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# Largest Product

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Age 11 to 14

Challenge Level

*Largest Product printable worksheet*

Here are some different ways in which we can split 100:

- $30 + 70 = 100$
- $20 + 80 = 100$
- $21 + 56 + 23 = 100$
- $10 + 10 + 10 + 10 + 10 + 10 + 20 + 20 = 100$

The products of these sets are all different:

- $30 \times70 = 2100$
- $20 \times 80 = 1600$
- $21 \times 56 \times23 = 27048$
- $10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 20 \times 20 = 400000000$

**What is the largest product that can be made from whole numbers that add up to 100?**

Choose another starting number and split it in a variety of ways.

What is the largest product this time?

Can you find a strategy for splitting any number so that you always get the largest product?

Click here for a poster of this problem.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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