By Derek W Haylock
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Extra resources for Numeracy for Teaching
Discussion and explanation of check-up 11 This check-up focuses on the reverse process of expressing proportions as percentages discussed in Check-ups 1, 2 and 18. 1 Most people know that 10% is also __ 10 (one-tenth). This is because 10% means ‘10 in 100’, which is equivalent to ‘1 in 10’. But, of course, this is a special case. 1 For example, 4% is not ‘1 in 4’ and 6% is not 6_ ! The proportion 4% is ‘4 in 100’, which, expressed in fraction notation, 4 is ___ 100. Cancelling 4, because this is a factor of both 4 and 100, this simplifies 1 to __ 25 .
D) Sometimes true. Discussion and explanation of check-up 12 The statements in (a) and (c) are known as the commutative laws of addition and multiplication. Remember that ab in algebraic notation is a shorthand for ‘a multiplied by b’. The generalisations that a + b = b + a and ab = ba, whatever numbers are chosen for a and b, state simply that it does not matter in which order you add two numbers together and it does not matter in which order you multiply them together. For example, using the commutative law of addition we could change 3 + 8999 into 8999 + 3.
This would be using the formula (A × B) × C. Either way you get the same result. This demonstrates what is called the associative law of multiplication: A × (B × C) = (A × B) × C, whatever numbers are chosen for A, B and C. This means that if you have three numbers to be multiplied together, the one in the middle can be 'associated' with either the first number or the last number and you get the same answer. This is very useful in mental calculations. e. 20 × 13, which equals 260. So, if I had to calculate 12 × 35 mentally, I would think of the 35 as (5 × 7) and then associate the 5 with the 12 as follows: 12 × 35 = 12 × (5 × 7) = (12 × 5) × 7 = 60 × 7 = 420.