Problem Teachers' Notes Hint Solution

# Forgot the Numbers

There were three main ways of working this one out.

1. Tom from Tattingstone School, UK used a step-by-step method.

As I divided I am going to reverse the process by timsing (multiplying) $3.125$ by whole numbers under $5$ to find the original numbers.
$1 \times 3.125 = 3.125$
$2 \times 3.125 = 6.25$
$3 \times 3.125 = 9.375$
$4 \times 3.125 = 12.5$
$5 \times 3.125 = 15.625$
$6 \times 3.125 = 18.75$
$7 \times 3.125 = 21.875$
$8 \times 3.125 = 25$
Therefore the original number $25\div{8} = 3.125$

2. Some people realised that $0.125$ is the same as $\frac{1}{8}$ and used this to help work out the answer. Well done to Daniel from Anglo-Chinese School, Singapore, Jesse from Tattingstone School, UK, Christina from Marlborough Primary School and Samantha.

Thomas from Tattingstone School wrote:

One of the numbers is $8$ and the other is $25$. I worked this out by first looking at the number $0.125$ and working out what fraction of $1$ it is. It turned out that it was an eighth. That meant that one of the numbers must be $8$. Then I looked at the remaining $3$ and multiplied the $8$ by it and that got me to $24$. Last but definitely not least I added on the one and that got me to the last answer $25$.

3. Ashley from Australia did it another way:

An easy way of working it out would be to say 'divide $3125$ by $1000$' ($3.125$). If I reduce it to its lowest terms, (divide by $125$) it is $25$ divided by $8$. This is the answer. It can't be $50$ divided by $16$, as the problem says that both numbers were under $50$.
Thank you also to Robert , Stephanie, Ben, Sofie, Scot from Moorgate Primary School, Staffordshire; Ellie, Sarah and Caroline from The Mount School York.