Multiplying and dividing rational expressions worksheets
Two fractions and one operation between them. Multiplying, anything on top may cancel with anything underneath; dividing, the second fraction turns over first. These free printable worksheets drill both.
The move that is new here is cancelling ACROSS. In a single fraction a bracket can only cancel with the one under it; the moment two fractions are multiplied they become one, and the bracket on top of the first cancels with the bracket under the second. Seeing that the two fractions are no longer separate is the whole lesson.
Why this sheet works
Dividing adds one step before any of that: turn the second fraction over and change the ÷ to a ×. It has to happen first. Cancelling across a division sign is not a move, and a child who does it will sometimes still land on the right answer — which is why the order is worth saying out loud rather than leaving the marks to teach it.
How this one works
One question from this sheet, worked through a step at a time.
(x + 4)/(x − 7) ÷ (x − 8)/(x − 7)
(x + 4)/(x − 7) ÷ (x − 8)/(x − 7)
(x + 4)/(x − 7) × (x − 7)/(x − 8)
(x + 4)/(x − 7) × (x − 7)/(x − 8)
(x − 7) cancels
(x + 4) / (x − 8)
x ≠ 7, 8
Dividing by a fraction is multiplying by it upside down, and that has to happen FIRST. Turn (x − 8)/(x − 7) over and change the ÷ to a ×. Cancelling before the flip is cancelling across a division sign, which is not a move.
Now it is one product, so anything on top may cancel with anything underneath — the two fractions are no longer separate. (x − 7) appears in both, so it goes.
What is left is (x + 4) / (x − 8).
One more thing, and it is the half that gets dropped: x may not be 7 or 8. Those are the numbers that made a denominator zero in the ORIGINAL — including (x − 7), which cancelled. A bracket does not stop mattering because it left the page.
