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## 'Pies' printed from http://nrich.maths.org/

**Matthew** and
**James**
recorded their answer as a fraction, 433
$\frac{1}{3}$ grams. **Helena** of
Bebington and Christina, of Malborough Primary School, recorded
their answers as decimal fractions. But each of these people used a
combination of fractions and decimals to arrive at their
solutions.

Can you follow their thinking as they
calculated the answer?

Matthew explained the procedure he used:

I got my answer of 433 $\frac{1}{3}$ grams by putting the
problem into an equation. These are the steps I took to get the
answer:

- First I did the sum $200$g. + $125$g. which equalled
$325$g.
- Then I wrote it down like this: $325$g. +
$\frac{1}{4}$ pie = pie

I then converted this to: $325$g. +$\frac{1}{4}$ pie =
$\frac{4}{4}$ pie (or one whole pie).
- Next, I took $\frac{1}{4}$ of a pie from each side leaving me
with: $325$g. = $\frac{3}{4}$ pie.
- I multiplied each side by $4$ which came out as: $1300$ = $3$
pies
But Matthew only wanted to find the weight of
one pie, so he did this last important step:

- I divided each side by $3$ and came to the final answer of:433
$\frac{1}{3}$ grams = $1$ pie."

Helena described her method this way:

$\frac{1}{4}$ pie = $325$g. divided by $3$, which is
$108.3$g.

So, $4 \times \frac{1}{4}$ of a pie = $4 \times108.3$g. or
$433.2$g.

$433.2$ grams is weight of a whole pie"