Equivalent fractions name the same amount using different-sized parts. 1/2 = 2/4 = 3/6 = 50/100. You generate equivalent fractions by multiplying (or dividing) both the numerator and denominator by the same nonzero number -- this is the same as multiplying by 1 in a different form (e.g., 2/2 or 3/3). Visually, equivalent fractions cover the same area or land on the same point on a number line. This concept is essential for comparing fractions, finding common denominators, and simplifying fractions.
Use fraction strips or fraction bars: physically overlay 2/4 on top of 1/2 to see they match. Draw area models partitioned different ways. On a number line, mark both 1/3 and 2/6 at the same point. Then formalize the multiplication/division rule, connecting it back to why it works (subdividing or combining equal parts does not change the total amount).
You already know that a fraction like 1/2 means one out of two equal parts of a whole. Now imagine taking that same half and drawing a line down the middle of it — suddenly you have four equal parts instead of two, and your piece covers two of them. So 1/2 and 2/4 describe exactly the same amount. They are equivalent fractions.
The key to generating equivalent fractions is multiplying both the numerator and denominator by the same nonzero whole number. For example: 1/2 × 3/3 = 3/6. Because 3/3 = 1, you haven't changed the value — you've just renamed it. Visually, you divided each of the two original parts into 3 smaller pieces, giving 6 total pieces with 3 of them filled. Same shaded area, different label.
A very common mistake is adding the same number to top and bottom instead of multiplying. It feels symmetric, but it breaks the value. 1/3 is about 0.33, but 2/4 = 0.5 — they are not the same. Addition does not preserve the ratio between numerator and denominator; multiplication does.
You can also go in reverse: if both the numerator and denominator share a common factor, divide both by it to get a simpler equivalent fraction. 8/12 ÷ 4/4 = 2/3. This is called simplifying (or reducing). The result is still the same fraction — just with smaller numbers.
Equivalent fractions are the foundation for everything you will do with fractions next: comparing fractions with different denominators, adding them, and subtracting them all require rewriting fractions in equivalent forms first.