Sum Equals Product

Problem | Solution | Printable page |
Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The sum of the numbers 4 and $1 \frac{1}{3}$ is the same as the product of 4 and $1 \frac{1}{3}$;
that is to say $4 +\frac{4}{3} = 4 \times \frac{4}{3}$. What other numbers have the sum equal to the product and can this be so for any whole numbers?

What relationship must exist between the numbers?
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Published November 1999.