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

To write $\frac{9}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{9}{5}$ by $\frac{8}{8}$ .

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

Step 4.2

Multiply $5$ by $8$ .

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

Step 4.3

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

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

Step 4.4

Multiply $8$ by $5$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $9$ by $8$ .

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

Step 6.2

Multiply $- 5$ by $5$ .

$\frac{72 - 25}{40} + \frac{35}{9}$

Step 6.3

Subtract $25$ from $72$ .

$\frac{47}{40} + \frac{35}{9}$

Step 7

To write $\frac{47}{40}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{47}{40} \cdot \frac{9}{9} + \frac{35}{9}$

Step 8

To write $\frac{35}{9}$ as a fraction with a common denominator, multiply by $\frac{40}{40}$ .

$\frac{47}{40} \cdot \frac{9}{9} + \frac{35}{9} \cdot \frac{40}{40}$

Step 9

Write each expression with a common denominator of $360$ , by multiplying each by an appropriate factor of $1$ .

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Step 9.1

Multiply $\frac{47}{40}$ by $\frac{9}{9}$ .

$\frac{47 \cdot 9}{40 \cdot 9} + \frac{35}{9} \cdot \frac{40}{40}$

Step 9.2

Multiply $40$ by $9$ .

$\frac{47 \cdot 9}{360} + \frac{35}{9} \cdot \frac{40}{40}$

Step 9.3

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

$\frac{47 \cdot 9}{360} + \frac{35 \cdot 40}{9 \cdot 40}$

Step 9.4

Multiply $9$ by $40$ .

$\frac{47 \cdot 9}{360} + \frac{35 \cdot 40}{360}$

Step 10

Combine the numerators over the common denominator.

$\frac{47 \cdot 9 + 35 \cdot 40}{360}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply $47$ by $9$ .

$\frac{423 + 35 \cdot 40}{360}$

Step 11.2

Multiply $35$ by $40$ .

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

Step 11.3

Add $423$ and $1400$ .

$\frac{1823}{360}$