Equivalent fractions
Maths · Key Stage 2 · The School
Same amount, different name
One half and two quarters look different. They are the same amount. Cut a pizza into 2 pieces and take 1: that is a half. Cut the same pizza into 4 pieces and take 2: that is also a half. The pizza never changed size. Only the number of cuts changed. The same idea works for any fraction. Every fraction has countless other names that all describe the exact same amount.
Making an equivalent fraction
To find an equivalent fraction, multiply the top and the bottom by the same number. One half becomes two quarters by multiplying both numbers by 2. It becomes three sixths by multiplying both by 3. Whatever you do to the bottom, you must do to the top too. Skip that second half of the rule, and the new fraction is no longer equal to the one you started with.
Simplifying the other way
Six eighths can be made simpler. Both 6 and 8 can be divided by 2. That gives three quarters. Both 3 and 4 share no common factor beyond 1, so three quarters cannot be simplified any further. A fraction in its simplest form has no number, other than 1, that divides both parts.
Comparing two fractions using equivalence
Which is bigger, two thirds or three quarters? Give them the same bottom number first. Two thirds becomes eight twelfths, by multiplying top and bottom by 4. Three quarters becomes nine twelfths, by multiplying top and bottom by 3. Nine twelfths is bigger than eight twelfths, so three quarters is the bigger fraction.