Pre-Algebra Examples

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

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.

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

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 $\frac{4}{4}$ .

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

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

Step 1.2.4.2

Add $8$ and $3$ .

$\frac{11}{4} + 4 \frac{1}{2} + \frac{7}{8}$

Step 2

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{11}{4} + 4 + \frac{1}{2} + \frac{7}{8}$

Step 2.2

Add $4$ and $\frac{1}{2}$ .

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Step 2.2.1

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

$\frac{11}{4} + 4 \cdot \frac{2}{2} + \frac{1}{2} + \frac{7}{8}$

Step 2.2.2

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

$\frac{11}{4} + \frac{4 \cdot 2}{2} + \frac{1}{2} + \frac{7}{8}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{11}{4} + \frac{4 \cdot 2 + 1}{2} + \frac{7}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $2$ .

$\frac{11}{4} + \frac{8 + 1}{2} + \frac{7}{8}$

Step 2.2.4.2

Add $8$ and $1$ .

$\frac{11}{4} + \frac{9}{2} + \frac{7}{8}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{11}{4}$ by $\frac{2}{2}$ .

$\frac{11}{4} \cdot \frac{2}{2} + \frac{9}{2} + \frac{7}{8}$

Step 3.2

Multiply $\frac{11}{4}$ by $\frac{2}{2}$ .

$\frac{11 \cdot 2}{4 \cdot 2} + \frac{9}{2} + \frac{7}{8}$

Step 3.3

Multiply $\frac{9}{2}$ by $\frac{4}{4}$ .

$\frac{11 \cdot 2}{4 \cdot 2} + \frac{9}{2} \cdot \frac{4}{4} + \frac{7}{8}$

Step 3.4

Multiply $\frac{9}{2}$ by $\frac{4}{4}$ .

$\frac{11 \cdot 2}{4 \cdot 2} + \frac{9 \cdot 4}{2 \cdot 4} + \frac{7}{8}$

Step 3.5

Reorder the factors of $4 \cdot 2$ .

$\frac{11 \cdot 2}{2 \cdot 4} + \frac{9 \cdot 4}{2 \cdot 4} + \frac{7}{8}$

Step 3.6

Multiply $2$ by $4$ .

$\frac{11 \cdot 2}{8} + \frac{9 \cdot 4}{2 \cdot 4} + \frac{7}{8}$

Step 3.7

Multiply $2$ by $4$ .

$\frac{11 \cdot 2}{8} + \frac{9 \cdot 4}{8} + \frac{7}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{11 \cdot 2 + 9 \cdot 4 + 7}{8}$

Step 5

Simplify each term.

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Step 5.1

Multiply $11$ by $2$ .

$\frac{22 + 9 \cdot 4 + 7}{8}$

Step 5.2

Multiply $9$ by $4$ .

$\frac{22 + 36 + 7}{8}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add $22$ and $36$ .

$\frac{58 + 7}{8}$

Step 6.2

Add $58$ and $7$ .

$\frac{65}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{65}{8}$

Decimal Form:

$8.125$

Mixed Number Form:

$8 \frac{1}{8}$