Algebra Examples

$8 \frac{1}{5} - 4 \frac{2}{5}$

Step 1

Convert $8 \frac{1}{5}$ to an improper fraction.

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Step 1.1

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

$8 + \frac{1}{5} - 4 \frac{2}{5}$

Step 1.2

Add $8$ and $\frac{1}{5}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$8 \cdot \frac{5}{5} + \frac{1}{5} - 4 \frac{2}{5}$

Step 1.2.2

Combine $8$ and $\frac{5}{5}$ .

$\frac{8 \cdot 5}{5} + \frac{1}{5} - 4 \frac{2}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 5 + 1}{5} - 4 \frac{2}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $5$ .

$\frac{40 + 1}{5} - 4 \frac{2}{5}$

Step 1.2.4.2

Add $40$ and $1$ .

$\frac{41}{5} - 4 \frac{2}{5}$

Step 2

Convert $4 \frac{2}{5}$ to an improper fraction.

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Step 2.1

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

$\frac{41}{5} - (4 + \frac{2}{5})$

Step 2.2

Add $4$ and $\frac{2}{5}$ .

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Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{41}{5} - (4 \cdot \frac{5}{5} + \frac{2}{5})$

Step 2.2.2

Combine $4$ and $\frac{5}{5}$ .

$\frac{41}{5} - (\frac{4 \cdot 5}{5} + \frac{2}{5})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{41}{5} - \frac{4 \cdot 5 + 2}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $5$ .

$\frac{41}{5} - \frac{20 + 2}{5}$

Step 2.2.4.2

Add $20$ and $2$ .

$\frac{41}{5} - \frac{22}{5}$

Step 3

Combine the numerators over the common denominator.

$\frac{41 - 22}{5}$

Step 4

Subtract $22$ from $41$ .

$\frac{19}{5}$

Step 5

Set up the division problem in long division format.

$5$

$1$

$9$

Step 6

Divide $19$ by $5$ . Place this digit in the quotient on top of the division symbol.

		$3$
$5$	$1$	$9$

Step 7

Multiply the newest quotient digit $(3)$ by the divisor $5$ .

		$3$
$5$	$1$	$9$
	$1$	$5$

Step 8

Subtract $15$ from $19$ .

		$3$
$5$	$1$	$9$
	$1$	$5$
		$4$

Step 9

The result of division of $\frac{19}{5}$ is $3$ with a remainder of $4$ .

$3 \frac{4}{5}$