Equivalent Fractions Worksheets

Find the missing number

Two fractions, an equals sign, one blank. Two thirds equals something over twelve. Work out what the denominator was multiplied by, then do the same to the numerator. Done.

The generator mixes missing-numerator and missing-denominator problems on the same sheet, deliberately. A page of one kind gets solved by pattern rather than by thinking, and mixing them forces the pupil to work out where the scale factor is visible before they can use it.

Four to sixty problems, twenty-four by default, with a maximum scale factor you set anywhere from two to twelve.

One amount, infinitely many names

A half, two quarters, five tenths, fifty hundredths. All the same quantity written differently, and the list never ends, because you can always cut the same amount into more and smaller pieces.

Say that out loud, because children routinely believe a fraction has one correct form. It is also what makes simplest form a convention rather than a truth: two quarters is not wrong, it is simply not the tidiest of the available names for that amount.

Establish it physically before any arithmetic happens. Fold a paper strip in half, shade one part. Fold the same strip into quarters and the shading now covers two parts without anything having moved. Nothing was added. The name changed.

Multiplying up is easy, dividing down is not

Both directions make an equivalent fraction. They are not equally hard, and treating them as one topic is why children stall.

Multiplying up works with any number you like. Times four gives eight twelfths; times ten gives twenty thirtieths; there is no wrong answer to find, only an answer to produce. Start here, because it is where a child builds the idea that the value stays put while the numbers change underneath it.

Dividing down only works when a common factor exists, and the child has to find it. That is not fraction work at all, it is factor recall wearing a fraction costume, and a pupil without secure times tables will fail it for reasons that have nothing to do with fractions.

Keep them on separate sheets until multiplying up is automatic.

Show them a fraction wall first

Rows of equal-width strips, cut into halves, thirds, quarters, fifths, and so on down the page. Line the rows up and a half visibly reaches exactly as far as two quarters and as far as three sixths.

Children who have looked at that picture stop producing the answer that a third is bigger than a half because three is bigger than two. It is the single most efficient thing you can put in front of a class on this topic.

It also does the groundwork for adding unlike fractions later, because the wall makes obvious why a common denominator is needed: you cannot combine strips that have been cut differently until you re-cut them the same way.