Pre-Algebra Examples

$\frac{5}{2} + \frac{9}{4} + \frac{37}{8}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{5}{2}$ by $\frac{4}{4}$ .

$\frac{5}{2} \cdot \frac{4}{4} + \frac{9}{4} + \frac{37}{8}$

Step 1.2

Multiply $\frac{5}{2}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 4}{2 \cdot 4} + \frac{9}{4} + \frac{37}{8}$

Step 1.3

Multiply $\frac{9}{4}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 4}{2 \cdot 4} + \frac{9}{4} \cdot \frac{2}{2} + \frac{37}{8}$

Step 1.4

Multiply $\frac{9}{4}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 4}{2 \cdot 4} + \frac{9 \cdot 2}{4 \cdot 2} + \frac{37}{8}$

Step 1.5

Multiply $2$ by $4$ .

$\frac{5 \cdot 4}{8} + \frac{9 \cdot 2}{4 \cdot 2} + \frac{37}{8}$

Step 1.6

Reorder the factors of $4 \cdot 2$ .

$\frac{5 \cdot 4}{8} + \frac{9 \cdot 2}{2 \cdot 4} + \frac{37}{8}$

Step 1.7

Multiply $2$ by $4$ .

$\frac{5 \cdot 4}{8} + \frac{9 \cdot 2}{8} + \frac{37}{8}$

Step 2

Combine the numerators over the common denominator.

$\frac{5 \cdot 4 + 9 \cdot 2 + 37}{8}$

Step 3

Simplify each term.

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Step 3.1

Multiply $5$ by $4$ .

$\frac{20 + 9 \cdot 2 + 37}{8}$

Step 3.2

Multiply $9$ by $2$ .

$\frac{20 + 18 + 37}{8}$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $20$ and $18$ .

$\frac{38 + 37}{8}$

Step 4.2

Add $38$ and $37$ .

$\frac{75}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{75}{8}$

Decimal Form:

$9.375$

Mixed Number Form:

$9 \frac{3}{8}$