Equivalent fractions are the same amount

1/2 = 2/4 = 3/6 is not a number trick. It says the same amount has been described using differently sized pieces.

Imagine splitting every half into two pieces: the amount has not changed, but the whole is now measured in quarters. Splitting again gives eighths.

Diagnostic: if you remember “multiply top and bottom by the same number” but cannot explain why that preserves the amount, stay here.

Why both numbers change

When the pieces get smaller, more pieces are needed to cover the same amount. That is why numerator and denominator must scale together.

Changing only the numerator changes how much is selected. Changing only the denominator changes the piece size without compensating for it.

Money makes the equivalence obvious

50p is 1/2 of £1 and also 2/4 of £1. Likewise 50¢ is 1/2 of $1 and two 25¢ amounts are 2/4 of $1.

Use familiar money arithmetic to reassure yourself that the abstract fraction rule is describing something ordinary.

Move on when…

You can generate an equivalent fraction, explain why it is equivalent, and spot why changing only the top or only the bottom would change the value.

Use the interactive learner lesson when useful

The learner page contains the visual examples and interactive practice. Use it as a tool rather than as a different course: return here when you want the explanation, diagnostic questions and bigger-picture connections.