Basic Math Examples

$\frac{6}{4} \div 1 \frac{2}{3} - \frac{2}{4}$

Step 1

Convert $1 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $1$ and $\frac{2}{3}$ .

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Step 1.2.1

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

$\frac{6}{4} \div (\frac{3}{3} + \frac{2}{3}) - \frac{2}{4}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{6}{4} \div \frac{3 + 2}{3} - \frac{2}{4}$

Step 1.2.3

Add $3$ and $2$ .

$\frac{6}{4} \div \frac{5}{3} - \frac{2}{4}$

Step 2

Simplify each term.

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Step 2.1

To divide by a fraction, multiply by its reciprocal.

$\frac{6}{4} \cdot \frac{3}{5} - \frac{2}{4}$

Step 2.2

Cancel the common factor of $6$ and $4$ .

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Step 2.2.1

Factor $2$ out of $6$ .

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

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $4$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

Step 2.3

Multiply $\frac{3}{2} \cdot \frac{3}{5}$ .

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Step 2.3.1

Multiply $\frac{3}{2}$ by $\frac{3}{5}$ .

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

Step 2.3.2

Multiply $3$ by $3$ .

$\frac{9}{2 \cdot 5} - \frac{2}{4}$

Step 2.3.3

Multiply $2$ by $5$ .

$\frac{9}{10} - \frac{2}{4}$

Step 2.4

Cancel the common factor of $2$ and $4$ .

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Step 2.4.1

Factor $2$ out of $2$ .

$\frac{9}{10} - \frac{2 (1)}{4}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $4$ .

$\frac{9}{10} - \frac{2 \cdot 1}{2 \cdot 2}$

Step 2.4.2.2

Cancel the common factor.

$\frac{9}{10} - \frac{2 \cdot 1}{2 \cdot 2}$

Step 2.4.2.3

Rewrite the expression.

$\frac{9}{10} - \frac{1}{2}$

Step 3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9}{10} - \frac{1}{2} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$\frac{9}{10} - \frac{5}{2 \cdot 5}$

Step 4.2

Multiply $2$ by $5$ .

$\frac{9}{10} - \frac{5}{10}$

Step 5

Simplify the expression.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{9 - 5}{10}$

Step 5.2

Subtract $5$ from $9$ .

$\frac{4}{10}$

Step 6

Cancel the common factor of $4$ and $10$ .

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Step 6.1

Factor $2$ out of $4$ .

$\frac{2 (2)}{10}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $10$ .

$\frac{2 \cdot 2}{2 \cdot 5}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 2}{2 \cdot 5}$

Step 6.2.3

Rewrite the expression.

$\frac{2}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{5}$

Decimal Form:

$0.4$