Why do we
need common denominators? This is not a question known to keep
people up all night worrying. However if you happen to be a
student with a fraction phobia, then read on – there may be
tidbits of information that will demystify one aspect of
commonly seen answer to the questions above is “we need common
denominators to add (or subtract) fractions.” For some this is
enough, but you may want more. You may then ask “why are common
denominators necessary when adding fractions?” The answer is a
direct conclusion from two fundamental concepts – when can we
add and what are fractions?
add (or subtract) only the same type of things, a rule
remembered as “you can’t add apples and oranges.” What would be
the result if you have 5 apples and were then given 1 orange.
You would have “5 apples and 1 orange.” However if you
renamed the fruit so that you began with 5 “fruit items” and
were then given another 1 “fruit item” you could then add the
same type of things together for a total of 6 “fruit items.”
consider fractions such as 5/9. Its denominator 9 identifies
the fraction’s type as ninths, such as when a pizza is cut into
9 equal sized slices; each slice is a ninth of the pizza. The
numerator 5 indicates how many of this type of fraction there
are. So if you had 5 slices of this pizza then you would have
5/9 of the pizza.
you are given 1/3 of another pizza. The total amount of pizza
you have is 5—ninths of a pizza and 1—third of a pizza,
different types of fractions that cannot be added any more that
5 apples and 1 orange can.
to add, one or both fractions must be renamed so the
fractions have common (the same) denominator. When the larger
1/3 of a pizza slice is further cut up into 3 slices, each of
these slices would be ninths. 1—third of a pizza has just been
renamed as 3—ninths of a pizza.
a common denominator, 5—ninths of a pizza increased by
3—ninths of a pizza gives us a total of 8—ninths of a pizza.
denominators are needed when adding (or subtracting) fractions
is an easy statement to memorise, but do you need to remember it
by rote? Not when you should already know when you can or
cannot add and what the two numerals that make up the fraction
signifies. These two fundamental ideas used together allow
anyone to explain why fractions need common denominators when
Carey's quiz on this topic:
Lowest Common Denominator
another explanation of why we need common denominators try the
information about fractions look at these sites.
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