Basic Math Examples

$\frac{1}{9} + \frac{1}{8} + \frac{1}{3} + \frac{8}{9}$

Step 1

To write $\frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{9} \cdot \frac{8}{8} + \frac{1}{8} + \frac{1}{3} + \frac{8}{9}$

Step 2

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{1}{9} \cdot \frac{8}{8} + \frac{1}{8} \cdot \frac{9}{9} + \frac{1}{3} + \frac{8}{9}$

Step 3

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{9}$ by $\frac{8}{8}$ .

$\frac{8}{9 \cdot 8} + \frac{1}{8} \cdot \frac{9}{9} + \frac{1}{3} + \frac{8}{9}$

Step 3.2

Multiply $9$ by $8$ .

$\frac{8}{72} + \frac{1}{8} \cdot \frac{9}{9} + \frac{1}{3} + \frac{8}{9}$

Step 3.3

Multiply $\frac{1}{8}$ by $\frac{9}{9}$ .

$\frac{8}{72} + \frac{9}{8 \cdot 9} + \frac{1}{3} + \frac{8}{9}$

Step 3.4

Multiply $8$ by $9$ .

$\frac{8}{72} + \frac{9}{72} + \frac{1}{3} + \frac{8}{9}$

Step 4

Combine the numerators over the common denominator.

$\frac{8 + 9}{72} + \frac{1}{3} + \frac{8}{9}$

Step 5

Add $8$ and $9$ .

$\frac{17}{72} + \frac{1}{3} + \frac{8}{9}$

Step 6

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{24}{24}$ .

$\frac{17}{72} + \frac{1}{3} \cdot \frac{24}{24} + \frac{8}{9}$

Step 7

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{1}{3}$ by $\frac{24}{24}$ .

$\frac{17}{72} + \frac{24}{3 \cdot 24} + \frac{8}{9}$

Step 7.2

Multiply $3$ by $24$ .

$\frac{17}{72} + \frac{24}{72} + \frac{8}{9}$

Step 8

Combine the numerators over the common denominator.

$\frac{17 + 24}{72} + \frac{8}{9}$

Step 9

Add $17$ and $24$ .

$\frac{41}{72} + \frac{8}{9}$

Step 10

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

$\frac{41}{72} + \frac{8}{9} \cdot \frac{8}{8}$

Step 11

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

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Step 11.1

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

$\frac{41}{72} + \frac{8 \cdot 8}{9 \cdot 8}$

Step 11.2

Multiply $9$ by $8$ .

$\frac{41}{72} + \frac{8 \cdot 8}{72}$

Step 12

Combine the numerators over the common denominator.

$\frac{41 + 8 \cdot 8}{72}$

Step 13

Simplify the numerator.

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Step 13.1

Multiply $8$ by $8$ .

$\frac{41 + 64}{72}$

Step 13.2

Add $41$ and $64$ .

$\frac{105}{72}$

Step 14

Cancel the common factor of $105$ and $72$ .

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Step 14.1

Factor $3$ out of $105$ .

$\frac{3 (35)}{72}$

Step 14.2

Cancel the common factors.

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Step 14.2.1

Factor $3$ out of $72$ .

$\frac{3 \cdot 35}{3 \cdot 24}$

Step 14.2.2

Cancel the common factor.

$\frac{3 \cdot 35}{3 \cdot 24}$

Step 14.2.3

Rewrite the expression.

$\frac{35}{24}$