Basic Math Examples

$b - 1 \frac{1}{3} = 4 \frac{1}{2}$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

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

$b - (1 + \frac{1}{3}) = 4 \frac{1}{2}$

Step 1.1.2

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

Tap for more steps...

Step 1.1.2.1

Write $1$ as a fraction with a common denominator.

$b - (\frac{3}{3} + \frac{1}{3}) = 4 \frac{1}{2}$

Step 1.1.2.2

Combine the numerators over the common denominator.

$b - \frac{3 + 1}{3} = 4 \frac{1}{2}$

Step 1.1.2.3

Add $3$ and $1$ .

$b - \frac{4}{3} = 4 \frac{1}{2}$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

$b - \frac{4}{3} = 4 + \frac{1}{2}$

Step 2.1.2

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

Tap for more steps...

Step 2.1.2.1

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

$b - \frac{4}{3} = 4 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.1.2.2

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

$b - \frac{4}{3} = \frac{4 \cdot 2}{2} + \frac{1}{2}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$b - \frac{4}{3} = \frac{4 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

Tap for more steps...

Step 2.1.2.4.1

Multiply $4$ by $2$ .

$b - \frac{4}{3} = \frac{8 + 1}{2}$

Step 2.1.2.4.2

Add $8$ and $1$ .

$b - \frac{4}{3} = \frac{9}{2}$

Step 3

Move all terms not containing $b$ to the right side of the equation.

Tap for more steps...

Step 3.1

Add $\frac{4}{3}$ to both sides of the equation.

$b = \frac{9}{2} + \frac{4}{3}$

Step 3.2

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = \frac{9}{2} \cdot \frac{3}{3} + \frac{4}{3}$

Step 3.3

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = \frac{9}{2} \cdot \frac{3}{3} + \frac{4}{3} \cdot \frac{2}{2}$

Step 3.4

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

Tap for more steps...

Step 3.4.1

Multiply $\frac{9}{2}$ by $\frac{3}{3}$ .

$b = \frac{9 \cdot 3}{2 \cdot 3} + \frac{4}{3} \cdot \frac{2}{2}$

Step 3.4.2

Multiply $2$ by $3$ .

$b = \frac{9 \cdot 3}{6} + \frac{4}{3} \cdot \frac{2}{2}$

Step 3.4.3

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$b = \frac{9 \cdot 3}{6} + \frac{4 \cdot 2}{3 \cdot 2}$

Step 3.4.4

Multiply $3$ by $2$ .

$b = \frac{9 \cdot 3}{6} + \frac{4 \cdot 2}{6}$

Step 3.5

Combine the numerators over the common denominator.

$b = \frac{9 \cdot 3 + 4 \cdot 2}{6}$

Step 3.6

Simplify the numerator.

Tap for more steps...

Step 3.6.1

Multiply $9$ by $3$ .

$b = \frac{27 + 4 \cdot 2}{6}$

Step 3.6.2

Multiply $4$ by $2$ .

$b = \frac{27 + 8}{6}$

Step 3.6.3

Add $27$ and $8$ .

$b = \frac{35}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$b = \frac{35}{6}$

Decimal Form:

$b = 5.8\overline{3}$

Mixed Number Form:

$b = 5 \frac{5}{6}$