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Study Tip - Mathematics - Times Tables, BIMDAS, Fractions and Algebra

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Posted by Studentbox user
on 21/07/2016 at in  Mathematics
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Posted by previous Studentbox member on February 2, 2014.

TIMES TABLES

It used to be by the time you got to year 8 you were expected to know how to multiply from 0 x 0 to 12 x 12.

Each year I am astounded at how these skills have deteriorated. Knowing your times tables up to about 15 x 15 for year 12 is useful and beneficial to succeeding in mathematics. Half your assessments are calculator free, knowing your times table is a significant component of these skills. It also helps when simplifying and factorising.

Also know your squared and cubed numbers. Squared 1 x 1 to 20 x 20, cubed 1 x 1 x 1 to 6 x 6 x 6

Knowing these by heart will be useful too:

  • 2 to the power of 0 - 8
  • 3 to the power of 0 - 4
  • 4-8 to the power of 0 - 3
  • 10 to the power of 0 - 6

BIMDAS

We learn BIMDAS or BIDMAS in primary school. Every mathematical equation, ever, follows the rules of BIMDAS.

So what is BIMDAS?

  • B = Brackets
  • I = Indices (power)
  • M = Multiplication
  • D = Division
  • A = Addition
  • S = Subtraction

M and D are interchangeable as are A and S. That is to say,

  • 15 ÷ 3 x 6 = 30 not 15/18 (or 5/6)
  • 10-6+5 = 9 not -1

FRACTIONS

I never got a grip on fractions until year 9, I wanted to be top of maths so I busted my butt until they made sense.

Here's the rules:

  • always convert any mixed fraction into an improper fraction to do calculations
    • 2 1/3 = 7/3 [(3 x 2 +1)/3] or (bottom x big + top)
    • convert the fraction back to mixed once you have finished
  • you can only add or subtract fractions if the denominator (the bottom number) is the same
    • 1/3 + 1/4 <- you must get the denominator the same, the denominator is the lowest common multiple (LCM)
      • the LCM of 3 and 4 is 12
      • you have to times each term by the relevant number (top and bottom) to get the denominator the same.
      • then you can add or subtract
      • so 1/3 + 1/4 = 1/3 x 4/4 + 1/4 x 3/3 = 4/12 + 3/12 = 7/12
  • multiplying fractions
    • always convert any mixed fraction into an improper fraction
    • 2 1/5 * 3 1/8 = 11/5 * 25/8 = 55/8 = 6 7/8 not 6 1/40 (2 x 3 + 1/5 x 1/8)
  • dividing fractions
    • always convert any mixed fraction into an improper fraction
    • 3/4 ÷ 1/2 = 3/4 * 2/1 (flip the fraction that you are dividing by) = 3/2
  • Get into the habit of leaving answers as improper fractions, what we call an exact solution. Only convert to decimal if the question asks for it, or it makes sense in the context of the question.

ALGEBRA

Ah the one word to bring terror to many eyes. It's a sad thing when I meet a student who is convinced they can't do algebra. I convince them, they can, and that they have been doing it for years.

  • 3 + □ = 6, what's the box? this is your year 1 start into algebra
  • it progresses to 3 + x = 6, what's x? around year 6/7
    • from here it's remembering that maths is all about balance
    • and algebra is about isolating the variable to find a solution
  • in the real world, every time you go shopping and have to work out if you can buy this, this and this with your $5 - well that is algebra

There are many skills that you need to know in order to do algebra correctly - expanding brackets, factorising, positives/negatives, fractions, grouping like terms. It's a lot of stuff to know - and each needs its own post.

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