Algebra Examples

$3 \frac{6}{7} + (- 1 \frac{1}{7})$

Step 1

Remove parentheses.

$3 \frac{6}{7} - 1 \frac{1}{7}$

Step 2

Convert $3 \frac{6}{7}$ to an improper fraction.

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Step 2.1

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

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

Step 2.2

Add $3$ and $\frac{6}{7}$ .

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Step 2.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$3 \cdot \frac{7}{7} + \frac{6}{7} - 1 \frac{1}{7}$

Step 2.2.2

Combine $3$ and $\frac{7}{7}$ .

$\frac{3 \cdot 7}{7} + \frac{6}{7} - 1 \frac{1}{7}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 7 + 6}{7} - 1 \frac{1}{7}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $7$ .

$\frac{21 + 6}{7} - 1 \frac{1}{7}$

Step 2.2.4.2

Add $21$ and $6$ .

$\frac{27}{7} - 1 \frac{1}{7}$

Step 3

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

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Step 3.1

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

$\frac{27}{7} - (1 + \frac{1}{7})$

Step 3.2

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

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Step 3.2.1

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

$\frac{27}{7} - (\frac{7}{7} + \frac{1}{7})$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{27}{7} - \frac{7 + 1}{7}$

Step 3.2.3

Add $7$ and $1$ .

$\frac{27}{7} - \frac{8}{7}$

Step 4

Combine the numerators over the common denominator.

$\frac{27 - 8}{7}$

Step 5

Subtract $8$ from $27$ .

$\frac{19}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{7}$

Decimal Form:

$2.\overline{714285}$

Mixed Number Form:

$2 \frac{5}{7}$