Basic Math Examples

$\frac{7}{5} z + \frac{4}{10} z = \frac{36}{10}$

Step 1

Simplify $\frac{7}{5} z + \frac{4}{10} z$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{7}{5}$ and $z$ .

$\frac{7 z}{5} + \frac{4}{10} z = \frac{36}{10}$

Step 1.1.2

Cancel the common factor of $4$ and $10$ .

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Step 1.1.2.1

Factor $2$ out of $4$ .

$\frac{7 z}{5} + \frac{2 (2)}{10} z = \frac{36}{10}$

Step 1.1.2.2

Cancel the common factors.

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Step 1.1.2.2.1

Factor $2$ out of $10$ .

$\frac{7 z}{5} + \frac{2 \cdot 2}{2 \cdot 5} z = \frac{36}{10}$

Step 1.1.2.2.2

Cancel the common factor.

$\frac{7 z}{5} + \frac{2 \cdot 2}{2 \cdot 5} z = \frac{36}{10}$

Step 1.1.2.2.3

Rewrite the expression.

$\frac{7 z}{5} + \frac{2}{5} z = \frac{36}{10}$

Step 1.1.3

Combine $\frac{2}{5}$ and $z$ .

$\frac{7 z}{5} + \frac{2 z}{5} = \frac{36}{10}$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$\frac{7 z + 2 z}{5} = \frac{36}{10}$

Step 1.2.2

Add $7 z$ and $2 z$ .

$\frac{9 z}{5} = \frac{36}{10}$

Step 2

Cancel the common factor of $36$ and $10$ .

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Step 2.1

Factor $2$ out of $36$ .

$\frac{9 z}{5} = \frac{2 (18)}{10}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $10$ .

$\frac{9 z}{5} = \frac{2 \cdot 18}{2 \cdot 5}$

Step 2.2.2

Cancel the common factor.

$\frac{9 z}{5} = \frac{2 \cdot 18}{2 \cdot 5}$

Step 2.2.3

Rewrite the expression.

$\frac{9 z}{5} = \frac{18}{5}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$9 z = 18$

Step 4

Divide each term in $9 z = 18$ by $9$ and simplify.

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Step 4.1

Divide each term in $9 z = 18$ by $9$ .

$\frac{9 z}{9} = \frac{18}{9}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $9$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{9 z}{9} = \frac{18}{9}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z = \frac{18}{9}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $18$ by $9$ .

$z = 2$