Basic Math Examples

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

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.

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

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.

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $3$ and $2$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Combine the numerators over the common denominator.

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

Step 2.2.3

Add $5$ and $1$ .

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

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $5$ .

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Step 3.1.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$3 + \frac{- 5}{3} \cdot \frac{6}{5}$

Step 3.1.2

Factor $5$ out of $- 5$ .

$3 + \frac{5 (- 1)}{3} \cdot \frac{6}{5}$

Step 3.1.3

Cancel the common factor.

$3 + \frac{5 \cdot - 1}{3} \cdot \frac{6}{5}$

Step 3.1.4

Rewrite the expression.

$3 + \frac{- 1}{3} \cdot 6$

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Factor $3$ out of $6$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$3 - 1 \cdot 2$

Step 3.3

Multiply $- 1$ by $2$ .

$3 - 2$

Step 4

Subtract $2$ from $3$ .

$1$