Equivalent Fractions

Equivalent fractions are fractions that look different but name the same amount. 1/2, 2/4, and 3/6 are all the same size slice of the same whole; only the number of pieces you cut it into changed, not how much you have.

What "equivalent" means here

Two fractions are equivalent when multiplying (or dividing) the top and bottom numbers by the same amount turns one into the other. Starting from 1/2, multiplying both numbers by 2 gives 2/4. Multiply both by 3 instead and you get 3/6. The rule only works when you do the same thing to the top and the bottom at the same time; changing just one of them changes the value, not just the look.

A picture makes this land faster than the rule does. Cut one paper strip in half and shade one half. Cut an identical strip into fourths and shade two of them. Lay the strips side by side: the shaded parts are the same length even though one strip has more, smaller pieces. That is the whole idea in one comparison.

Where kids get stuck

The most common mix-up is applying the rule to only one number, so 1/2 becomes "2/2" or "1/4" instead of 2/4. The second most common one is assuming a fraction with bigger numbers must be bigger overall, when 2/4 and 1/2 are the exact same size. Both mistakes usually clear up once a child has folded, drawn, or measured the comparison themselves rather than only calculated it.

Picture a 4th grader, call him Marcus (an illustrative example, not a real student): he kept the two straight by asking himself the same question every time, "did I do the exact same thing to both numbers?" If the answer was yes, the fraction changed size on paper but not in real life.

For a full walkthrough of this topic, including how it connects to comparing and adding fractions, see the grade 4 equivalent fractions lesson. Or watch the free Explanova demo: a 75-second recording of Coach Nova working a problem step by step on a whiteboard.