Transcript 5.1 - David Beydler`s Math

Math 50
5.1 – Fractions, Mixed Numbers, and
Rational Expressions
1
A number that describes a part of a whole is
called a __________.
A fraction whose numerator and denominator
are integers is called a ____________________.
2
A number that describes a part of a whole is
fraction
called a __________.
A fraction whose numerator and denominator
are integers is called a ____________________.
3
A number that describes a part of a whole is
fraction
called a __________.
A fraction whose numerator and denominator
rational number
are integers is called a ____________________.
4
Ex 1.
Name the fraction represented by each shaded
region.
5
Ex 1.
Name the fraction represented by each shaded
region.
𝟑
𝟖
6
Ex 1.
Name the fraction represented by each shaded
region.
𝟑
𝟖
7
Ex 1.
Name the fraction represented by each shaded
region.
𝟑
𝟖
𝟑
𝟖
8
Ex 2.
3
Graph on a number line.
4
9
Ex 2.
3
Graph on a number line.
4
10
Ex 2.
3
Graph on a number line.
4
11
Ex 2.
3
Graph on a number line.
4
12
Ex 2.
3
Graph on a number line.
4
13
Ex 2.
3
Graph on a number line.
4
14
Ex 2.
5
Graph − on a number line.
8
Note: All of these are equal:
5
−
8
=
−5
8
=
5
−8
15
Ex 2.
5
Graph − on a number line.
8
Note: All of these are equal:
5
−
8
=
−5
8
=
5
−8
16
Ex 2.
5
Graph − on a number line.
8
Note: All of these are equal:
5
−
8
=
−5
8
=
5
−8
17
Ex 2.
5
Graph − on a number line.
8
Note: All of these are equal:
5
−
8
=
−5
8
=
5
−8
18
Ex 2.
5
Graph − on a number line.
8
Note: All of these are equal:
5
−
8
=
−5
8
=
5
−8
19
20
1
3
21
1
3
2
6
22
1
3
2
6
4
12
23
1
3
2
6
4
12
1 2
4
= =
3 6 12
24
When two fractions name the same number
(ex:
1 2
, ,
3 6
and
4
),
12
we call them
____________________.
We can get equivalent fractions by multiplying
or dividing the top and bottom by the same
number.
25
When two fractions name the same number
(ex:
1 2
, ,
3 6
and
4
),
12
we call them
equivalent fractions
____________________.
We can get equivalent fractions by multiplying
or dividing the top and bottom by the same
number.
26
When two fractions name the same number
(ex:
1 2
, ,
3 6
and
4
),
12
we call them
equivalent fractions
____________________.
We can get equivalent fractions by multiplying
or dividing the top and bottom by the same
number.
27
Ex 4.
Fill in the missing number so that the fractions
are equivalent.
5
=
9 36
−24 4
=
42
28
Ex 5.
Write the following fractions in simplest form:
3 𝟏
=
6 𝟐
4
=𝟒
1
0
=𝟎
5
8
0
undefined
7
=𝟏
7
29
Ex 5.
Write the following fractions in simplest form:
3 𝟏
=
6 𝟐
4
=𝟒
1
0
=𝟎
5
8
0
undefined
7
=𝟏
7
30
Ex 5.
Write the following fractions in simplest form:
3 𝟏
=
6 𝟐
4
=𝟒
1
0
=𝟎
5
8
0
undefined
7
=𝟏
7
31
Ex 5.
Write the following fractions in simplest form:
3 𝟏
=
6 𝟐
4
=𝟒
1
0
=𝟎
5
8
0
undefined
7
=𝟏
7
32
Ex 5.
Write the following fractions in simplest form:
3 𝟏
=
6 𝟐
4
=𝟒
1
0
=𝟎
5
8
0
undefined
7
=𝟏
7
33
Ex 5.
Write the following fractions in simplest form:
3 𝟏
=
6 𝟐
4
=𝟒
1
0
=𝟎
5
8
0
undefined
7
=𝟏
7
34
When comparing fractions with the same
denominator, just compare numerators.
(ex:
3
8
<
5
)
8
When they have different denominators
1
2
2
),
3
(like and then you have to write equivalent
fractions that have the same denominator
before comparing.
35
When comparing fractions with the same
denominator, just compare numerators.
(ex:
3
8
<
5
)
8
When they have different denominators
1
2
2
),
5
(like and then you have to write equivalent
fractions that have the same denominator
before comparing.
36
Ex 6.
Use <, >, or = to write a true statement.
1 2

2 5
2
12
−  −
7
42
6
15

8
20
37
A fraction where absolute value of numerator is
bigger than or equal to the absolute value of
denominator is called an __________________.
ex:
11
4
−7
2
8
8
38
A fraction where absolute value of numerator is
bigger than or equal to the absolute value of
improper fraction
denominator is called an __________________.
ex:
11
4
−7
2
8
8
39
A fraction where absolute value of numerator is
bigger than or equal to the absolute value of
improper fraction
denominator is called an __________________.
ex:
11
4
−7
2
8
8
40
An integer combined with a fraction is called a
__________________.
ex:
1
2
4
2
−5
3
1
1
2
41
An integer combined with a fraction is called a
mixed number
__________________.
ex:
1
2
4
2
−5
3
1
1
2
42
An integer combined with a fraction is called a
mixed number
__________________.
ex:
1
2
4
2
−5
3
1
1
2
43
Note:
1
2
4
=2+
1
4
44
45
9
1
=2
4
4
46
To convert improper fractions to mixed
numbers, ____________, write the quotient,
and then the remainder over the denominator.
Ex 7.
13
Write as a mixed number.
3
Ex 8.
37
Write − as a mixed number.
4
47
To convert improper fractions to mixed
divide
numbers, ____________,
write the quotient,
and then the remainder over the denominator.
Ex 7.
13
Write as a mixed number.
3
Ex 8.
37
Write − as a mixed number.
4
48
To convert improper fractions to mixed
divide
numbers, ____________,
write the quotient,
and then the remainder over the denominator.
Ex 7.
13
Write as a mixed number.
3
Ex 8.
37
Write − as a mixed number.
4
49
To convert mixed numbers to improper fractions,
____________ the whole part by the denominator, add
the numerator, and put the result over the denominator.
Ex 9.
2
Write 6 as an improper fraction.
3
Ex 10.
2
Write −11 as an improper fraction.
9
Ex 11.
Write 14 as an improper fraction.
50
To convert mixed numbers to improper fractions,
multiply
____________
the whole part by the denominator, add
the numerator, and put the result over the denominator.
Ex 9.
2
Write 6 as an improper fraction.
3
Ex 10.
2
Write −11 as an improper fraction.
9
Ex 11.
Write 14 as an improper fraction.
51
To convert mixed numbers to improper fractions,
multiply
____________
the whole part by the denominator, add
the numerator, and put the result over the denominator.
Ex 9.
2
Write 6 as an improper fraction.
3
Ex 10.
2
Write −11 as an improper fraction.
9
Ex 11.
Write 14 as an improper fraction.
52