Pre-Algebra Examples

$4 \frac{3}{4} + 4 \frac{5}{6} + 4 \frac{2}{3}$

Step 1

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

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Step 1.1

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

$4 + \frac{3}{4} + 4 \frac{5}{6} + 4 \frac{2}{3}$

Step 1.2

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

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Step 1.2.1

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

$4 \cdot \frac{4}{4} + \frac{3}{4} + 4 \frac{5}{6} + 4 \frac{2}{3}$

Step 1.2.2

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

$\frac{4 \cdot 4}{4} + \frac{3}{4} + 4 \frac{5}{6} + 4 \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 + 3}{4} + 4 \frac{5}{6} + 4 \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $4$ .

$\frac{16 + 3}{4} + 4 \frac{5}{6} + 4 \frac{2}{3}$

Step 1.2.4.2

Add $16$ and $3$ .

$\frac{19}{4} + 4 \frac{5}{6} + 4 \frac{2}{3}$

Step 2

Convert $4 \frac{5}{6}$ to an improper fraction.

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Step 2.1

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

$\frac{19}{4} + 4 + \frac{5}{6} + 4 \frac{2}{3}$

Step 2.2

Add $4$ and $\frac{5}{6}$ .

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Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{19}{4} + 4 \cdot \frac{6}{6} + \frac{5}{6} + 4 \frac{2}{3}$

Step 2.2.2

Combine $4$ and $\frac{6}{6}$ .

$\frac{19}{4} + \frac{4 \cdot 6}{6} + \frac{5}{6} + 4 \frac{2}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{19}{4} + \frac{4 \cdot 6 + 5}{6} + 4 \frac{2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $6$ .

$\frac{19}{4} + \frac{24 + 5}{6} + 4 \frac{2}{3}$

Step 2.2.4.2

Add $24$ and $5$ .

$\frac{19}{4} + \frac{29}{6} + 4 \frac{2}{3}$

Step 3

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

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Step 3.1

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

$\frac{19}{4} + \frac{29}{6} + 4 + \frac{2}{3}$

Step 3.2

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

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Step 3.2.1

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

$\frac{19}{4} + \frac{29}{6} + 4 \cdot \frac{3}{3} + \frac{2}{3}$

Step 3.2.2

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

$\frac{19}{4} + \frac{29}{6} + \frac{4 \cdot 3}{3} + \frac{2}{3}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{19}{4} + \frac{29}{6} + \frac{4 \cdot 3 + 2}{3}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $4$ by $3$ .

$\frac{19}{4} + \frac{29}{6} + \frac{12 + 2}{3}$

Step 3.2.4.2

Add $12$ and $2$ .

$\frac{19}{4} + \frac{29}{6} + \frac{14}{3}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{19}{4}$ by $\frac{3}{3}$ .

$\frac{19}{4} \cdot \frac{3}{3} + \frac{29}{6} + \frac{14}{3}$

Step 4.2

Multiply $\frac{19}{4}$ by $\frac{3}{3}$ .

$\frac{19 \cdot 3}{4 \cdot 3} + \frac{29}{6} + \frac{14}{3}$

Step 4.3

Multiply $\frac{29}{6}$ by $\frac{2}{2}$ .

$\frac{19 \cdot 3}{4 \cdot 3} + \frac{29}{6} \cdot \frac{2}{2} + \frac{14}{3}$

Step 4.4

Multiply $\frac{29}{6}$ by $\frac{2}{2}$ .

$\frac{19 \cdot 3}{4 \cdot 3} + \frac{29 \cdot 2}{6 \cdot 2} + \frac{14}{3}$

Step 4.5

Multiply $\frac{14}{3}$ by $\frac{4}{4}$ .

$\frac{19 \cdot 3}{4 \cdot 3} + \frac{29 \cdot 2}{6 \cdot 2} + \frac{14}{3} \cdot \frac{4}{4}$

Step 4.6

Multiply $\frac{14}{3}$ by $\frac{4}{4}$ .

$\frac{19 \cdot 3}{4 \cdot 3} + \frac{29 \cdot 2}{6 \cdot 2} + \frac{14 \cdot 4}{3 \cdot 4}$

Step 4.7

Reorder the factors of $4 \cdot 3$ .

$\frac{19 \cdot 3}{3 \cdot 4} + \frac{29 \cdot 2}{6 \cdot 2} + \frac{14 \cdot 4}{3 \cdot 4}$

Step 4.8

Multiply $3$ by $4$ .

$\frac{19 \cdot 3}{12} + \frac{29 \cdot 2}{6 \cdot 2} + \frac{14 \cdot 4}{3 \cdot 4}$

Step 4.9

Reorder the factors of $6 \cdot 2$ .

$\frac{19 \cdot 3}{12} + \frac{29 \cdot 2}{2 \cdot 6} + \frac{14 \cdot 4}{3 \cdot 4}$

Step 4.10

Multiply $2$ by $6$ .

$\frac{19 \cdot 3}{12} + \frac{29 \cdot 2}{12} + \frac{14 \cdot 4}{3 \cdot 4}$

Step 4.11

Multiply $3$ by $4$ .

$\frac{19 \cdot 3}{12} + \frac{29 \cdot 2}{12} + \frac{14 \cdot 4}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{19 \cdot 3 + 29 \cdot 2 + 14 \cdot 4}{12}$

Step 6

Simplify each term.

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Step 6.1

Multiply $19$ by $3$ .

$\frac{57 + 29 \cdot 2 + 14 \cdot 4}{12}$

Step 6.2

Multiply $29$ by $2$ .

$\frac{57 + 58 + 14 \cdot 4}{12}$

Step 6.3

Multiply $14$ by $4$ .

$\frac{57 + 58 + 56}{12}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Add $57$ and $58$ .

$\frac{115 + 56}{12}$

Step 7.2

Add $115$ and $56$ .

$\frac{171}{12}$

Step 7.3

Cancel the common factor of $171$ and $12$ .

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Step 7.3.1

Factor $3$ out of $171$ .

$\frac{3 (57)}{12}$

Step 7.3.2

Cancel the common factors.

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Step 7.3.2.1

Factor $3$ out of $12$ .

$\frac{3 \cdot 57}{3 \cdot 4}$

Step 7.3.2.2

Cancel the common factor.

$\frac{3 \cdot 57}{3 \cdot 4}$

Step 7.3.2.3

Rewrite the expression.

$\frac{57}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{57}{4}$

Decimal Form:

$14.25$

Mixed Number Form:

$14 \frac{1}{4}$