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FRACTIONS
Common Fractions and Decimal Fraction
Need
for Fractions
Fractions
are needed whenever we use measures,
whether in cooking or in measuring lengths.
To measure a length, we may apply a ruler
to it. If the ruler had no divisions smaller than inches, we could not measure
very precisely. For more precise measurement each inch is divided into a number
of equal parts. The larger the number of parts into which the inch is divided,
the smaller each part is and the more precisely we can measure. To show the
size of the parts of an inch and the number of these parts we are using, we
write a fraction.
The
diagram shows that these fractions are equal.
Meanings
of Fractions
The example on the preceding page
illustrates this fact:
I.
A fraction can be thought of as showing the number of equal parts into which a
whole has been divided and the number of these parts being considered.
The
integer which shows the total number of equal parts in the whole is called the denominator;
it is written below the line. The integer which shows the number of parts
considered is called the numerator; it
is written above the line. The numerator and denominator are called the terms
of the fraction.
Dividing a group of
objects into a number of equal parts also leads to a fraction. The 3 squares
shown below are to be divided into 4 equal parts. We first divide each square
into quarters. This gives 12 quarters. There will be 3 of these quarters in
each of the 4 parts.
3 / 4
is thus one of the 4
equal parts of 3 objects or 3
/
4.
This example illustrates this fact:
I
II.
A fraction can also be thought of as showing one of a number of equal parts of
a group of objects.
A fraction may be less than, equal to, or
greater than a whole.
If
the numerator is less than the denominator, the fraction is called a
proper fraction. For example,
8/ 11
is a proper fraction.
If the numerator is equal to or greater
than the denominator, it is an improper
fraction.
11
/ 11
and
15 / 11
are improper fractions.
Working
with Fractions
1.
In the first diagram each third was divided into two equal parts. What part of
the whole is each new part?
2.
Using the diagram, explain why
2/3 = 4/6
.
3.
Using the second diagram, explain why
2/3 = 6/9
.
4.
Draw a diagram to show that
4/5 = 8/10 and
that
4/5 = 12/15
.
The above exercises illustrate the fundamental
principle of fractions, which is:
If
the numerator and denominator of a fraction are both multiplied by the same
number, or both divided by the same number, the value of the fraction is not
changed. Here it is understood that we
never multiply or divide by 0.
When the numerator and
denominator cannot be further divided by the same number, the fraction is in lowest
terms. Equal fractions are also called equivalent.
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