Pre-Algebra Examples

- 1 \frac{2}{5} + 5

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

Step 1

Convert

1 \frac{2}{5}

$1 \frac{2}{5}$ 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}) + 5

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

Step 1.2

Add

1

$1$ and

\frac{2}{5}

$\frac{2}{5}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

- (\frac{5}{5} + \frac{2}{5}) + 5

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

Step 1.2.2

Combine the numerators over the common denominator.

- \frac{5 + 2}{5} + 5

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

Step 1.2.3

Add

5

$5$ and

2

$2$ .

- \frac{7}{5} + 5

$- \frac{7}{5} + 5$

- \frac{7}{5} + 5

$- \frac{7}{5} + 5$

- \frac{7}{5} + 5

$- \frac{7}{5} + 5$

Step 2

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

- \frac{7}{5} + 5 \cdot \frac{5}{5}

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

Step 3

Combine

5

$5$ and

\frac{5}{5}

$\frac{5}{5}$ .

- \frac{7}{5} + \frac{5 \cdot 5}{5}

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

Step 4

Combine the numerators over the common denominator.

\frac{- 7 + 5 \cdot 5}{5}

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply

5

$5$ by

5

$5$ .

\frac{- 7 + 25}{5}

$\frac{- 7 + 25}{5}$

Step 5.2

Add

- 7

$- 7$ and

25

$25$ .

\frac{18}{5}

$\frac{18}{5}$

\frac{18}{5}

$\frac{18}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{18}{5}

$\frac{18}{5}$

Decimal Form:

3.6

$3.6$

Mixed Number Form:

3 \frac{3}{5}

$3 \frac{3}{5}$