Question #b2995

1 Answer
Mar 28, 2016

Answer:

One is half of 2

Explanation:

#color(blue)("Discussion about what a fraction is.")#

A fraction has two parts, the top and bottom number. I want you to think of the top number as the count and the bottom number as an indicator of size. Proper names are #("numerator")/("denominator")#

Consider the fraction #3/5#. Strait away you can see that we have three of them (top number) but how do we think about the 'size'

The number of 5 means that we need 5 of them to make a whole of something. Suppose you have a plank of wood and split it into 2 equal lengths. We have a count of 2 but the size is also 2 so we have #2/2#. Which is the equivalent of 1 whole plank. Glue them back together and you have a whole plank again.
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#color(magenta)("Example: suppose we had 3 is half of what?")#

I am using the sign #-># this means there is a connection of some sort

Remember that half is #1/2# so

#3-> 1/2#

But for all of something we need the count part of #1/2# to become 2 so we end up with #2/2#

To change the count of 1 into a count of 2 we have 1+1

It is the same with fractions

To change the count of 1 (of size 2) we add another 1 (of size 2)

That is #2/2" "=" "1/2+1/2" "=" "(1+1)/2#

#color(red)("You must not do this "1/2+1/2=2/4#
#color(red)("You are adding counts of one size. The 4 means you have changed size")#
#color(red)("As long they are all the same size, adding counts does not change the size")#

If we have doubled the right hand side of #3->1/2#
Then we need to double the left as well

#3+3->1/2+1/2#

So#" " 6->2/2" "# as we now have #2/2# we have all of the something

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#color(blue)("Answering your question")#

1 is #1/2" of something "#

#1->1/2#

#1+1->1/2+1/2 = (1+1)/2#

#color(blue)(2-> 2/2 -> "All of the something")#