Download Ch 5.3

Ch5.3 The Rational Numbers
Section 5.3 Notes Page 1
The set of rational numbers consists of all the numbers that can be expressed as a quotient of
𝑎
two integers( 𝑏) , with the denominator not 0. The integer a is called the numerator, and the
integer b is called the denominator.
The Fundamental Principle of rational Numbers: If
other than 0,
𝑎∙𝑐
𝑏∙𝑐
𝑎
= 𝑏. The rational numbers
𝑎
𝑏
and
𝑎
is a rational number and c is any number
𝑏
𝑎∙𝑐
𝑏∙𝑐
are called equivalent fractions.
A mixed number consists of the sum of an integer and a rational number, expressed without the
use of an addition sign. 3
4
5
An improper fraction is a rational number whose numerator is greater than its denominator.
The least common multiple of the denominators is called the least common denominator.
Ex1. Reduce each rational number to its lowest terms.
a)
10
15
b)
32
c)
80
70
130
d) 455
90
Ex2. Convert each mixed number to an improper fraction.
7
a) 2 9
4
b) 35
5
c) −2 8
Ex3. Convert each improper fraction to a mixed number.
a)
47
8
b)
5
3
c)
42
5
19
5
Section 5.3 Notes Page 2
Ex4. Express each rational number as a decimal.
a)
3
b)
5
5
c)
8
7
11
Ex5. Express each termination decimal as a quotient of integers. If possible, reduce to lowest
terms.
a) 0.7
b) 0.49
c) 0.048
Ex6. Express each repeating decimal as a quotient of integers.
a) 0. 6
b) 0. 53
c) 0. 79
Ex7. Multiply. If possible, reduce the product to its lowest terms:
a)
3
5
∙
8 11
2
9
b) − 3 ∙ (− 4)
2
1
c) 3 3 ∙ (1 4)
4
2
d) -11 ∙ 3
2 1
e) 3 5 ∙ 2
Section 5.3 Notes Page 3
Ex8. Divide. If possible, reduce the quotient to its lowest terms:
b)
4
1
3
7
3
b) − 5 ÷ 11
÷ 10
5
1
9
c) 4 4 ÷ 1 2
5
d) − 11 ÷ (− 4)
Ex9. Perform the indicated operations:
a)
3
2
3
1
b) 4 + 6
+7
7
1
3
1
c) 5 + 4
7
d) 15 − 24
3
7
e) 10 − 12
Ex10. Simplify:
1 3
1
3 2
a) (2) − (2 − 4) (−4)
1
1
1
1
b) (2 + 4) ÷ (2 + 3)
9 1
3
5
c) − 4 (2) + 4 ÷ 6
Section 5.3 Notes Page 4
Ex11. Find the rational number halfway between the two numbers in each pair.
a)
1
𝑎𝑛𝑑
2
3
4
1
b) 3 𝑎𝑛𝑑
1
2