Basic Math Examples

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

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.

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

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 $\frac{5}{5}$ .

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $5$ .

$\frac{10 + 1}{5} \cdot 3 + 4 \cdot 2 \frac{1}{4}$

Step 1.2.4.2

Add $10$ and $1$ .

$\frac{11}{5} \cdot 3 + 4 \cdot 2 \frac{1}{4}$

Step 2

Multiply $\frac{11}{5} \cdot 3$ .

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Step 2.1

Combine $\frac{11}{5}$ and $3$ .

$\frac{11 \cdot 3}{5} + 4 \cdot 2 \frac{1}{4}$

Step 2.2

Multiply $11$ by $3$ .

$\frac{33}{5} + 4 \cdot 2 \frac{1}{4}$

Step 3

Convert $2 \frac{1}{4}$ to an improper fraction.

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Step 3.1

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

$\frac{33}{5} + 4 \cdot (2 + \frac{1}{4})$

Step 3.2

Add $2$ and $\frac{1}{4}$ .

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Step 3.2.1

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

$\frac{33}{5} + 4 \cdot (2 \cdot \frac{4}{4} + \frac{1}{4})$

Step 3.2.2

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

$\frac{33}{5} + 4 \cdot (\frac{2 \cdot 4}{4} + \frac{1}{4})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{33}{5} + 4 \cdot \frac{2 \cdot 4 + 1}{4}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $4$ .

$\frac{33}{5} + 4 \cdot \frac{8 + 1}{4}$

Step 3.2.4.2

Add $8$ and $1$ .

$\frac{33}{5} + 4 \cdot \frac{9}{4}$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Cancel the common factor.

$\frac{33}{5} + 4 \cdot \frac{9}{4}$

Step 4.2

Rewrite the expression.

$\frac{33}{5} + 9$

Step 5

To write $9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{33}{5} + 9 \cdot \frac{5}{5}$

Step 6

Combine $9$ and $\frac{5}{5}$ .

$\frac{33}{5} + \frac{9 \cdot 5}{5}$

Step 7

Combine the numerators over the common denominator.

$\frac{33 + 9 \cdot 5}{5}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $9$ by $5$ .

$\frac{33 + 45}{5}$

Step 8.2

Add $33$ and $45$ .

$\frac{78}{5}$