Solve the Fraction Division: Finding the Missing Number in 1/3 : x = 3/8

The colon (:) is another way to write division, just like the ÷ symbol! So $\frac{1}{3} : x = \frac{3}{8}$ means $\frac{1}{3} \div x = \frac{3}{8}$.

Dividing by a fraction is the same as multiplying by its reciprocal! When you divide $\frac{1}{3} \div \frac{3}{8}$, you flip $\frac{3}{8}$ to get $\frac{8}{3}$ and multiply instead.

If $\frac{1}{3} \div x = \frac{3}{8}$, then x must equal $\frac{1}{3} \div \frac{3}{8}$. Think: "What number divided into $\frac{1}{3}$ gives $\frac{3}{8}$?"

Absolutely! Substitute $x = \frac{8}{9}$ back into the original: $\frac{1}{3} \div \frac{8}{9} = \frac{1}{3} \times \frac{9}{8} = \frac{9}{24} = \frac{3}{8}$ ✓

Remember: you only flip the fraction you're dividing by! In $\frac{1}{3} \div \frac{3}{8}$, you flip $\frac{3}{8}$ to $\frac{8}{3}$, but leave $\frac{1}{3}$ alone.