GCSE Maths Tutor Blog

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GCSE Maths Tuition Fractions


Question

(From Grade 9 Target GCSE Maths)


In Jodie's school, one fifth of the pupils are in year 7.  The ratio of girls to boys in year 7 is 3:2 and 20% of the girls in year 7 have blonde hair.


a) What fraction of girls In year 7 have blonde hair?


So let's turn this into an OF question (OF in maths more often than not means times)


20% or 1/5 of the girls in y7 have blonde hair.


We know the ratio of girls in y7 to boys is 3:2.  Therefore girls in y7 are 3/5 of the pupils in y7.


We are also told pupils in y7 are 1/5 of the school pupils.


Therefore the girls with blonde hair are 1/5 of y7 girls which is 3/5 of y7 pupils which is 1/5 of school pupils.


So as of in maths more often than not means times we have


1/5 x 3/5 x 1/5 = 3/125


Therefore the fraction of the girls in school with blonde hair is 3/125.

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Multiplying Maths Decimals


Ignore them! Well ignore the decimal points anyway.


So 2.4 x 1.2 = 24 x 12


24 x 10 = 240

24 x 2    =  48

24 x 12  = 288


So 2.4 x 1.2 = 288 ?


Ok we can't completely ignore the decimals.


We now have to put a decimal in the answer where it 'makes sense' or matches the total number of decimal places (2) in the question.


So 2.4 x 1.2             = 2.88

(2dp in question)      (2dp in answer)

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Maths - dividing by teen numbers and above


So 240 ÷ 8 = 30 is fairly straightforward if you know your 8 times tables and can do 'bus stop' or short division. 


But what about dividing by numbers higher than 12 which aren't prime.


Well this week a year 7 tutee of mine suggested the following method. Dividing by two factors instead of the whole number.


e.g.


1344 ÷ 24 = (1344 ÷ 8 ) ÷ 3

                   = (168) ÷ 3

                   = 56


1728 ÷ 48 = (1728 ÷ 8) ÷ 6

                   = (216) ÷ 6

                   = 36


1125 ÷ 15 = (1125 ÷ 5) ÷ 3

                   = (225) ÷ 3

                    = 75


Not a 24, 48 or 15 times table in sight.  Not bad eh.