Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Convert $3 \frac{2}{5}$ to an improper fraction.

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Step 2.1

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

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

Step 2.2

Add $3$ and $\frac{2}{5}$ .

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Step 2.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 2.2.2

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

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $5$ .

$\frac{15 + 2}{5} - 7 \frac{1}{5}$

Step 2.2.4.2

Add $15$ and $2$ .

$\frac{17}{5} - 7 \frac{1}{5}$

Step 3

Convert $7 \frac{1}{5}$ to an improper fraction.

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Step 3.1

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

$\frac{17}{5} - (7 + \frac{1}{5})$

Step 3.2

Add $7$ and $\frac{1}{5}$ .

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Step 3.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{17}{5} - (7 \cdot \frac{5}{5} + \frac{1}{5})$

Step 3.2.2

Combine $7$ and $\frac{5}{5}$ .

$\frac{17}{5} - (\frac{7 \cdot 5}{5} + \frac{1}{5})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{17}{5} - \frac{7 \cdot 5 + 1}{5}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $7$ by $5$ .

$\frac{17}{5} - \frac{35 + 1}{5}$

Step 3.2.4.2

Add $35$ and $1$ .

$\frac{17}{5} - \frac{36}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{17 - 36}{5}$

Step 5

Simplify the expression.

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Step 5.1

Subtract $36$ from $17$ .

$\frac{- 19}{5}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{19}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{19}{5}$

Decimal Form:

$- 3.8$

Mixed Number Form:

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