On the number line, $\frac{4}{4}$ and 1 named the same point. Different fractions can share a point too. They are called equivalent fractions.
Why it works
Start with $\frac{1}{2}$ of a bar. Cut each half into 2 equal pieces: now the bar has 4 pieces, and the shaded part is 2 of them, $\frac{2}{4}$. You made more pieces, but each piece is half as big, so the shaded amount did not change. That is why bigger numbers in a fraction do not mean a bigger amount.
Key idea
Equivalent fractions are the same size and sit at the same point on the number line, like $\frac{1}{2} = \frac{2}{4}$ and $\frac{2}{3} = \frac{4}{6}$.
Worked example: Halves and fourths
$\frac{1}{2} = \frac{\square}{4}$
- Each half is the same as 2 fourths.
- So 1 half is 2 fourths.
Answer: $2$
Worked example: Thirds and sixths
$\frac{2}{3} = \frac{\square}{6}$
- Each third is 2 sixths.
- 2 thirds is $2 \times 2 = 4$ sixths.
Answer: $4$
Worked example: Going back
$\frac{6}{8} = \frac{\square}{4}$
- 2 eighths make 1 fourth.
- 6 eighths make $6 \div 2 = 3$ fourths.
Answer: $3$
Common mistake
Thinking $\frac{2}{4}$ is bigger than $\frac{1}{2}$ because its numbers are bigger. The 4 means smaller pieces. Line the bars up: the shading for $\frac{2}{4}$ ends exactly where the shading for $\frac{1}{2}$ ends.