Basic Math Examples

$\frac{5}{6} + \frac{z}{8} + \frac{4}{3}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{5}{6}$ by $\frac{4}{4}$ .

$\frac{5}{6} \cdot \frac{4}{4} + \frac{z}{8} + \frac{4}{3}$

Step 1.2

Multiply $\frac{5}{6}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 4}{6 \cdot 4} + \frac{z}{8} + \frac{4}{3}$

Step 1.3

Multiply $\frac{z}{8}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 4}{6 \cdot 4} + \frac{z}{8} \cdot \frac{3}{3} + \frac{4}{3}$

Step 1.4

Multiply $\frac{z}{8}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 4}{6 \cdot 4} + \frac{z \cdot 3}{8 \cdot 3} + \frac{4}{3}$

Step 1.5

Multiply $\frac{4}{3}$ by $\frac{8}{8}$ .

$\frac{5 \cdot 4}{6 \cdot 4} + \frac{z \cdot 3}{8 \cdot 3} + \frac{4}{3} \cdot \frac{8}{8}$

Step 1.6

Multiply $\frac{4}{3}$ by $\frac{8}{8}$ .

$\frac{5 \cdot 4}{6 \cdot 4} + \frac{z \cdot 3}{8 \cdot 3} + \frac{4 \cdot 8}{3 \cdot 8}$

Step 1.7

Reorder the factors of $6 \cdot 4$ .

$\frac{5 \cdot 4}{4 \cdot 6} + \frac{z \cdot 3}{8 \cdot 3} + \frac{4 \cdot 8}{3 \cdot 8}$

Step 1.8

Multiply $4$ by $6$ .

$\frac{5 \cdot 4}{24} + \frac{z \cdot 3}{8 \cdot 3} + \frac{4 \cdot 8}{3 \cdot 8}$

Step 1.9

Reorder the factors of $8 \cdot 3$ .

$\frac{5 \cdot 4}{24} + \frac{z \cdot 3}{3 \cdot 8} + \frac{4 \cdot 8}{3 \cdot 8}$

Step 1.10

Multiply $3$ by $8$ .

$\frac{5 \cdot 4}{24} + \frac{z \cdot 3}{24} + \frac{4 \cdot 8}{3 \cdot 8}$

Step 1.11

Multiply $3$ by $8$ .

$\frac{5 \cdot 4}{24} + \frac{z \cdot 3}{24} + \frac{4 \cdot 8}{24}$

Step 2

Combine the numerators over the common denominator.

$\frac{5 \cdot 4 + z \cdot 3 + 4 \cdot 8}{24}$

Step 3

Simplify each term.

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Step 3.1

Multiply $5$ by $4$ .

$\frac{20 + z \cdot 3 + 4 \cdot 8}{24}$

Step 3.2

Move $3$ to the left of $z$ .

$\frac{20 + 3 \cdot z + 4 \cdot 8}{24}$

Step 3.3

Multiply $4$ by $8$ .

$\frac{20 + 3 z + 32}{24}$

Step 4

Add $20$ and $32$ .

$\frac{3 z + 52}{24}$