Division of algebraic expressions

In $\frac{8x}{4}$, the coefficient is $8$ and the variable is $x$. We are dividing the whole term by $4$.

$\frac{8x}{4}=\frac{8}{4}\times x=2\times x=2x$

The variable $x$ stays unchanged. The simplified expression is $2x$.

We need to divide the term $8x$ by $4$, which means dividing the coefficient by $4$ and keeping the variable.

$8x$ is the original expression before any division — no simplification has been done. This is incorrect.

$4x$ would result from $8x÷2$, not $8x÷4$. The coefficient $8$ divided by $4$ is $2$, not $4$.

$2$ ignores the variable $x$ entirely. When dividing a term by a number, the variable is kept — so the answer must include $x$.

$2x$ correctly divides the coefficient ($8÷4=2$) and keeps the variable, giving $2x$.

Cutting $15x$ cm into 5 equal pieces means dividing by 5: $\text{Length}=\frac{15x}{5}$

$\frac{15x}{5}=\frac{15}{5}\times x=3\times x=3x$

Each piece is $3x$ cm long. The unit (cm) stays the same because we divided by a pure number.

The fabric is being shared equally into 5 pieces, so we divide $15x$ by $5$.

$5x$ would come from $15x÷3$, not $15x÷5$. This uses the wrong divisor.

$10x$ would come from $15x-5x$, which is subtraction, not division. This is incorrect.

$3$ drops the variable $x$. Since the total length contains $x$, each piece must also contain $x$. The variable cannot disappear when dividing by a number.

$3x$ cm is correct: $15x÷5=3x$, keeping the variable and the unit.