Solve the proportion x/8 = 11/6.

Step-by-step solution

1. 1

   Multiply both sides by the denominator under $x$. Since $x$ is divided by $8$, multiplying by $8$ undoes it:

   $x=8\cdot\frac{11}{6}=\frac{88}{6}$

   Only the numerator is multiplied by $8$ — the denominator $6$ stays put, because $8\cdot\tfrac{11}{6}=\tfrac{8\cdot11}{6}$.

2. 2

   Reduce the fraction. Both $88$ and $6$ are even, so divide each by $\gcd(88,6)=2$:

   $x=\frac{88}{6}=\frac{44}{3}$

   Since $44=2^{2}\cdot11$ and $3$ is prime, no further cancellation is possible — the fraction is in lowest terms.

3. 3

   Cross-multiplication gives the same thing. From $\tfrac{x}{8}=\tfrac{11}{6}$, equating the cross products gives $6x=8\cdot11=88$, hence $x=\tfrac{88}{6}=\tfrac{44}{3}$ ✓. Cross-multiplying is simply doing both denominators at once, and it is safe here because neither denominator is zero.

4. 4

   Express the answer three ways. As an improper fraction $\tfrac{44}{3}$; as a mixed number $14\tfrac23$, since $3\times14=42$ with remainder $2$; as a decimal $14.\overline{6}\approx14.667$, which repeats because the denominator $3$ is not built only from $2$s and $5$s.

5. 5

   Verify in the original proportion. $\dfrac{44/3}{8}=\dfrac{44}{24}=\dfrac{11}{6}$ ✓ — dividing $\tfrac{44}{3}$ by $8$ multiplies the denominator by $8$, and $\tfrac{44}{24}$ reduces by $4$ to $\tfrac{11}{6}$ exactly. Confirmed in exact rational arithmetic ✓.