Topics: Starter | Algebra | Place Value | Puzzles

• Tom, Birmingham
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• 75-57?
  
  I think the answer will be a multiple of 9?
• Paul, Coventry
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• Yes, and when you add the digits of a two digit multiple of 9 the answer is always 9
• JM, Ysgol Friars
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• AB - BA = (Ax10+B)-(Bx10+A) = 9A-9B = 9(A-B)
• CF, Lancshire
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• This is a great starter it is a quick way to see who can subtract without a calculator and it is a good way to demonstrate the use of algebra to generalise and prove things.
• Amy, Carlow Ireland
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• 65-56=09 0+9=9 cool it really works.
• Gianni, Milan
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• 52-25=27!
  Not every number is like that!
• Miss Hughes, London
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• My Year 4 class worked out that by reversing the numbers it always came to a multiple of 9. I was able to spot the pattern that when you use consecutive numbers (45, 56, 67, 78, 89) the answer will always be 09, as the lower tens digit will become the units and you will always have to borrow. Can anyone help me explain why ANY number, even a prime number, will result in a multiple of 9?
• Year 4, St Alban's Warrington
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• Our Year 4 class found this interesting. Some found it hard and some found it easy. It is a good starter for the day.
• Nigel Martin, Havant Academy
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• Declan one of my KS4 students used 99, which does not work.
• P6/5, Balfron Primary
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• We enjoyed this challenge but still aren't sure why the answer is always 9!
• Mr Jones, UK
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• If the digits are x and y then one number is 10x+y and the other is 10y+x.
  When you subtract the 2 numbers you are left with 9x-9y which factorises to 9(x-y) and as x-y is greater than zero as the digits are not equal and you have subtracted the smaller number, the solution will always be a multiple of 9.
• Mr Hulbert, Kellett School HK
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• Great starter for my Y6 class!
  We asked if three different digits would make a certain number?
  So far it has always been 18 ...
  Four digit numbers?
• Mr Marshall, Denmark
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• My year 6 class enjoyed this starter.

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