 155854}{2615}$

Step 6.3

Subtract $155854$ from $- 107640$ .

$\frac{- 263494}{2615}$

Step 7

Move the negative in front of the fraction.

$- \frac{263494}{2615}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{263494}{2615}$

Decimal Form:

$- 100.76252390 \dots$

Mixed Number Form:

$- 100 \frac{1994}{2615}$