Basic Math Examples

$\frac{z}{4} + \frac{4}{5} = \frac{5}{8}$

Step 1

Move all terms not containing $z$ to the right side of the equation.

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Step 1.1

Subtract $\frac{4}{5}$ from both sides of the equation.

$\frac{z}{4} = \frac{5}{8} - \frac{4}{5}$

Step 1.2

To write $\frac{5}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{z}{4} = \frac{5}{8} \cdot \frac{5}{5} - \frac{4}{5}$

Step 1.3

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{z}{4} = \frac{5}{8} \cdot \frac{5}{5} - \frac{4}{5} \cdot \frac{8}{8}$

Step 1.4

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{5}{8}$ by $\frac{5}{5}$ .

$\frac{z}{4} = \frac{5 \cdot 5}{8 \cdot 5} - \frac{4}{5} \cdot \frac{8}{8}$

Step 1.4.2

Multiply $8$ by $5$ .

$\frac{z}{4} = \frac{5 \cdot 5}{40} - \frac{4}{5} \cdot \frac{8}{8}$

Step 1.4.3

Multiply $\frac{4}{5}$ by $\frac{8}{8}$ .

$\frac{z}{4} = \frac{5 \cdot 5}{40} - \frac{4 \cdot 8}{5 \cdot 8}$

Step 1.4.4

Multiply $5$ by $8$ .

$\frac{z}{4} = \frac{5 \cdot 5}{40} - \frac{4 \cdot 8}{40}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{z}{4} = \frac{5 \cdot 5 - 4 \cdot 8}{40}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $5$ by $5$ .

$\frac{z}{4} = \frac{25 - 4 \cdot 8}{40}$

Step 1.6.2

Multiply $- 4$ by $8$ .

$\frac{z}{4} = \frac{25 - 32}{40}$

Step 1.6.3

Subtract $32$ from $25$ .

$\frac{z}{4} = \frac{- 7}{40}$

Step 1.7

Move the negative in front of the fraction.

$\frac{z}{4} = - \frac{7}{40}$

Step 2

Multiply both sides of the equation by $4$ .

$4 \frac{z}{4} = 4 (- \frac{7}{40})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1

Cancel the common factor.

$4 \frac{z}{4} = 4 (- \frac{7}{40})$

Step 3.1.1.2

Rewrite the expression.

$z = 4 (- \frac{7}{40})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $4 (- \frac{7}{40})$ .

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Step 3.2.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{7}{40}$ into the numerator.

$z = 4 (\frac{- 7}{40})$

Step 3.2.1.1.2

Factor $4$ out of $40$ .

$z = 4 \frac{- 7}{4 (10)}$

Step 3.2.1.1.3

Cancel the common factor.

$z = 4 \frac{- 7}{4 \cdot 10}$

Step 3.2.1.1.4

Rewrite the expression.

$z = \frac{- 7}{10}$

Step 3.2.1.2

Move the negative in front of the fraction.

$z = - \frac{7}{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{7}{10}$

Decimal Form:

$z = - 0.7$