Solve for j j+1/2=3 9/14

$j + \frac{1}{2} = 3 \frac{9}{14}$

Step 1

Simplify the right side.

Convert $3 \frac{9}{14}$ to an improper fraction.

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

$j + \frac{1}{2} = 3 + \frac{9}{14}$

Add $3$ and $\frac{9}{14}$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$j + \frac{1}{2} = 3 \cdot \frac{14}{14} + \frac{9}{14}$

Combine $3$ and $\frac{14}{14}$ .

$j + \frac{1}{2} = \frac{3 \cdot 14}{14} + \frac{9}{14}$

Combine the numerators over the common denominator.

$j + \frac{1}{2} = \frac{3 \cdot 14 + 9}{14}$

Simplify the numerator.

Multiply $3$ by $14$ .

$j + \frac{1}{2} = \frac{42 + 9}{14}$

Add $42$ and $9$ .

$j + \frac{1}{2} = \frac{51}{14}$

Step 2

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

Subtract $\frac{1}{2}$ from both sides of the equation.

$j = \frac{51}{14} - \frac{1}{2}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$j = \frac{51}{14} - \frac{1}{2} \cdot \frac{7}{7}$

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$j = \frac{51}{14} - \frac{7}{2 \cdot 7}$

Multiply $2$ by $7$ .

$j = \frac{51}{14} - \frac{7}{14}$

Combine the numerators over the common denominator.

$j = \frac{51 - 7}{14}$

Subtract $7$ from $51$ .

$j = \frac{44}{14}$

Cancel the common factor of $44$ and $14$ .

Factor $2$ out of $44$ .

$j = \frac{2 (22)}{14}$

Cancel the common factors.

Factor $2$ out of $14$ .

$j = \frac{2 \cdot 22}{2 \cdot 7}$

Cancel the common factor.

$j = \frac{2 \cdot 22}{2 \cdot 7}$

Rewrite the expression.

$j = \frac{22}{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$j = \frac{22}{7}$

Decimal Form:

$j = 3.\overline{142857}$

Mixed Number Form:

$j = 3 \frac{1}{7}$

Solve for j j+1/2=3 9/14

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