Basic Math Examples

$\frac{z}{8} + \frac{z}{7} = \frac{9}{8}$

Step 1

Simplify $\frac{z}{8} + \frac{z}{7}$ .

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Step 1.1

To write $\frac{z}{8}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{z}{8} \cdot \frac{7}{7} + \frac{z}{7} = \frac{9}{8}$

Step 1.2

To write $\frac{z}{7}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{z}{8} \cdot \frac{7}{7} + \frac{z}{7} \cdot \frac{8}{8} = \frac{9}{8}$

Step 1.3

Write each expression with a common denominator of $56$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{z}{8}$ by $\frac{7}{7}$ .

$\frac{z \cdot 7}{8 \cdot 7} + \frac{z}{7} \cdot \frac{8}{8} = \frac{9}{8}$

Step 1.3.2

Multiply $8$ by $7$ .

$\frac{z \cdot 7}{56} + \frac{z}{7} \cdot \frac{8}{8} = \frac{9}{8}$

Step 1.3.3

Multiply $\frac{z}{7}$ by $\frac{8}{8}$ .

$\frac{z \cdot 7}{56} + \frac{z \cdot 8}{7 \cdot 8} = \frac{9}{8}$

Step 1.3.4

Multiply $7$ by $8$ .

$\frac{z \cdot 7}{56} + \frac{z \cdot 8}{56} = \frac{9}{8}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{z \cdot 7 + z \cdot 8}{56} = \frac{9}{8}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $7$ to the left of $z$ .

$\frac{7 \cdot z + z \cdot 8}{56} = \frac{9}{8}$

Step 1.5.2

Move $8$ to the left of $z$ .

$\frac{7 z + 8 \cdot z}{56} = \frac{9}{8}$

Step 1.5.3

Add $7 z$ and $8 z$ .

$\frac{15 z}{56} = \frac{9}{8}$

Step 2

Multiply both sides of the equation by $\frac{56}{15}$ .

$\frac{56}{15} \cdot \frac{15 z}{56} = \frac{56}{15} \cdot \frac{9}{8}$

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

Simplify $\frac{56}{15} \cdot \frac{15 z}{56}$ .

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Step 3.1.1.1

Cancel the common factor of $56$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{56}{15} \cdot \frac{15 z}{56} = \frac{56}{15} \cdot \frac{9}{8}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{15} (15 z) = \frac{56}{15} \cdot \frac{9}{8}$

Step 3.1.1.2

Cancel the common factor of $15$ .

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Step 3.1.1.2.1

Factor $15$ out of $15 z$ .

$\frac{1}{15} (15 (z)) = \frac{56}{15} \cdot \frac{9}{8}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{15} (15 z) = \frac{56}{15} \cdot \frac{9}{8}$

Step 3.1.1.2.3

Rewrite the expression.

$z = \frac{56}{15} \cdot \frac{9}{8}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{56}{15} \cdot \frac{9}{8}$ .

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Step 3.2.1.1

Cancel the common factor of $8$ .

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Step 3.2.1.1.1

Factor $8$ out of $56$ .

$z = \frac{8 (7)}{15} \cdot \frac{9}{8}$

Step 3.2.1.1.2

Cancel the common factor.

$z = \frac{8 \cdot 7}{15} \cdot \frac{9}{8}$

Step 3.2.1.1.3

Rewrite the expression.

$z = \frac{7}{15} \cdot 9$

Step 3.2.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.2.1

Factor $3$ out of $15$ .

$z = \frac{7}{3 (5)} \cdot 9$

Step 3.2.1.2.2

Factor $3$ out of $9$ .

$z = \frac{7}{3 \cdot 5} \cdot (3 \cdot 3)$

Step 3.2.1.2.3

Cancel the common factor.

$z = \frac{7}{3 \cdot 5} \cdot (3 \cdot 3)$

Step 3.2.1.2.4

Rewrite the expression.

$z = \frac{7}{5} \cdot 3$

Step 3.2.1.3

Combine $\frac{7}{5}$ and $3$ .

$z = \frac{7 \cdot 3}{5}$

Step 3.2.1.4

Multiply $7$ by $3$ .

$z = \frac{21}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = \frac{21}{5}$

Decimal Form:

$z = 4.2$

Mixed Number Form:

$z = 4 \frac{1}{5}$