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?
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 14 Challenge 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
Which beaker has the stronger tasting lemonade?
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?
How about a graphical approach?
Do you always use the same strategy?
Describe some occasions when one strategy might be more efficient than another.
In the original example, the first glass had 200ml of lemon juice and 300ml of water, and the second glass had 100ml of lemon juice and 200ml of water.
If I mix the two glasses of lemonade together, the mixture is weaker than the first glass was, but stronger than the second glass.
Try the same with some other mixtures.
Is the strength of the combined mixture always between the strengths of the originals? Can you justify your findings?
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.