Basic Math Examples

$\frac{5}{8} z + \frac{3}{64} z$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{5}{8}$ and $z$ .

$\frac{5 z}{8} + \frac{3}{64} z$

Step 1.2

Combine $\frac{3}{64}$ and $z$ .

$\frac{5 z}{8} + \frac{3 z}{64}$

Step 2

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

$\frac{5 z}{8} \cdot \frac{8}{8} + \frac{3 z}{64}$

Step 3

Write each expression with a common denominator of $64$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{5 z \cdot 8}{8 \cdot 8} + \frac{3 z}{64}$

Step 3.2

Multiply $8$ by $8$ .

$\frac{5 z \cdot 8}{64} + \frac{3 z}{64}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 z \cdot 8 + 3 z}{64}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $z$ out of $5 z \cdot 8 + 3 z$ .

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Step 5.1.1

Factor $z$ out of $5 z \cdot 8$ .

$\frac{z (5 \cdot 8) + 3 z}{64}$

Step 5.1.2

Factor $z$ out of $3 z$ .

$\frac{z (5 \cdot 8) + z \cdot 3}{64}$

Step 5.1.3

Factor $z$ out of $z (5 \cdot 8) + z \cdot 3$ .

$\frac{z (5 \cdot 8 + 3)}{64}$

Step 5.2

Multiply $5$ by $8$ .

$\frac{z (40 + 3)}{64}$

Step 5.3

Add $40$ and $3$ .

$\frac{z \cdot 43}{64}$

Step 6

Move $43$ to the left of $z$ .

$\frac{43 z}{64}$