Basic Math Examples

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

Step 1

Convert $2 \frac{1}{5}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $2$ and $\frac{1}{5}$ .

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $5$ .

$\frac{10 + 1}{5} \cdot 1 \frac{3}{4}$

Step 1.2.4.2

Add $10$ and $1$ .

$\frac{11}{5} \cdot 1 \frac{3}{4}$

Step 2

Convert $1 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

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

Step 2.2

Add $1$ and $\frac{3}{4}$ .

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{11}{5} \cdot (\frac{4}{4} + \frac{3}{4})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{11}{5} \cdot \frac{4 + 3}{4}$

Step 2.2.3

Add $4$ and $3$ .

$\frac{11}{5} \cdot \frac{7}{4}$

Step 3

Multiply $\frac{11}{5} \cdot \frac{7}{4}$ .

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Step 3.1

Multiply $\frac{11}{5}$ by $\frac{7}{4}$ .

$\frac{11 \cdot 7}{5 \cdot 4}$

Step 3.2

Multiply $11$ by $7$ .

$\frac{77}{5 \cdot 4}$

Step 3.3

Multiply $5$ by $4$ .

$\frac{77}{20}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{77}{20}$

Decimal Form:

$3.85$

Mixed Number Form:

$3 \frac{17}{20}$