Download Rational Numbers and Operations

MPM 1DX
Unit 1 Day 3
Rational Numbers
Simple Definition: A rational number is a number that can be written as a fraction.
1
2
Examples:
, - , 5, 0, …
3
4
All natural numbers (N) are rational.
All whole numbers (W) are rational.
All integers (I) are rational.
 These numbers plus the rational
numbers make up the REAL numbers
Mathematical Definition: A rational number is any number that can be written in the
m
form
where m and n are both integers but n cannot be zero.
n
Set builder notation: Q =
 mn
m, n  I, n  0

Note: Integers are rational numbers, but rational numbers are not necessarily integers.
Examples: a) - 3 
_________ b)
2

5
 _______________
Which of the following are rationals?
a)
1
-5
d) 0.125
b) 3
1
2
e) -5.41
c) -0.1
.
f) 0. 3
All integers and terminating or repeating decimals are rational numbers.
Any number that cannot be written as a terminating or repeating decimal is an
irrational number. Examples: π , 2
MPM 1DX
Unit 1 Day 3
1. Express three rational numbers equivalent to each of the following.
a) -
4
5
c) -
-3
7
2. List in order from smallest to largest.
-
3 1 -4
,
,
5 -3 3
b) - 2
1
4
-2-
MPM 1DX
Unit 1 Day 3
Operations with Rational Numbers
1. Addition and Subtraction
- convert mixed fractions to improper
- write each fraction with a single sign
- determine a common denominator
- write equivalent fractions
- add or subtract the numerators only
- reduce fractions to lowest terms
Evaluate.
7 1

a)
10 10
d)
2 5

9
6
b)
1 2

2 3
 3  5
e)      

 8   4
2 1
c) 4  1
3 2
1
1
f)  5  3
2
3
-3-
MPM 1DX
Unit 1 Day 3
2. Multiplication
- convert mixed fractions to improper
- write each fraction with a single sign
- multiply numerators together, then denominators (or reduce if possible)
- reduce fractions to lowest terms
Evaluate.
3 1

a)
4 2
d)
2  3
 1 
5  7
b)
1 4

8 5
c)
 4  3


7  5
2   9   3  5 

e)   2 



3  4   5   6 

3. Division
- convert mixed fractions to improper
- write each fraction with a single sign
- invert the second fraction and change the divide sign to multiply
- multiply numerators together, then denominators (or reduce if possible)
- reduce fractions to lowest terms
Evaluate.
2 4
a) 


 3   5
1
 3  
b)  10  
 4 
2
 5 
-4-