What is on this worksheet
Every pair on this sheet was built by multiplying a simple fraction top and bottom by the same number, so the two sides are genuinely equal rather than approximately so. That construction is also the method: a child who spots that the bottom number went from four to twelve knows it was multiplied by three, and the top must follow. Half the questions leave out the numerator and half the denominator, so the same idea has to be applied in both directions instead of becoming a routine.
How to use it
Print the sheet and write the missing number so the two fractions are worth the same. Work out what the known part was multiplied by, then do the same to the other number.
Three ways to practice
Find the multiplier first
Look at the pair of numbers that are both shown and work out what one was multiplied by to get the other. Everything else follows from that single number, and naming it out loud makes the step explicit.
Check by simplifying
Take the finished fraction and divide top and bottom by the multiplier. If you land back on the fraction you started with, the answer is right. Checking backwards catches mistakes the forward step hides.
Draw one to prove it
Pick a pair and draw two identical bars, splitting one into the smaller number of parts and one into the larger. Shading each to match shows the same amount covered, which is what equivalent means.
A tip worth knowing
Whatever you do to the top you must do to the bottom. Finding the multiplier from the pair of numbers you can see is the whole method, and it works in both directions.
Printing this sheet
Frequently asked questions
What makes two fractions equivalent?
They cover the same amount even though the numbers differ. Two quarters and one half are the same quantity described with different sized pieces, which is why multiplying top and bottom by the same number does not change the value.
Why is the missing number sometimes on top and sometimes below?
So the same idea has to be applied in both directions. A sheet that always asks for the numerator lets a child settle into a routine rather than understanding why the routine works.
Are the answers always whole numbers?
Yes. Every pair is built by multiplying a simple fraction by a whole number, so no question on this sheet has a fractional or decimal answer.