Transcript Comparing Rational Numbers - Lesson 7

a
Numbers which can be expressed in the form ,
b
where a and b are integers and b is not equal to 0
are called rational numbers.
Rational numbers may appear in different forms but all of
them can be written as a fraction in the form a over b.
0.9
0.66
Number
2
1
4
5
a
Form
b
2

1
21
5
9
10
2
3
Rational
0 1 1
8 4
1
2
1
The number line can be used to compare numbers with exactly
one of the following being true:
a<b
a would be to the left of b.
a=b
They are at the same position and have
the same value.
a>b
a is to the right of b.
While using the number line works well for many
numbers and some familiar fractions, how else can we
compare rational numbers?
• A Fraction consists of two numbers
separated by a line.
• The top number (or numerator) tells how
many fractional pieces there are. In the
fraction 3/8, we have three pieces.
• The denominator of a fraction tells how
many pieces an object was divided into.
The fraction 3/8 tells us that the whole
object was divided into 8 pieces.
• If the denominators of two fractions are the
same, the fraction with the largest
numerator is the larger fraction.
• For example 5/8 is larger than 3/8
because all of the pieces are the same
and five pieces are more than three
pieces.
• If the numerators of two fractions are the same,
the fraction with the smaller denominator is the
larger fraction.
• For example 5/8 is larger than 5/16 because
each fraction says there are five pieces. If an
object is divided into 8 pieces, each piece will be
larger than if the object were split into 16 pieces.
Therefore five larger pieces are more than
five smaller pieces
a
c
For any rational numbers and , with b > 0 and d > 0
b
d
1.
a c
if  , then ad  bc , and
b d
2.
a c
if ad  bc , then  .
b d
3
2
Compare and .
8
5
Set up the problem as follows:
3 <
2
____
8
5
Multiply the numerator on the left by the denominator on
15
the right.
Multiply the numerator on the right by the denominator on
the left.
16
15 < 16 therefore, 3/8 is less than 2/5.
• Just convert each fraction to decimals,
and then compare the decimals.
• For Example: Which is bigger: 3/8 or
5/12 ?
• You need to convert each fraction to a
decimal. You can do this using your
calculator (3÷8 and 5÷12),
• 3/8 = 0.375, and 5/12 = 0.4166...
• So, 5/12 > 3/8
• Use > or < or = to make the statement true
• 1)
7
8
• 3) 6
8
5
8
5
7
3
7
3
13
3
4)
5
6
9
2)