Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $2$ and $1$ .

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

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Combine the numerators over the common denominator.

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

Step 4.2.3

Add $3$ and $1$ .

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

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$1 + \frac{1}{4} \cdot 4$

Step 6

Cancel the common factor of $4$ .

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Step 6.1

Cancel the common factor.

$1 + \frac{1}{4} \cdot 4$

Step 6.2

Rewrite the expression.

$1 + 1$

Step 7

Add $1$ and $1$ .

$2$