Date post: | 09-Jul-2015 |
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Education |
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Division and rational number. Any two integers have
such that xq = y. The process for finding q when three
such an integer is called division, and q is called the
quotient. Since division is not always possible in the
set of integers, it is advantageous to create a larger
set of number which division is possible in more
casess. The number which are introduced for this
prpose are the fractions, and the union of the set of
fractions and the set of integers is the set of rational
number
Division is splitting into
equal parts or groups.
It is the result of "fair
sharing".
12 Chocolates 12 Chocolates Divided by 3
Answer: 12 divided by 3 is 4: they get 4 each.
We use the ÷ symbol,
or sometimes
the / symbol to
mean divide:
12 ÷ 3 = 4
12 / 3 = 4
÷ /
Division is the opposite of multiplying. When we know a multiplication fact we can find a division fact:
Example: 3 × 5 =
15, so 15 / 5 = 3.
Also 15 / 3 = 5.
Multiplication... ...Division
3 groups of 5 make 15... so 15 divided by 3 is 5
and also:
5 groups of 3 make 15... so 15 divided by 5 is 3.
So there are four related facts:
3 × 5 = 15
5 × 3 = 15
1a5 / 3 = 5
15 / 5 = 3
Answer: 28 ÷ 7 = 4
Searching around
the multiplication
table we find that
28 is 4 × 7, so 28
divided by 7 must
be 4.?
There are special
names for each
number in a
division:
dividend ÷ divisor
= quotient
Example: in 12 ÷ 3 = 4:
12 is the dividend
3 is the divisor
4 is the quotient
Example: There are 7 bones
to share with 2 pups.
But 7 cannot be divided exactly
into 2 groups,
so each pup gets 3 bones,
but there will be 1 left over:
Hahahaha...
:D
A Rational Number is a real number that can be written
as a simple fraction (i.e. as
a ratio).
Example:
1.5 is a rational number because 1.5 = 3/2 (it can be written as a fraction)
Number As a Fraction Rational?
5 5/1 Yes
1.75 7/4 Yes
.001 1/1000 Yes
0.111... 1/9 Yes
√2(square root of 2) ? NO !
More formally we would say:
A rational number is a
number that can be in the
form p/q
where p and q are integers a
nd q is not equal to zero.
So, a rational number can be:
p
q
P q p / q =
1 1 1/1 1
1 2 ½ 0.5
55 100 55/100 0.55
1 1000 1/1000 0.001
253 10 253/10 25.3
7 0 7/0No! "q"
can't be zero!
If a rational number is still in the
form "p/q" it can be a little
difficult to use, so I have a
special page on how to:
Using Rational Numbers
Add, Subtract, Multiply and Divide
Rational Numbers
The ancient greek mathematician Pythagoras believed that all numbers were rational (could be written as a fraction), but
one of his students Hippasus proved (using geometry, it is
thought) that you could not represent the square root of 2 as
a fraction, and so it was irrational.
However Pythagoras could not accept the existence of irrational numbers, because he believed that all numbers had
perfect values. But he could not disprove Hippasus' "irrational
numbers" and so Hippasus was thrown overboard and
drowned!