Basic Math Examples

$(2 \frac{3}{4} + 2 \frac{2}{5}) - (\frac{5}{6} \cdot \frac{1}{3})$

Step 1

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$2 + \frac{3}{4} + 2 \frac{2}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 1.2

Add $2$ and $\frac{3}{4}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$2 \cdot \frac{4}{4} + \frac{3}{4} + 2 \frac{2}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 1.2.2

Combine $2$ and $\frac{4}{4}$ .

$\frac{2 \cdot 4}{4} + \frac{3}{4} + 2 \frac{2}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 3}{4} + 2 \frac{2}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$\frac{8 + 3}{4} + 2 \frac{2}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 1.2.4.2

Add $8$ and $3$ .

$\frac{11}{4} + 2 \frac{2}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 2

Convert $2 \frac{2}{5}$ to an improper fraction.

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Step 2.1

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

$\frac{11}{4} + 2 + \frac{2}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 2.2

Add $2$ and $\frac{2}{5}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{11}{4} + 2 \cdot \frac{5}{5} + \frac{2}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 2.2.2

Combine $2$ and $\frac{5}{5}$ .

$\frac{11}{4} + \frac{2 \cdot 5}{5} + \frac{2}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{11}{4} + \frac{2 \cdot 5 + 2}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $5$ .

$\frac{11}{4} + \frac{10 + 2}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 2.2.4.2

Add $10$ and $2$ .

$\frac{11}{4} + \frac{12}{5} - (\frac{5}{6} \cdot \frac{1}{3})$

Step 3

Multiply $\frac{5}{6} \cdot \frac{1}{3}$ .

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Step 3.1

Multiply $\frac{5}{6}$ by $\frac{1}{3}$ .

$\frac{11}{4} + \frac{12}{5} - \frac{5}{6 \cdot 3}$

Step 3.2

Multiply $6$ by $3$ .

$\frac{11}{4} + \frac{12}{5} - \frac{5}{18}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{11}{4}$ by $\frac{45}{45}$ .

$\frac{11}{4} \cdot \frac{45}{45} + \frac{12}{5} - \frac{5}{18}$

Step 4.2

Multiply $\frac{11}{4}$ by $\frac{45}{45}$ .

$\frac{11 \cdot 45}{4 \cdot 45} + \frac{12}{5} - \frac{5}{18}$

Step 4.3

Multiply $\frac{12}{5}$ by $\frac{36}{36}$ .

$\frac{11 \cdot 45}{4 \cdot 45} + \frac{12}{5} \cdot \frac{36}{36} - \frac{5}{18}$

Step 4.4

Multiply $\frac{12}{5}$ by $\frac{36}{36}$ .

$\frac{11 \cdot 45}{4 \cdot 45} + \frac{12 \cdot 36}{5 \cdot 36} - \frac{5}{18}$

Step 4.5

Multiply $\frac{5}{18}$ by $\frac{10}{10}$ .

$\frac{11 \cdot 45}{4 \cdot 45} + \frac{12 \cdot 36}{5 \cdot 36} - (\frac{5}{18} \cdot \frac{10}{10})$

Step 4.6

Multiply $\frac{5}{18}$ by $\frac{10}{10}$ .

$\frac{11 \cdot 45}{4 \cdot 45} + \frac{12 \cdot 36}{5 \cdot 36} - \frac{5 \cdot 10}{18 \cdot 10}$

Step 4.7

Multiply $4$ by $45$ .

$\frac{11 \cdot 45}{180} + \frac{12 \cdot 36}{5 \cdot 36} - \frac{5 \cdot 10}{18 \cdot 10}$

Step 4.8

Multiply $5$ by $36$ .

$\frac{11 \cdot 45}{180} + \frac{12 \cdot 36}{180} - \frac{5 \cdot 10}{18 \cdot 10}$

Step 4.9

Reorder the factors of $18 \cdot 10$ .

$\frac{11 \cdot 45}{180} + \frac{12 \cdot 36}{180} - \frac{5 \cdot 10}{10 \cdot 18}$

Step 4.10

Multiply $10$ by $18$ .

$\frac{11 \cdot 45}{180} + \frac{12 \cdot 36}{180} - \frac{5 \cdot 10}{180}$

Step 5

Combine the numerators over the common denominator.

$\frac{11 \cdot 45 + 12 \cdot 36 - 5 \cdot 10}{180}$

Step 6

Simplify each term.

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Step 6.1

Multiply $11$ by $45$ .

$\frac{495 + 12 \cdot 36 - 5 \cdot 10}{180}$

Step 6.2

Multiply $12$ by $36$ .

$\frac{495 + 432 - 5 \cdot 10}{180}$

Step 6.3

Multiply $- 5$ by $10$ .

$\frac{495 + 432 - 50}{180}$

Step 7

Simplify by adding and subtracting.

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Step 7.1

Add $495$ and $432$ .

$\frac{927 - 50}{180}$

Step 7.2

Subtract $50$ from $927$ .

$\frac{877}{180}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{877}{180}$

Decimal Form:

$4.87\overline{2}$

Mixed Number Form:

$4 \frac{157}{180}$