Pre-Algebra Examples

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

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.

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

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 $\frac{4}{4}$ .

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

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

Step 1.2.4.2

Add $8$ and $3$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Combine the numerators over the common denominator.

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

Step 2.2.3

Add $2$ and $1$ .

$\frac{11}{4} + \frac{3}{2} + \frac{2}{3}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{11}{4}$ by $\frac{3}{3}$ .

$\frac{11}{4} \cdot \frac{3}{3} + \frac{3}{2} + \frac{2}{3}$

Step 3.2

Multiply $\frac{11}{4}$ by $\frac{3}{3}$ .

$\frac{11 \cdot 3}{4 \cdot 3} + \frac{3}{2} + \frac{2}{3}$

Step 3.3

Multiply $\frac{3}{2}$ by $\frac{6}{6}$ .

$\frac{11 \cdot 3}{4 \cdot 3} + \frac{3}{2} \cdot \frac{6}{6} + \frac{2}{3}$

Step 3.4

Multiply $\frac{3}{2}$ by $\frac{6}{6}$ .

$\frac{11 \cdot 3}{4 \cdot 3} + \frac{3 \cdot 6}{2 \cdot 6} + \frac{2}{3}$

Step 3.5

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$\frac{11 \cdot 3}{4 \cdot 3} + \frac{3 \cdot 6}{2 \cdot 6} + \frac{2}{3} \cdot \frac{4}{4}$

Step 3.6

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$\frac{11 \cdot 3}{4 \cdot 3} + \frac{3 \cdot 6}{2 \cdot 6} + \frac{2 \cdot 4}{3 \cdot 4}$

Step 3.7

Reorder the factors of $4 \cdot 3$ .

$\frac{11 \cdot 3}{3 \cdot 4} + \frac{3 \cdot 6}{2 \cdot 6} + \frac{2 \cdot 4}{3 \cdot 4}$

Step 3.8

Multiply $3$ by $4$ .

$\frac{11 \cdot 3}{12} + \frac{3 \cdot 6}{2 \cdot 6} + \frac{2 \cdot 4}{3 \cdot 4}$

Step 3.9

Multiply $2$ by $6$ .

$\frac{11 \cdot 3}{12} + \frac{3 \cdot 6}{12} + \frac{2 \cdot 4}{3 \cdot 4}$

Step 3.10

Multiply $3$ by $4$ .

$\frac{11 \cdot 3}{12} + \frac{3 \cdot 6}{12} + \frac{2 \cdot 4}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{11 \cdot 3 + 3 \cdot 6 + 2 \cdot 4}{12}$

Step 5

Simplify each term.

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Step 5.1

Multiply $11$ by $3$ .

$\frac{33 + 3 \cdot 6 + 2 \cdot 4}{12}$

Step 5.2

Multiply $3$ by $6$ .

$\frac{33 + 18 + 2 \cdot 4}{12}$

Step 5.3

Multiply $2$ by $4$ .

$\frac{33 + 18 + 8}{12}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add $33$ and $18$ .

$\frac{51 + 8}{12}$

Step 6.2

Add $51$ and $8$ .

$\frac{59}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{59}{12}$

Decimal Form:

$4.91\overline{6}$

Mixed Number Form:

$4 \frac{11}{12}$