Basic Math Examples

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

Step 1

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

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Step 1.1

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

$- (1 + \frac{2}{5}) \div 2 \frac{1}{3}$

Step 1.2

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

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Step 1.2.1

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

$- (\frac{5}{5} + \frac{2}{5}) \div 2 \frac{1}{3}$

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $5$ and $2$ .

$- \frac{7}{5} \div 2 \frac{1}{3}$

Step 2

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

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Step 2.1

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

$- \frac{7}{5} \div (2 + \frac{1}{3})$

Step 2.2

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

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{7}{5} \div (2 \cdot \frac{3}{3} + \frac{1}{3})$

Step 2.2.2

Combine $2$ and $\frac{3}{3}$ .

$- \frac{7}{5} \div (\frac{2 \cdot 3}{3} + \frac{1}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{7}{5} \div \frac{2 \cdot 3 + 1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $3$ .

$- \frac{7}{5} \div \frac{6 + 1}{3}$

Step 2.2.4.2

Add $6$ and $1$ .

$- \frac{7}{5} \div \frac{7}{3}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$- \frac{7}{5} \cdot \frac{3}{7}$

Step 4

Cancel the common factor of $7$ .

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Step 4.1

Move the leading negative in $- \frac{7}{5}$ into the numerator.

$\frac{- 7}{5} \cdot \frac{3}{7}$

Step 4.2

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{5} \cdot \frac{3}{7}$

Step 4.3

Cancel the common factor.

$\frac{7 \cdot - 1}{5} \cdot \frac{3}{7}$

Step 4.4

Rewrite the expression.

$\frac{- 1}{5} \cdot 3$

Step 5

Combine $\frac{- 1}{5}$ and $3$ .

$\frac{- 1 \cdot 3}{5}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $- 1$ by $3$ .

$\frac{- 3}{5}$

Step 6.2

Move the negative in front of the fraction.

$- \frac{3}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{5}$

Decimal Form:

$- 0.6$