Pre-Algebra Examples

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

Step 1

Convert $4 \frac{1}{3}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

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

Step 1.2

Add $4$ and $\frac{1}{3}$ .

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $4$ by $3$ .

$\frac{12 + 1}{3} + 2 \frac{1}{3} + 6 \frac{1}{2}$

Step 1.2.4.2

Add $12$ and $1$ .

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

Step 2

Convert $2 \frac{1}{3}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

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

Step 2.2

Add $2$ and $\frac{1}{3}$ .

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

Combine $2$ and $\frac{3}{3}$ .

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $2$ by $3$ .

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

Step 2.2.4.2

Add $6$ and $1$ .

$\frac{13}{3} + \frac{7}{3} + 6 \frac{1}{2}$

Step 3

Convert $6 \frac{1}{2}$ to an improper fraction.

Tap for more steps...

Step 3.1

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

$\frac{13}{3} + \frac{7}{3} + 6 + \frac{1}{2}$

Step 3.2

Add $6$ and $\frac{1}{2}$ .

Tap for more steps...

Step 3.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13}{3} + \frac{7}{3} + 6 \cdot \frac{2}{2} + \frac{1}{2}$

Step 3.2.2

Combine $6$ and $\frac{2}{2}$ .

$\frac{13}{3} + \frac{7}{3} + \frac{6 \cdot 2}{2} + \frac{1}{2}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{13}{3} + \frac{7}{3} + \frac{6 \cdot 2 + 1}{2}$

Step 3.2.4

Simplify the numerator.

Tap for more steps...

Step 3.2.4.1

Multiply $6$ by $2$ .

$\frac{13}{3} + \frac{7}{3} + \frac{12 + 1}{2}$

Step 3.2.4.2

Add $12$ and $1$ .

$\frac{13}{3} + \frac{7}{3} + \frac{13}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{13 + 7}{3} + \frac{13}{2}$

Step 5

Add $13$ and $7$ .

$\frac{20}{3} + \frac{13}{2}$

Step 6

To write $\frac{20}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{20}{3} \cdot \frac{2}{2} + \frac{13}{2}$

Step 7

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

$\frac{20}{3} \cdot \frac{2}{2} + \frac{13}{2} \cdot \frac{3}{3}$

Step 8

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

Tap for more steps...

Step 8.1

Multiply $\frac{20}{3}$ by $\frac{2}{2}$ .

$\frac{20 \cdot 2}{3 \cdot 2} + \frac{13}{2} \cdot \frac{3}{3}$

Step 8.2

Multiply $3$ by $2$ .

$\frac{20 \cdot 2}{6} + \frac{13}{2} \cdot \frac{3}{3}$

Step 8.3

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

$\frac{20 \cdot 2}{6} + \frac{13 \cdot 3}{2 \cdot 3}$

Step 8.4

Multiply $2$ by $3$ .

$\frac{20 \cdot 2}{6} + \frac{13 \cdot 3}{6}$

Step 9

Combine the numerators over the common denominator.

$\frac{20 \cdot 2 + 13 \cdot 3}{6}$

Step 10

Simplify the numerator.

Tap for more steps...

Step 10.1

Multiply $20$ by $2$ .

$\frac{40 + 13 \cdot 3}{6}$

Step 10.2

Multiply $13$ by $3$ .

$\frac{40 + 39}{6}$

Step 10.3

Add $40$ and $39$ .

$\frac{79}{6}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{79}{6}$

Decimal Form:

$13.1\overline{6}$

Mixed Number Form:

$13 \frac{1}{6}$