Basic Math Examples

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

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

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:

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