Finite Math Examples

$(\frac{13}{5}) a^{2} + (\frac{17}{9}) a - \frac{11}{10} a^{2} - 5 a + (\frac{10}{9}) a$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{13}{5}$ and $a^{2}$ .

$\frac{13 a^{2}}{5} + (\frac{17}{9}) a - \frac{11}{10} a^{2} - 5 a + (\frac{10}{9}) a$

Step 1.2

Combine $\frac{17}{9}$ and $a$ .

$\frac{13 a^{2}}{5} + \frac{17 a}{9} - \frac{11}{10} a^{2} - 5 a + (\frac{10}{9}) a$

Step 1.3

Combine $a^{2}$ and $\frac{11}{10}$ .

$\frac{13 a^{2}}{5} + \frac{17 a}{9} - \frac{a^{2} \cdot 11}{10} - 5 a + (\frac{10}{9}) a$

Step 1.4

Move $11$ to the left of $a^{2}$ .

$\frac{13 a^{2}}{5} + \frac{17 a}{9} - \frac{11 \cdot a^{2}}{10} - 5 a + (\frac{10}{9}) a$

Step 1.5

Combine $\frac{10}{9}$ and $a$ .

$\frac{13 a^{2}}{5} + \frac{17 a}{9} - \frac{11 a^{2}}{10} - 5 a + \frac{10 a}{9}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$- 5 a + \frac{13 a^{2}}{5} + \frac{17 a + 10 a}{9} + \frac{- 11 a^{2}}{10}$

Step 2.2

Add $17 a$ and $10 a$ .

$- 5 a + \frac{13 a^{2}}{5} + \frac{27 a}{9} + \frac{- 11 a^{2}}{10}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $27$ and $9$ .

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Step 3.1.1

Factor $9$ out of $27 a$ .

$- 5 a + \frac{13 a^{2}}{5} + \frac{9 (3 a)}{9} + \frac{- 11 a^{2}}{10}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $9$ out of $9$ .

$- 5 a + \frac{13 a^{2}}{5} + \frac{9 (3 a)}{9 (1)} + \frac{- 11 a^{2}}{10}$

Step 3.1.2.2

Cancel the common factor.

$- 5 a + \frac{13 a^{2}}{5} + \frac{9 (3 a)}{9 \cdot 1} + \frac{- 11 a^{2}}{10}$

Step 3.1.2.3

Rewrite the expression.

$- 5 a + \frac{13 a^{2}}{5} + \frac{3 a}{1} + \frac{- 11 a^{2}}{10}$

Step 3.1.2.4

Divide $3 a$ by $1$ .

$- 5 a + \frac{13 a^{2}}{5} + 3 a + \frac{- 11 a^{2}}{10}$

Step 3.2

Move the negative in front of the fraction.

$- 5 a + \frac{13 a^{2}}{5} + 3 a - \frac{11 a^{2}}{10}$

Step 4

Add $- 5 a$ and $3 a$ .

$\frac{13 a^{2}}{5} - 2 a - \frac{11 a^{2}}{10}$

Step 5

To write $\frac{13 a^{2}}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 a + \frac{13 a^{2}}{5} \cdot \frac{2}{2} - \frac{11 a^{2}}{10}$

Step 6

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{13 a^{2}}{5}$ by $\frac{2}{2}$ .

$- 2 a + \frac{13 a^{2} \cdot 2}{5 \cdot 2} - \frac{11 a^{2}}{10}$

Step 6.2

Multiply $5$ by $2$ .

$- 2 a + \frac{13 a^{2} \cdot 2}{10} - \frac{11 a^{2}}{10}$

Step 7

Combine the numerators over the common denominator.

$- 2 a + \frac{13 a^{2} \cdot 2 - 11 a^{2}}{10}$

Step 8

Simplify each term.

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Step 8.1

Simplify the numerator.

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Step 8.1.1

Factor $a^{2}$ out of $13 a^{2} \cdot 2 - 11 a^{2}$ .

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Step 8.1.1.1

Factor $a^{2}$ out of $13 a^{2} \cdot 2$ .

$- 2 a + \frac{a^{2} (13 \cdot 2) - 11 a^{2}}{10}$

Step 8.1.1.2

Factor $a^{2}$ out of $- 11 a^{2}$ .

$- 2 a + \frac{a^{2} (13 \cdot 2) + a^{2} \cdot - 11}{10}$

Step 8.1.1.3

Factor $a^{2}$ out of $a^{2} (13 \cdot 2) + a^{2} \cdot - 11$ .

$- 2 a + \frac{a^{2} (13 \cdot 2 - 11)}{10}$

Step 8.1.2

Multiply $13$ by $2$ .

$- 2 a + \frac{a^{2} (26 - 11)}{10}$

Step 8.1.3

Subtract $11$ from $26$ .

$- 2 a + \frac{a^{2} \cdot 15}{10}$

Step 8.2

Cancel the common factor of $15$ and $10$ .

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Step 8.2.1

Factor $5$ out of $a^{2} \cdot 15$ .

$- 2 a + \frac{5 (a^{2} \cdot 3)}{10}$

Step 8.2.2

Cancel the common factors.

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Step 8.2.2.1

Factor $5$ out of $10$ .

$- 2 a + \frac{5 (a^{2} \cdot 3)}{5 (2)}$

Step 8.2.2.2

Cancel the common factor.

$- 2 a + \frac{5 (a^{2} \cdot 3)}{5 \cdot 2}$

Step 8.2.2.3

Rewrite the expression.

$- 2 a + \frac{a^{2} \cdot 3}{2}$

Step 8.3

Move $3$ to the left of $a^{2}$ .

$- 2 a + \frac{3 a^{2}}{2}$