Full solution

Q. Simplify. Write your answer using whole numbers and variables.

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\frac{2j -8}{6j}

Identify Terms and Factors: First, we need to identify the terms in the expression and look for common factors. $\newline$ The expression is $2j - (\frac{8}{6}j)$ . We can simplify the fraction $\frac{8}{6}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $8 \div 2 = 4$ $\newline$ $6 \div 2 = 3$ $\newline$ So, $\frac{8}{6}$ simplifies to $\frac{4}{3}$ .
Simplify Fraction: Now, we rewrite the expression with the simplified fraction. $2j - \frac{8}{6}j$ becomes $2j - \frac{4}{3}j$ .
Rewrite Expression: Next, we can combine the terms by finding a common denominator for the $j$ terms. Since the second term has a denominator of $3$ , we multiply the first term by $\frac{3}{3}$ to get a common denominator. $\newline$ $(2j \times \frac{3}{3}) - \frac{4}{3}j = (\frac{6}{3}j) - \frac{4}{3}j$
Combine Terms: Now, we subtract the numerators and keep the common denominator. $\newline$ $(6 - 4)/3j = 2/3j$
Subtract Numerators: Finally, we can write the simplified expression. $\newline$ The simplified form of $2j - \frac{8}{6}j$ is $\frac{2}{3}j$ .