Transcript Math 71 – 1.1

Math 50
5.3 – Multiplying Fractions, Mixed Numbers,
and Rational Expressions
1
To multiply fractions, __________ across their
numerators and denominators.
2
multiply across their
To multiply fractions, __________
numerators and denominators.
3
Ex 1.
Multiply and write the product in lowest terms.
5 3
∙
9 10
Ex 2.
Multiply and write the product in lowest terms.
18 30
− ∙
20 32
Ex 3.
Multiply and 2write the product in lowest terms.
18𝑥𝑦
10𝑥
∙ − 2
5
21𝑦
4
To multiply mixed numbers, convert to
__________________, multiply, and convert
result to mixed number.
5
To multiply mixed numbers, convert to
improper fractions multiply, and convert
__________________,
result to mixed number.
6
Ex 4.
Multiply and write the product as a mixed
number in lowest terms.
1
3
3
∙
2
1
5
Note: We could get an estimate of the product
by multiplying the closest whole numbers (in
previous example, 3 ∙ 1 = 3). This is a good
sanity check when we get our answer.
7
Ex 4.
Multiply and write the product as a mixed
number in lowest terms.
1
3
3
∙
2
1
5
Note: We could get an estimate of the product
by multiplying the closest whole numbers (in
above example, 3 ∙ 1 = 3). This is a good sanity
check when we get our answer.
8
Ex 5.
Estimate, then find the product as a mixed
number in simplest form.
2
1
5 ∙2
3
7
Ex 6.
Estimate, then find the product as a mixed
number in simplest form.
3
2 ∙ (−12)
8
9
Ex 7.
Simplify
2 3
5
=
2 3
5
2 2 2
⋅ ⋅
5 5 5
In general,
=
𝒂 𝒏
𝒃
𝟖
𝟏𝟐𝟓
=
𝒂𝒏
𝒃𝒏
(for 𝑏 ≠ 0)
10
Ex 7.
Simplify
2 3
5
=
2 3
5
2 2 2
⋅ ⋅
5 5 5
In general,
=
𝒂 𝒏
𝒃
𝟖
𝟏𝟐𝟓
=
𝒂𝒏
𝒃𝒏
(for 𝑏 ≠ 0)
11
Ex 7.
Simplify
2 3
5
=
2 3
5
2 2 2
⋅ ⋅
5 5 5
In general,
=
𝒂 𝒏
𝒃
𝟖
𝟏𝟐𝟓
=
𝒂𝒏
𝒃𝒏
(for 𝑏 ≠ 0)
12
Ex 7.
Simplify
2 3
5
=
2 3
5
2 2 2
⋅ ⋅
5 5 5
In general,
=
𝒂 𝒏
𝒃
𝟖
𝟏𝟐𝟓
=
𝒂𝒏
𝒃𝒏
(for 𝑏 ≠ 0)
13
Ex 8.
Simplify
3𝑥 2
4𝑧
3
14
A fraction of a whole number translates to
3
3
multiplication: “ of 32 people” becomes ∙
4
4
32 = 24
A whole number out of a whole number
translates to a fraction: “35 out of 39 people”
35
becomes
39
15
A fraction of a whole number translates to
3
3
multiplication: “ of 32 people” becomes ∙
4
4
32 = 24
A whole number out of a whole number
translates to a fraction: “35 out of 39 people”
35
becomes
39
16
A fraction of a whole number translates to
3
3
multiplication: “ of 32 people” becomes ∙
4
4
32 = 24
A whole number out of a whole number
translates to a fraction: “35 out of 39 people”
35
becomes
39
17
Ex 9.
An ad says that 4 out of 5 dentists choose Crest
toothpaste. In a room with 345 dentists, how
many would you expect to choose Crest’s
toothpaste?
18
Ex 10.
3
A study finds that of Mt. SAC students like Taco
1
5
4
Nazo, and of these students don’t like fish
tacos. What fraction of Mt. SAC students like
Taco Nazo but don’t like fish tacos?
19
Area of a triangle is given by:
𝟏
𝑨 = 𝒃𝒉
𝟐
(𝑏 is base, and ℎ is height)
20
Ex 11.
Find the area of a triangle with a base of
2
7
3
meters and a height of
4
4
5
meters.
21
The distance from the center to any point on the
circle is called the _________.
The distance across a circle through the center is
called the ____________.
22
The distance from the center to any point on the
radius
circle is called the _________.
The distance across a circle through the center is
called the ____________.
23
The distance from the center to any point on the
radius
circle is called the _________.
The distance across a circle through the center is
diameter
called the ____________.
24
The distance from the center to any point on the
radius
circle is called the _________.
The distance across a circle through the center is
diameter
called the ____________.
25
Ex 12.
3
Find the diameter of a circle with radius 2 feet.
5
26
The distance around a circle is called the
______________.
It turns out that for any circle the circumference
divided by the diameter is the same number
(approximately 3.1415926 …), which we call pi, and
𝐶
write 𝜋. That is, = 𝜋
𝑑
From this, we get a formula for the circumference
of a circle:
𝑪 = 𝝅𝒅 (or 𝑪 = 𝟐𝝅𝒓)
27
The distance around a circle is called the
circumference
______________.
It turns out that for any circle the circumference
divided by the diameter is the same number
(approximately 3.1415926 …), which we call pi, and
𝐶
write 𝜋. That is, = 𝜋
𝑑
From this, we get a formula for the circumference
of a circle:
𝑪 = 𝝅𝒅 (or 𝑪 = 𝟐𝝅𝒓)
28
The distance around a circle is called the
circumference
______________.
It turns out that for any circle the circumference
divided by the diameter is the same number
(approximately 3.1415926 …), which we call pi, and
𝐶
write 𝜋. That is, = 𝜋
𝑑
From this, we get a formula for the circumference
of a circle:
𝑪 = 𝝅𝒅 (or 𝑪 = 𝟐𝝅𝒓)
29
The distance around a circle is called the
circumference
______________.
It turns out that for any circle the circumference
divided by the diameter is the same number
(approximately 3.1415926 …), which we call pi, and
𝐶
write 𝜋. That is, = 𝜋
𝑑
From this, we get a formula for the circumference
of a circle:
𝑪 = 𝝅𝒅 (or 𝑪 = 𝟐𝝅𝒓)
30
Note: 𝜋 is an ________________ (that is, it
22
can’t be written as a rational number), but is
7
a pretty good approximation.
So, 𝜋 ≈
22
.
7
31
irrational number (that is, it
Note: 𝜋 is an ________________
22
can’t be written as a rational number), but is
7
a pretty good approximation.
So, 𝜋 ≈
22
.
7
32
Ex 13.
Find the circumference of the following circle
22
(use 𝜋 ≈ ).
7
33