1. Adding and subtracting fractions
[N2.2 Core Plenary]
A very common mistake is to add or subtract the numerators and denominators,
like this:
The correct answer is:
1) Compare the correct answer with the wrong answer. Which is larger?
2) How does the size of the wrong answer compare with the size of the two fractions being added?
3) Investigate “right” and “wrong” answers with some fractions of your own, but make sure your “right” answers are correct! (Hint: choose some simple fractions!)
4) Do you get the same results when two fractions are subtracted? Investigate.
Preamble
This activity directly confronts the all too common error of “add the top and add the
bottom” when applied to the addition of fractions. There are obvious opportunities to
practice the vocabulary of fractions. Some guidance may be needed for (4), in fact
given time pressures it may not be feasible for all pupils to attempt, especially as it
breaks and gives a negative result (a useful lesson for pupils who are convinced there
is always a pattern!).
Possible content
Addition and subtraction of fractions, comparing fractions.
Resources
None.
Solution/Notes
1) The wrong answer is smaller:
2) The wrong answer is between the two fraction being added:
3) The above rule appears to be true for all additions of fractions.
4) Problems arise when subtraction as negative numbers (or worse) occurs,
for example:
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010