Pre-Algebra Examples

$4 \frac{1}{4} + 2 \frac{1}{4} + 6 \frac{1}{3}$

Step 1

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

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Step 1.1

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

$4 + \frac{1}{4} + 2 \frac{1}{4} + 6 \frac{1}{3}$

Step 1.2

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

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Step 1.2.1

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

$4 \cdot \frac{4}{4} + \frac{1}{4} + 2 \frac{1}{4} + 6 \frac{1}{3}$

Step 1.2.2

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

$\frac{4 \cdot 4}{4} + \frac{1}{4} + 2 \frac{1}{4} + 6 \frac{1}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 + 1}{4} + 2 \frac{1}{4} + 6 \frac{1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $4$ .

$\frac{16 + 1}{4} + 2 \frac{1}{4} + 6 \frac{1}{3}$

Step 1.2.4.2

Add $16$ and $1$ .

$\frac{17}{4} + 2 \frac{1}{4} + 6 \frac{1}{3}$

Step 2

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

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Step 2.1

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

$\frac{17}{4} + 2 + \frac{1}{4} + 6 \frac{1}{3}$

Step 2.2

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

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Step 2.2.1

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

$\frac{17}{4} + 2 \cdot \frac{4}{4} + \frac{1}{4} + 6 \frac{1}{3}$

Step 2.2.2

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

$\frac{17}{4} + \frac{2 \cdot 4}{4} + \frac{1}{4} + 6 \frac{1}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{17}{4} + \frac{2 \cdot 4 + 1}{4} + 6 \frac{1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $4$ .

$\frac{17}{4} + \frac{8 + 1}{4} + 6 \frac{1}{3}$

Step 2.2.4.2

Add $8$ and $1$ .

$\frac{17}{4} + \frac{9}{4} + 6 \frac{1}{3}$

Step 3

Convert $6 \frac{1}{3}$ to an improper fraction.

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Step 3.1

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

$\frac{17}{4} + \frac{9}{4} + 6 + \frac{1}{3}$

Step 3.2

Add $6$ and $\frac{1}{3}$ .

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Step 3.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{17}{4} + \frac{9}{4} + 6 \cdot \frac{3}{3} + \frac{1}{3}$

Step 3.2.2

Combine $6$ and $\frac{3}{3}$ .

$\frac{17}{4} + \frac{9}{4} + \frac{6 \cdot 3}{3} + \frac{1}{3}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{17}{4} + \frac{9}{4} + \frac{6 \cdot 3 + 1}{3}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $6$ by $3$ .

$\frac{17}{4} + \frac{9}{4} + \frac{18 + 1}{3}$

Step 3.2.4.2

Add $18$ and $1$ .

$\frac{17}{4} + \frac{9}{4} + \frac{19}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{17 + 9}{4} + \frac{19}{3}$

Step 5

Add $17$ and $9$ .

$\frac{26}{4} + \frac{19}{3}$

Step 6

Cancel the common factor of $26$ and $4$ .

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Step 6.1

Factor $2$ out of $26$ .

$\frac{2 (13)}{4} + \frac{19}{3}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 13}{2 \cdot 2} + \frac{19}{3}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 13}{2 \cdot 2} + \frac{19}{3}$

Step 6.2.3

Rewrite the expression.

$\frac{13}{2} + \frac{19}{3}$

Step 7

To write $\frac{13}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{13}{2} \cdot \frac{3}{3} + \frac{19}{3}$

Step 8

To write $\frac{19}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13}{2} \cdot \frac{3}{3} + \frac{19}{3} \cdot \frac{2}{2}$

Step 9

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 9.1

Multiply $\frac{13}{2}$ by $\frac{3}{3}$ .

$\frac{13 \cdot 3}{2 \cdot 3} + \frac{19}{3} \cdot \frac{2}{2}$

Step 9.2

Multiply $2$ by $3$ .

$\frac{13 \cdot 3}{6} + \frac{19}{3} \cdot \frac{2}{2}$

Step 9.3

Multiply $\frac{19}{3}$ by $\frac{2}{2}$ .

$\frac{13 \cdot 3}{6} + \frac{19 \cdot 2}{3 \cdot 2}$

Step 9.4

Multiply $3$ by $2$ .

$\frac{13 \cdot 3}{6} + \frac{19 \cdot 2}{6}$

Step 10

Combine the numerators over the common denominator.

$\frac{13 \cdot 3 + 19 \cdot 2}{6}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply $13$ by $3$ .

$\frac{39 + 19 \cdot 2}{6}$

Step 11.2

Multiply $19$ by $2$ .

$\frac{39 + 38}{6}$

Step 11.3

Add $39$ and $38$ .

$\frac{77}{6}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{77}{6}$

Decimal Form:

$12.8\overline{3}$

Mixed Number Form:

$12 \frac{5}{6}$