Showing posts with label fraction division. Show all posts
Showing posts with label fraction division. Show all posts
Saturday, 29 April 2017
Friday, 3 February 2017
Saturday, 24 May 2014
fraction division
this method has been suggested by Caleb Gattegno, using an understanding that division is the inverse of multiplication and that the reciprocal is the multiplicative inverse (producing 1)
providing students with a few calculations of the form:
and encouraging them to cancel the result down will reveal a simple to see pattern
reasons for this can be fairly easily established
then, maybe following a simpler case (e.g. 2 x 3 x 4 = 24 with 2 x 3 = 24/4), it can be seen from:
that an equivalent statement can be formed
providing students with a few calculations of the form:
and encouraging them to cancel the result down will reveal a simple to see pattern
reasons for this can be fairly easily established
then, maybe following a simpler case (e.g. 2 x 3 x 4 = 24 with 2 x 3 = 24/4), it can be seen from:
that an equivalent statement can be formed
dividing fraction views
the intention of these resources is to present three ways of making some sense of how to divide by a fraction, linking a diagram to what happens numerically (/algebraically)
firstly, what happens when a whole number is divided by a fraction?
secondly, Fawn Nguyen's lovely approach uses rectangles to change a division of fractions into one with common denominators
this method was advocated by Caleb Gattegno
I have altered Fawn's text slightly, thinking that you could present this to students
(Fawn has much to say, in general ways, about how to utilise rectangles to make sense of problems)
when you have common denominators to both fractions you could multiply the dividend and divisor by this common denominator but (with language being used) 'an' somethings divided by 'bm' somethings should be the result required
algebraically:
thirdly, Mr Novak's approach (from moveitmaththesource) uses the idea that when you are presented with a division sum you can adapt it by multiplying both parts of a division (dividend and divisor) by the same amount - in this case the reciprocal of the divisor - without changing the sum
just as when you divide e.g. 7 by 3 the remainder is expressed in terms of the divisor
firstly, what happens when a whole number is divided by a fraction?
secondly, Fawn Nguyen's lovely approach uses rectangles to change a division of fractions into one with common denominators
this method was advocated by Caleb Gattegno
I have altered Fawn's text slightly, thinking that you could present this to students
(Fawn has much to say, in general ways, about how to utilise rectangles to make sense of problems)
when you have common denominators to both fractions you could multiply the dividend and divisor by this common denominator but (with language being used) 'an' somethings divided by 'bm' somethings should be the result required
algebraically:
thirdly, Mr Novak's approach (from moveitmaththesource) uses the idea that when you are presented with a division sum you can adapt it by multiplying both parts of a division (dividend and divisor) by the same amount - in this case the reciprocal of the divisor - without changing the sum
just as when you divide e.g. 7 by 3 the remainder is expressed in terms of the divisor
Wednesday, 27 April 2011
division = subtraction?
can you find a general rule?
can you justify a general rule?
Tuesday, 9 November 2010
fraction division simplification
explore, by substituting some numbers
obtain a general result by substituting some numbers
and maybe establish this result algebraically
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