Pre-Algebra Examples

$\frac{3}{7} + \frac{1}{2} - 2 \frac{3}{4}$

Step 1

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$\frac{3}{7} + \frac{1}{2} - (2 + \frac{3}{4})$

Step 1.2

Add $2$ and $\frac{3}{4}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{7} + \frac{1}{2} - (2 \cdot \frac{4}{4} + \frac{3}{4})$

Step 1.2.2

Combine $2$ and $\frac{4}{4}$ .

$\frac{3}{7} + \frac{1}{2} - (\frac{2 \cdot 4}{4} + \frac{3}{4})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3}{7} + \frac{1}{2} - \frac{2 \cdot 4 + 3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$\frac{3}{7} + \frac{1}{2} - \frac{8 + 3}{4}$

Step 1.2.4.2

Add $8$ and $3$ .

$\frac{3}{7} + \frac{1}{2} - \frac{11}{4}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{3}{7}$ by $\frac{4}{4}$ .

$\frac{3}{7} \cdot \frac{4}{4} + \frac{1}{2} - \frac{11}{4}$

Step 2.2

Multiply $\frac{3}{7}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 4}{7 \cdot 4} + \frac{1}{2} - \frac{11}{4}$

Step 2.3

Multiply $\frac{1}{2}$ by $\frac{14}{14}$ .

$\frac{3 \cdot 4}{7 \cdot 4} + \frac{1}{2} \cdot \frac{14}{14} - \frac{11}{4}$

Step 2.4

Multiply $\frac{1}{2}$ by $\frac{14}{14}$ .

$\frac{3 \cdot 4}{7 \cdot 4} + \frac{14}{2 \cdot 14} - \frac{11}{4}$

Step 2.5

Multiply $\frac{11}{4}$ by $\frac{7}{7}$ .

$\frac{3 \cdot 4}{7 \cdot 4} + \frac{14}{2 \cdot 14} - (\frac{11}{4} \cdot \frac{7}{7})$

Step 2.6

Multiply $\frac{11}{4}$ by $\frac{7}{7}$ .

$\frac{3 \cdot 4}{7 \cdot 4} + \frac{14}{2 \cdot 14} - \frac{11 \cdot 7}{4 \cdot 7}$

Step 2.7

Reorder the factors of $7 \cdot 4$ .

$\frac{3 \cdot 4}{4 \cdot 7} + \frac{14}{2 \cdot 14} - \frac{11 \cdot 7}{4 \cdot 7}$

Step 2.8

Multiply $4$ by $7$ .

$\frac{3 \cdot 4}{28} + \frac{14}{2 \cdot 14} - \frac{11 \cdot 7}{4 \cdot 7}$

Step 2.9

Multiply $2$ by $14$ .

$\frac{3 \cdot 4}{28} + \frac{14}{28} - \frac{11 \cdot 7}{4 \cdot 7}$

Step 2.10

Multiply $4$ by $7$ .

$\frac{3 \cdot 4}{28} + \frac{14}{28} - \frac{11 \cdot 7}{28}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 + 14 - 11 \cdot 7}{28}$

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $4$ .

$\frac{12 + 14 - 11 \cdot 7}{28}$

Step 4.2

Multiply $- 11$ by $7$ .

$\frac{12 + 14 - 77}{28}$

Step 5

Simplify the expression.

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Step 5.1

Add $12$ and $14$ .

$\frac{26 - 77}{28}$

Step 5.2

Subtract $77$ from $26$ .

$\frac{- 51}{28}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{51}{28}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{51}{28}$

Decimal Form:

$- 1.82142857 \dots$

Mixed Number Form:

$- 1 \frac{23}{28}$