Basic Math Examples

$\frac{9}{5} - \frac{5}{8} + 3 \frac{8}{9}$

Step 1

Convert $3 \frac{8}{9}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{9}{5} - \frac{5}{8} + 3 + \frac{8}{9}$

Step 1.2

Add $3$ and $\frac{8}{9}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{9}{5} - \frac{5}{8} + 3 \cdot \frac{9}{9} + \frac{8}{9}$

Step 1.2.2

Combine $3$ and $\frac{9}{9}$ .

$\frac{9}{5} - \frac{5}{8} + \frac{3 \cdot 9}{9} + \frac{8}{9}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{9}{5} - \frac{5}{8} + \frac{3 \cdot 9 + 8}{9}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $9$ .

$\frac{9}{5} - \frac{5}{8} + \frac{27 + 8}{9}$

Step 1.2.4.2

Add $27$ and $8$ .

$\frac{9}{5} - \frac{5}{8} + \frac{35}{9}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{9}{5}$ by $\frac{72}{72}$ .

$\frac{9}{5} \cdot \frac{72}{72} - \frac{5}{8} + \frac{35}{9}$

Step 2.2

Multiply $\frac{9}{5}$ by $\frac{72}{72}$ .

$\frac{9 \cdot 72}{5 \cdot 72} - \frac{5}{8} + \frac{35}{9}$

Step 2.3

Multiply $\frac{5}{8}$ by $\frac{45}{45}$ .

$\frac{9 \cdot 72}{5 \cdot 72} - (\frac{5}{8} \cdot \frac{45}{45}) + \frac{35}{9}$

Step 2.4

Multiply $\frac{5}{8}$ by $\frac{45}{45}$ .

$\frac{9 \cdot 72}{5 \cdot 72} - \frac{5 \cdot 45}{8 \cdot 45} + \frac{35}{9}$

Step 2.5

Multiply $\frac{35}{9}$ by $\frac{40}{40}$ .

$\frac{9 \cdot 72}{5 \cdot 72} - \frac{5 \cdot 45}{8 \cdot 45} + \frac{35}{9} \cdot \frac{40}{40}$

Step 2.6

Multiply $\frac{35}{9}$ by $\frac{40}{40}$ .

$\frac{9 \cdot 72}{5 \cdot 72} - \frac{5 \cdot 45}{8 \cdot 45} + \frac{35 \cdot 40}{9 \cdot 40}$

Step 2.7

Multiply $5$ by $72$ .

$\frac{9 \cdot 72}{360} - \frac{5 \cdot 45}{8 \cdot 45} + \frac{35 \cdot 40}{9 \cdot 40}$

Step 2.8

Multiply $8$ by $45$ .

$\frac{9 \cdot 72}{360} - \frac{5 \cdot 45}{360} + \frac{35 \cdot 40}{9 \cdot 40}$

Step 2.9

Multiply $9$ by $40$ .

$\frac{9 \cdot 72}{360} - \frac{5 \cdot 45}{360} + \frac{35 \cdot 40}{360}$

Step 3

Combine the numerators over the common denominator.

$\frac{9 \cdot 72 - 5 \cdot 45 + 35 \cdot 40}{360}$

Step 4

Simplify each term.

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Step 4.1

Multiply $9$ by $72$ .

$\frac{648 - 5 \cdot 45 + 35 \cdot 40}{360}$

Step 4.2

Multiply $- 5$ by $45$ .

$\frac{648 - 225 + 35 \cdot 40}{360}$

Step 4.3

Multiply $35$ by $40$ .

$\frac{648 - 225 + 1400}{360}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract $225$ from $648$ .

$\frac{423 + 1400}{360}$

Step 5.2

Add $423$ and $1400$ .

$\frac{1823}{360}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1823}{360}$

Decimal Form:

$5.063\overline{8}$

Mixed Number Form:

$5 \frac{23}{360}$