Simplify the Algebraic Fraction: 14a/(2a×3a) Challenge

$14a/(2a\cdot3a)=\text{?}$

The problem asks us to simplify the expression $\frac{14a}{2a \cdot 3a}$.

First, simplify the expression in the denominator:

• The denominator $2a \cdot 3a$ can be expanded by multiplying the constants and variables separately: $2 \cdot 3 \cdot a \cdot a = 6a^2$.

Now, the expression becomes:

• $\frac{14a}{6a^2}$

Next, simplify the fraction by canceling out common factors in the numerator and the denominator:

• Both the numerator and the denominator contain the variable $a$. We can divide both by $a$, resulting in:
• $\frac{14}{6a}$

Further simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

• $\frac{14 \div 2}{6 \div 2a} = \frac{7}{3a}$

Thus, the simplified form of the expression is $\frac{7}{3a}$.

Therefore, the solution to the problem is $\frac{7}{3a}$.