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Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM... ### Sum Equals Product

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 ï¿½ 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers? ### Special Sums and Products

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

##### Age 11 to 14Challenge Level I mixed up some lemonade in two glasses.

The first glass had $200$ml of lemon juice and $300$ml of water.
The second glass had $100$ml of lemon juice and $200$ml of water.

Which mixture has the stronger tasting lemonade?
How do you know?

Use the interactivity below to compare different mixtures of lemonade and develop a strategy for deciding which is stronger each time.

Click the New Mixes button to generate new mixtures

Beaker A

Lemon ???
Water ???

Beaker B

Lemon ???
Water ???

Which beaker has the stronger tasting lemonade?

Score: 0

Once you are confident that you can always work out which mixture is stronger, here are some questions to consider:

How might you use fractions to help you to work out which mixture is stronger?
How might you use ratios?