Basic Math Examples

$(\frac{1}{4} z^{2} - \frac{1}{5} z) - (- \frac{3}{20} z^{2} + \frac{1}{10} z - \frac{13}{20})$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{4}$ and $z^{2}$ .

$\frac{z^{2}}{4} - \frac{1}{5} z - (- \frac{3}{20} z^{2} + \frac{1}{10} z - \frac{13}{20})$

Step 1.2

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

$\frac{z^{2}}{4} - \frac{z}{5} - (- \frac{3}{20} z^{2} + \frac{1}{10} z - \frac{13}{20})$

Step 1.3

Simplify each term.

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Step 1.3.1

Combine $z^{2}$ and $\frac{3}{20}$ .

$\frac{z^{2}}{4} - \frac{z}{5} - (- \frac{z^{2} \cdot 3}{20} + \frac{1}{10} z - \frac{13}{20})$

Step 1.3.2

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

$\frac{z^{2}}{4} - \frac{z}{5} - (- \frac{3 \cdot z^{2}}{20} + \frac{1}{10} z - \frac{13}{20})$

Step 1.3.3

Combine $\frac{1}{10}$ and $z$ .

$\frac{z^{2}}{4} - \frac{z}{5} - (- \frac{3 z^{2}}{20} + \frac{z}{10} - \frac{13}{20})$

Step 1.4

Apply the distributive property.

$\frac{z^{2}}{4} - \frac{z}{5} - - \frac{3 z^{2}}{20} - \frac{z}{10} - - \frac{13}{20}$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $- - \frac{3 z^{2}}{20}$ .

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Step 1.5.1.1

Multiply $- 1$ by $- 1$ .

$\frac{z^{2}}{4} - \frac{z}{5} + 1 \frac{3 z^{2}}{20} - \frac{z}{10} - - \frac{13}{20}$

Step 1.5.1.2

Multiply $\frac{3 z^{2}}{20}$ by $1$ .

$\frac{z^{2}}{4} - \frac{z}{5} + \frac{3 z^{2}}{20} - \frac{z}{10} - - \frac{13}{20}$

Step 1.5.2

Multiply $- - \frac{13}{20}$ .

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Step 1.5.2.1

Multiply $- 1$ by $- 1$ .

$\frac{z^{2}}{4} - \frac{z}{5} + \frac{3 z^{2}}{20} - \frac{z}{10} + 1 (\frac{13}{20})$

Step 1.5.2.2

Multiply $\frac{13}{20}$ by $1$ .

$\frac{z^{2}}{4} - \frac{z}{5} + \frac{3 z^{2}}{20} - \frac{z}{10} + \frac{13}{20}$

Step 2

To write $\frac{z^{2}}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{z}{5} + \frac{z^{2}}{4} \cdot \frac{5}{5} + \frac{3 z^{2}}{20} - \frac{z}{10} + \frac{13}{20}$

Step 3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{z^{2}}{4}$ by $\frac{5}{5}$ .

$- \frac{z}{5} + \frac{z^{2} \cdot 5}{4 \cdot 5} + \frac{3 z^{2}}{20} - \frac{z}{10} + \frac{13}{20}$

Step 3.2

Multiply $4$ by $5$ .

$- \frac{z}{5} + \frac{z^{2} \cdot 5}{20} + \frac{3 z^{2}}{20} - \frac{z}{10} + \frac{13}{20}$

Step 4

Simplify terms.

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Step 4.1

Combine the numerators over the common denominator.

$- \frac{z}{5} + \frac{z^{2} \cdot 5 + 3 z^{2}}{20} - \frac{z}{10} + \frac{13}{20}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{- z}{5} + \frac{z^{2} \cdot 5 + 3 z^{2} + 13}{20} + \frac{- z}{10}$

Step 5

Move $5$ to the left of $z^{2}$ .

$\frac{- z}{5} + \frac{5 z^{2} + 3 z^{2} + 13}{20} + \frac{- z}{10}$

Step 6

Add $5 z^{2}$ and $3 z^{2}$ .

$\frac{- z}{5} + \frac{8 z^{2} + 13}{20} + \frac{- z}{10}$

Step 7

Find the common denominator.

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Step 7.1

Multiply $\frac{- z}{5}$ by $\frac{4}{4}$ .

$\frac{- z}{5} \cdot \frac{4}{4} + \frac{8 z^{2} + 13}{20} + \frac{- z}{10}$

Step 7.2

Multiply $\frac{- z}{5}$ by $\frac{4}{4}$ .

$\frac{- z \cdot 4}{5 \cdot 4} + \frac{8 z^{2} + 13}{20} + \frac{- z}{10}$

Step 7.3

Multiply $\frac{- z}{10}$ by $\frac{2}{2}$ .

$\frac{- z \cdot 4}{5 \cdot 4} + \frac{8 z^{2} + 13}{20} + \frac{- z}{10} \cdot \frac{2}{2}$

Step 7.4

Multiply $\frac{- z}{10}$ by $\frac{2}{2}$ .

$\frac{- z \cdot 4}{5 \cdot 4} + \frac{8 z^{2} + 13}{20} + \frac{- z \cdot 2}{10 \cdot 2}$

Step 7.5

Reorder the factors of $5 \cdot 4$ .

$\frac{- z \cdot 4}{4 \cdot 5} + \frac{8 z^{2} + 13}{20} + \frac{- z \cdot 2}{10 \cdot 2}$

Step 7.6

Multiply $4$ by $5$ .

$\frac{- z \cdot 4}{20} + \frac{8 z^{2} + 13}{20} + \frac{- z \cdot 2}{10 \cdot 2}$

Step 7.7

Reorder the factors of $10 \cdot 2$ .

$\frac{- z \cdot 4}{20} + \frac{8 z^{2} + 13}{20} + \frac{- z \cdot 2}{2 \cdot 10}$

Step 7.8

Multiply $2$ by $10$ .

$\frac{- z \cdot 4}{20} + \frac{8 z^{2} + 13}{20} + \frac{- z \cdot 2}{20}$

Step 8

Combine the numerators over the common denominator.

$\frac{- z \cdot 4 + 8 z^{2} + 13 - z \cdot 2}{20}$

Step 9

Simplify each term.

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Step 9.1

Multiply $4$ by $- 1$ .

$\frac{- 4 z + 8 z^{2} + 13 - z \cdot 2}{20}$

Step 9.2

Multiply $2$ by $- 1$ .

$\frac{- 4 z + 8 z^{2} + 13 - 2 z}{20}$

Step 10

Simplify by adding terms.

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Step 10.1

Subtract $2 z$ from $- 4 z$ .

$\frac{- 6 z + 8 z^{2} + 13}{20}$

Step 10.2

Reorder $- 6 z$ and $8 z^{2}$ .

$\frac{8 z^{2} - 6 z + 13}{20}$