A4 Fraction Addition

Well done to everybody who had a go at this problem.

The children from Ridgeway Primary School sent in an image of their solution. You can click on the image to make it bigger:

Olive from Cranham Primary School had a systematic approach to find all of the possible solutions:

I started working out this problem by adding all the fractions I had created to 1$\frac{1}{2}$. I started off adding 1$\frac{1}{2}$ as the largest fraction to 1$\frac{1}{2}$. I carried on with the fractions getting smaller, so 1$\frac{1}{2}$ + 1$\frac{1}{4}$, 1$\frac{1}{2}$ + 1$\frac{1}{8}$ and 1$\frac{1}{2}$ + 1$\frac{1}{16}$.

Then, I did the same with 1$\frac{1}{4}$, taking care not to use 1$\frac{1}{2}$ again, otherwise I would have the same sum twice. I repeated that with 1$\frac{1}{8}$, avoiding using 1$\frac{1}{4}$ or 1$\frac{1}{2}$, and I repeated it again with 1$\frac{1}{16}$ without using 1$\frac{1}{8}$, 1$\frac{1}{4}$ or 1$\frac{1}{2}$.

With just a few simple steps, I worked out this problem carefully and methodically. I knew that the answer I had found was correct by going over all the possible solutions.

Good ideas!

We received a few solutions from the children at Aston Rowant C of E Primary School in England. George explained a similar method to Olive's:

First I did the half and there was 4 different sums; then the quarters and there were 3 sums; then the eighths, there were 2 sums; and the sixteenths, there was 1 sum left.

Harvey wrote out all of the possible solutions:

1. First I added the wholes which in every case the answer was 2

2. Then I added the fractions together to get my answers and I used all the options that I found

3. When I had finished I found 10 possible sums. They were:

1$\frac{1}{4}$ + 1$\frac{1}{2}$ = 2$\frac{3}{4}$

1$\frac{1}{2}$ + 1$\frac{1}{16}$ = 2$\frac{9}{16}$

1$\frac{1}{2}$ + 1$\frac{1}{2}$ = 3

1$\frac{1}{2}$ + 1$\frac{1}{8}$ = 2$\frac{5}{8}$

1$\frac{1}{8}$ + 1$\frac{1}{4}$ = 2$\frac{3}{8}$

1$\frac{1}{8}$ + 1$\frac{1}{16}$ = 2$\frac{3}{16}$

1$\frac{1}{8}$ + 1$\frac{1}{8}$ = 2$\frac{1}{4}$

1$\frac{1}{16}$ + 1$\frac{1}{4}$ = 2$\frac{5}{16}$

1$\frac{1}{16}$ + 1$\frac{1}{16}$ = 2$\frac{1}{8}$

1$\frac{1}{4}$ + 1$\frac{1}{4}$ = 2$\frac{1}{2}$

James from Hamstel Junior School in the UK sent in these images, which you can click on to enlarge:

The first part of this challenge involved thinking about the different ways to fold and cut a piece of paper in half to show a half, a quarter, an eighth and two sixteenths.

I liked working in different colours and laying them out to clearly see the different combinations that could be made. It is interesting to see the different shapes that still represent the same fraction amount. I found 8 combinations.
The next part involved using just two of the combinations and making mixed fractions using a whole piece of paper and a fraction. I had to identify the value of each combination.

Next, I made a list of all the different addition number sentences that are possible from adding one from each combination.

Thank you all for sharing your ideas about this task with us.