Basic Math Examples

$5 \frac{1}{5} - 2 \frac{3}{4}$

Step 1

Convert $5 \frac{1}{5}$ to an improper fraction.

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Step 1.1

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

$5 + \frac{1}{5} - 2 \frac{3}{4}$

Step 1.2

Add $5$ and $\frac{1}{5}$ .

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $5$ .

$\frac{25 + 1}{5} - 2 \frac{3}{4}$

Step 1.2.4.2

Add $25$ and $1$ .

$\frac{26}{5} - 2 \frac{3}{4}$

Step 2

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

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Step 2.1

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

$\frac{26}{5} - (2 + \frac{3}{4})$

Step 2.2

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

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Step 2.2.1

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

$\frac{26}{5} - (2 \cdot \frac{4}{4} + \frac{3}{4})$

Step 2.2.2

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

$\frac{26}{5} - (\frac{2 \cdot 4}{4} + \frac{3}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{26}{5} - \frac{2 \cdot 4 + 3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $4$ .

$\frac{26}{5} - \frac{8 + 3}{4}$

Step 2.2.4.2

Add $8$ and $3$ .

$\frac{26}{5} - \frac{11}{4}$

Step 3

To write $\frac{26}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{26}{5} \cdot \frac{4}{4} - \frac{11}{4}$

Step 4

To write $- \frac{11}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{26}{5} \cdot \frac{4}{4} - \frac{11}{4} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{26}{5}$ by $\frac{4}{4}$ .

$\frac{26 \cdot 4}{5 \cdot 4} - \frac{11}{4} \cdot \frac{5}{5}$

Step 5.2

Multiply $5$ by $4$ .

$\frac{26 \cdot 4}{20} - \frac{11}{4} \cdot \frac{5}{5}$

Step 5.3

Multiply $\frac{11}{4}$ by $\frac{5}{5}$ .

$\frac{26 \cdot 4}{20} - \frac{11 \cdot 5}{4 \cdot 5}$

Step 5.4

Multiply $4$ by $5$ .

$\frac{26 \cdot 4}{20} - \frac{11 \cdot 5}{20}$

Step 6

Combine the numerators over the common denominator.

$\frac{26 \cdot 4 - 11 \cdot 5}{20}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $26$ by $4$ .

$\frac{104 - 11 \cdot 5}{20}$

Step 7.2

Multiply $- 11$ by $5$ .

$\frac{104 - 55}{20}$

Step 7.3

Subtract $55$ from $104$ .

$\frac{49}{20}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{49}{20}$

Decimal Form:

$2.45$

Mixed Number Form:

$2 \frac{9}{20}$