Pre-Algebra Examples

$5 \frac{1}{3} + 9 \frac{1}{2} + 13 \frac{1}{6}$

Step 1

Convert $5 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$5 + \frac{1}{3} + 9 \frac{1}{2} + 13 \frac{1}{6}$

Step 1.2

Add $5$ and $\frac{1}{3}$ .

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Step 1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$5 \cdot \frac{3}{3} + \frac{1}{3} + 9 \frac{1}{2} + 13 \frac{1}{6}$

Step 1.2.2

Combine $5$ and $\frac{3}{3}$ .

$\frac{5 \cdot 3}{3} + \frac{1}{3} + 9 \frac{1}{2} + 13 \frac{1}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 1}{3} + 9 \frac{1}{2} + 13 \frac{1}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $3$ .

$\frac{15 + 1}{3} + 9 \frac{1}{2} + 13 \frac{1}{6}$

Step 1.2.4.2

Add $15$ and $1$ .

$\frac{16}{3} + 9 \frac{1}{2} + 13 \frac{1}{6}$

Step 2

Convert $9 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{16}{3} + 9 + \frac{1}{2} + 13 \frac{1}{6}$

Step 2.2

Add $9$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{16}{3} + 9 \cdot \frac{2}{2} + \frac{1}{2} + 13 \frac{1}{6}$

Step 2.2.2

Combine $9$ and $\frac{2}{2}$ .

$\frac{16}{3} + \frac{9 \cdot 2}{2} + \frac{1}{2} + 13 \frac{1}{6}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{16}{3} + \frac{9 \cdot 2 + 1}{2} + 13 \frac{1}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $9$ by $2$ .

$\frac{16}{3} + \frac{18 + 1}{2} + 13 \frac{1}{6}$

Step 2.2.4.2

Add $18$ and $1$ .

$\frac{16}{3} + \frac{19}{2} + 13 \frac{1}{6}$

Step 3

Convert $13 \frac{1}{6}$ to an improper fraction.

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Step 3.1

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

$\frac{16}{3} + \frac{19}{2} + 13 + \frac{1}{6}$

Step 3.2

Add $13$ and $\frac{1}{6}$ .

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Step 3.2.1

To write $13$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{16}{3} + \frac{19}{2} + 13 \cdot \frac{6}{6} + \frac{1}{6}$

Step 3.2.2

Combine $13$ and $\frac{6}{6}$ .

$\frac{16}{3} + \frac{19}{2} + \frac{13 \cdot 6}{6} + \frac{1}{6}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{16}{3} + \frac{19}{2} + \frac{13 \cdot 6 + 1}{6}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $13$ by $6$ .

$\frac{16}{3} + \frac{19}{2} + \frac{78 + 1}{6}$

Step 3.2.4.2

Add $78$ and $1$ .

$\frac{16}{3} + \frac{19}{2} + \frac{79}{6}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{16}{3}$ by $\frac{2}{2}$ .

$\frac{16}{3} \cdot \frac{2}{2} + \frac{19}{2} + \frac{79}{6}$

Step 4.2

Multiply $\frac{16}{3}$ by $\frac{2}{2}$ .

$\frac{16 \cdot 2}{3 \cdot 2} + \frac{19}{2} + \frac{79}{6}$

Step 4.3

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

$\frac{16 \cdot 2}{3 \cdot 2} + \frac{19}{2} \cdot \frac{3}{3} + \frac{79}{6}$

Step 4.4

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

$\frac{16 \cdot 2}{3 \cdot 2} + \frac{19 \cdot 3}{2 \cdot 3} + \frac{79}{6}$

Step 4.5

Reorder the factors of $3 \cdot 2$ .

$\frac{16 \cdot 2}{2 \cdot 3} + \frac{19 \cdot 3}{2 \cdot 3} + \frac{79}{6}$

Step 4.6

Multiply $2$ by $3$ .

$\frac{16 \cdot 2}{6} + \frac{19 \cdot 3}{2 \cdot 3} + \frac{79}{6}$

Step 4.7

Multiply $2$ by $3$ .

$\frac{16 \cdot 2}{6} + \frac{19 \cdot 3}{6} + \frac{79}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{16 \cdot 2 + 19 \cdot 3 + 79}{6}$

Step 6

Simplify each term.

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Step 6.1

Multiply $16$ by $2$ .

$\frac{32 + 19 \cdot 3 + 79}{6}$

Step 6.2

Multiply $19$ by $3$ .

$\frac{32 + 57 + 79}{6}$

Step 7

Simplify the expression.

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Step 7.1

Add $32$ and $57$ .

$\frac{89 + 79}{6}$

Step 7.2

Add $89$ and $79$ .

$\frac{168}{6}$

Step 7.3

Divide $168$ by $6$ .

$28$