Pre-Algebra Examples

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

Step 1

Convert $8 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $8$ and $\frac{2}{3}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.2.2

Combine $8$ and $\frac{3}{3}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $3$ .

$\frac{24 + 2}{3} + 4 \frac{1}{2} + 3 \frac{3}{4}$

Step 1.2.4.2

Add $24$ and $2$ .

$\frac{26}{3} + 4 \frac{1}{2} + 3 \frac{3}{4}$

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.

$\frac{26}{3} + 4 + \frac{1}{2} + 3 \frac{3}{4}$

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 $\frac{2}{2}$ .

$\frac{26}{3} + 4 \cdot \frac{2}{2} + \frac{1}{2} + 3 \frac{3}{4}$

Step 2.2.2

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

$\frac{26}{3} + \frac{4 \cdot 2}{2} + \frac{1}{2} + 3 \frac{3}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{26}{3} + \frac{4 \cdot 2 + 1}{2} + 3 \frac{3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $2$ .

$\frac{26}{3} + \frac{8 + 1}{2} + 3 \frac{3}{4}$

Step 2.2.4.2

Add $8$ and $1$ .

$\frac{26}{3} + \frac{9}{2} + 3 \frac{3}{4}$

Step 3

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

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Step 3.1

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

$\frac{26}{3} + \frac{9}{2} + 3 + \frac{3}{4}$

Step 3.2

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

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Step 3.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{26}{3} + \frac{9}{2} + 3 \cdot \frac{4}{4} + \frac{3}{4}$

Step 3.2.2

Combine $3$ and $\frac{4}{4}$ .

$\frac{26}{3} + \frac{9}{2} + \frac{3 \cdot 4}{4} + \frac{3}{4}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{26}{3} + \frac{9}{2} + \frac{3 \cdot 4 + 3}{4}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $3$ by $4$ .

$\frac{26}{3} + \frac{9}{2} + \frac{12 + 3}{4}$

Step 3.2.4.2

Add $12$ and $3$ .

$\frac{26}{3} + \frac{9}{2} + \frac{15}{4}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{26}{3}$ by $\frac{4}{4}$ .

$\frac{26}{3} \cdot \frac{4}{4} + \frac{9}{2} + \frac{15}{4}$

Step 4.2

Multiply $\frac{26}{3}$ by $\frac{4}{4}$ .

$\frac{26 \cdot 4}{3 \cdot 4} + \frac{9}{2} + \frac{15}{4}$

Step 4.3

Multiply $\frac{9}{2}$ by $\frac{6}{6}$ .

$\frac{26 \cdot 4}{3 \cdot 4} + \frac{9}{2} \cdot \frac{6}{6} + \frac{15}{4}$

Step 4.4

Multiply $\frac{9}{2}$ by $\frac{6}{6}$ .

$\frac{26 \cdot 4}{3 \cdot 4} + \frac{9 \cdot 6}{2 \cdot 6} + \frac{15}{4}$

Step 4.5

Multiply $\frac{15}{4}$ by $\frac{3}{3}$ .

$\frac{26 \cdot 4}{3 \cdot 4} + \frac{9 \cdot 6}{2 \cdot 6} + \frac{15}{4} \cdot \frac{3}{3}$

Step 4.6

Multiply $\frac{15}{4}$ by $\frac{3}{3}$ .

$\frac{26 \cdot 4}{3 \cdot 4} + \frac{9 \cdot 6}{2 \cdot 6} + \frac{15 \cdot 3}{4 \cdot 3}$

Step 4.7

Multiply $3$ by $4$ .

$\frac{26 \cdot 4}{12} + \frac{9 \cdot 6}{2 \cdot 6} + \frac{15 \cdot 3}{4 \cdot 3}$

Step 4.8

Multiply $2$ by $6$ .

$\frac{26 \cdot 4}{12} + \frac{9 \cdot 6}{12} + \frac{15 \cdot 3}{4 \cdot 3}$

Step 4.9

Reorder the factors of $4 \cdot 3$ .

$\frac{26 \cdot 4}{12} + \frac{9 \cdot 6}{12} + \frac{15 \cdot 3}{3 \cdot 4}$

Step 4.10

Multiply $3$ by $4$ .

$\frac{26 \cdot 4}{12} + \frac{9 \cdot 6}{12} + \frac{15 \cdot 3}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{26 \cdot 4 + 9 \cdot 6 + 15 \cdot 3}{12}$

Step 6

Simplify each term.

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Step 6.1

Multiply $26$ by $4$ .

$\frac{104 + 9 \cdot 6 + 15 \cdot 3}{12}$

Step 6.2

Multiply $9$ by $6$ .

$\frac{104 + 54 + 15 \cdot 3}{12}$

Step 6.3

Multiply $15$ by $3$ .

$\frac{104 + 54 + 45}{12}$

Step 7

Simplify by adding numbers.

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Step 7.1

Add $104$ and $54$ .

$\frac{158 + 45}{12}$

Step 7.2

Add $158$ and $45$ .

$\frac{203}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{203}{12}$

Decimal Form:

$16.91\overline{6}$

Mixed Number Form:

$16 \frac{11}{12}$