1150 day 8
TRANSCRIPT
Rational Numbers
Integers: …, -3, -2, -1, 0, 1, 2, 3, …
A Rational Number can be written in the form , where a and b are integers and b ≠ 0.
www.visualfractions.com
b
a
3
2
Representing fractions
Area model
Number Line Model
Set model
3
2
0 13
1
3
2
Equivalent (equal) fractions represent the same number.
3
2
6
4
3
2
9
6
2
2
3
3
Fundamental Law of Fractionscb
ca
b
a
Show that and are equal by finding a common denominator.
The least common denominator of two fractions is the LCM of their denominators.
LCM(3,9) = 9
3
2
9
6
3
2
9
6
3
3
Show that and are equal by simplifying both fractions.
A fraction is in simplest form if its numerator and denominator have no
common factor other than 1.
3
2
9
6
3
2
3
2
3
3
9
6is simplified
Show that and are equal by cross multiplying.
3
2
9
6
bcadifd
c
b
a
9
6
3
2
18 18 18 = 18so
9
6
3
2
Ordering rational numbers
Place <, > or = between the two numbers:
<
>
<
7
3
7
2
7
10 17
2
7
3
7
4
7
5
7
6
7
7
5
3
5
1
4
1
5
15
1
4
1
Find one rational number between and 4
1
5
1
5
1
4
1 LCD = 204
4
5
5
20
4
20
5
2
2
2
2
40
8
40
1040
9
Find two rational numbers between and 5
1
6
1
6
1
5
1 LCD = 305
5
6
6
30
5
30
6
2
2
2
2
60
10
60
12
120
23,
120
22,
120
212
2
2
2
120
20
120
24
A mixed number represents the sum of an integer and a fraction.
211
211
211
211
0 1 2-1-2 2112
11
Change to an improper fraction.
An improper fraction has a numerator that is greater than or equal to its denominator.
321
132
321
32
33
35
Change to a mixed number.25
1 121
212
22 5
41
2 R 1
212
Adding Rational Numbers
4
1
4
1
4
2
2
1
3
1
4
1
1212
3
3
4
4
12
4
12
3
12
7
43
32 21
321
432
1281
1292
44
33
12173
1254
43
32 21
321
432
35
411
1253
1254
44
33
1220
1233
Subtracting Rational Numbers
12
1
9
2
4
4
3
3
36
3
36
8
36
5
2
1
5
2
2
2
5
5
10
5
10
4
10
1
32
51 14
32
51
1
433
55
1510
153
1
43
18
2 158
32
51 14
5
21
3
5
3
3
5
5
15
63
15
25
15
38
15
82
Multiplication of Rational Numbers
3 · 2= 6
3 groups of 2
3 · ½ = 1 ½ or
3 groups of ½
=
2
3
4
1
3
2
db
ca
d
c
b
a
Rectangle model
3
2
4
1
12
2=
21
41 12 )1)(2(
21
41
2
3
4
9
8
27
8
33
Dividing rational numbers
6 3= 2
How many threes are in six?
3 3
6 2= 3
How many twos are in six?
2 2 2
6 ½ = 12
How many one-halfs are in six?
6 ¼ = 24
How many one-fourths are in six?
How many one-sixths are in one-third?
6
1
3
1= 2
c
d
b
a
d
c
b
a
23
6
1
6
3
1
6
1
3
1
Jane has 20 yards of fabric. How many blouses can she make if each blouse requires:
a) 2 yards of fabric
20 2 = 10 blouses
Jane has 20 yards of fabric. How many blouses can she make if each blouse requires:
b) 2 ½ yards of fabric
21220
2520
52
120
540 = 8
8 blouses
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Jane has 20 yards of fabric. How many blouses can she make if each blouse requires:
c) 2 yards of fabric
d) How many yards of fabric is left over?Fabric used: Fabric left:
31220
3720
73
120
760
8 blouses
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
3
1
748
3128
378
356 yards
3218
321820 yards
311