Basic Math Examples

$\frac{7}{8} \cdot 2 \frac{1}{3} \cdot 33 \cdot 3 \frac{1}{3}$

Step 1

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$\frac{7}{8} \cdot (2 + \frac{1}{3}) \cdot 33 \cdot 3 \frac{1}{3}$

Step 1.2

Add $2$ and $\frac{1}{3}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7}{8} \cdot (2 \cdot \frac{3}{3} + \frac{1}{3}) \cdot 33 \cdot 3 \frac{1}{3}$

Step 1.2.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{7}{8} \cdot (\frac{2 \cdot 3}{3} + \frac{1}{3}) \cdot 33 \cdot 3 \frac{1}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{7}{8} \cdot \frac{2 \cdot 3 + 1}{3} \cdot 33 \cdot 3 \frac{1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $3$ .

$\frac{7}{8} \cdot \frac{6 + 1}{3} \cdot 33 \cdot 3 \frac{1}{3}$

Step 1.2.4.2

Add $6$ and $1$ .

$\frac{7}{8} \cdot \frac{7}{3} \cdot 33 \cdot 3 \frac{1}{3}$

Step 2

Convert $3 \frac{1}{3}$ to an improper fraction.

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Step 2.1

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

$\frac{7}{8} \cdot \frac{7}{3} \cdot 33 \cdot (3 + \frac{1}{3})$

Step 2.2

Add $3$ and $\frac{1}{3}$ .

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Step 2.2.1

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

$\frac{7}{8} \cdot \frac{7}{3} \cdot 33 \cdot (3 \cdot \frac{3}{3} + \frac{1}{3})$

Step 2.2.2

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

$\frac{7}{8} \cdot \frac{7}{3} \cdot 33 \cdot (\frac{3 \cdot 3}{3} + \frac{1}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{7}{8} \cdot \frac{7}{3} \cdot 33 \cdot \frac{3 \cdot 3 + 1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $3$ .

$\frac{7}{8} \cdot \frac{7}{3} \cdot 33 \cdot \frac{9 + 1}{3}$

Step 2.2.4.2

Add $9$ and $1$ .

$\frac{7}{8} \cdot \frac{7}{3} \cdot 33 \cdot \frac{10}{3}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Factor $3$ out of $\frac{7}{8} \cdot \frac{7}{3} \cdot 33$ .

$3 (\frac{7}{8} \cdot \frac{7}{3} \cdot 11) \cdot \frac{10}{3}$

Step 3.2

Cancel the common factor.

$3 (\frac{7}{8} \cdot \frac{7}{3} \cdot 11) \cdot \frac{10}{3}$

Step 3.3

Rewrite the expression.

$\frac{7}{8} \cdot \frac{7}{3} \cdot 11 \cdot 10$

Step 4

Multiply $\frac{7}{8}$ by $\frac{7}{3}$ .

$\frac{7 \cdot 7}{8 \cdot 3} \cdot 11 \cdot 10$

Step 5

Multiply.

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Step 5.1

Multiply $7$ by $7$ .

$\frac{49}{8 \cdot 3} \cdot 11 \cdot 10$

Step 5.2

Multiply $8$ by $3$ .

$\frac{49}{24} \cdot 11 \cdot 10$

Step 6

Combine $\frac{49}{24}$ and $11$ .

$\frac{49 \cdot 11}{24} \cdot 10$

Step 7

Multiply $49$ by $11$ .

$\frac{539}{24} \cdot 10$

Step 8

Combine $\frac{539}{24}$ and $10$ .

$\frac{539 \cdot 10}{24}$

Step 9

Multiply $539$ by $10$ .

$\frac{5390}{24}$

Step 10

Cancel the common factor of $5390$ and $24$ .

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Step 10.1

Factor $2$ out of $5390$ .

$\frac{2 (2695)}{24}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $24$ .

$\frac{2 \cdot 2695}{2 \cdot 12}$

Step 10.2.2

Cancel the common factor.

$\frac{2 \cdot 2695}{2 \cdot 12}$

Step 10.2.3

Rewrite the expression.

$\frac{2695}{12}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{2695}{12}$

Decimal Form:

$224.58\overline{3}$

Mixed Number Form:

$224 \frac{7}{12}$