Download Chapter 4

SECTION 4.1
How to find the GCF You Tube Video
Venn Diagram of factors:
18
24
Factor tree:
18
24
Ladder method:
1. Divide out the numbers they have in common.
18
24
GCF=
100
40
GCF=
Find the GCF.
1) 18
8
2) 36 64
3)
18
45
36
Fractions You Tube Video
2 thirds
2 out of 3
2 over 3
2 divided by 3
2
3
1
4
2
4
3
4
4
4
Accurately shade the following:
1
2
Continuous quantities- measured objects
2
Show me 5 of the box.
3
4
5
6
5
8
Discrete quantities- countable objects
2
Show me 5 of a 10 person team.
The "Sharing Equally" view: Jim has 3 candy bars to share equally among his 4 friends. How much does
each friend get?
3
3
÷
4
=
4
An American ruler is divided into inch, 1/2 inch, 1/4 inch, 1/8 inch, and 1/16 inch increments. Represent 3/4 of
an inch for the following 1 inch long block below.
Represent 3/8 of an inch for the following 1 inch long block below.
A ton is equal to 2,000 lb. What fractional part of a ton is 250 lb?
If Tommy has 4 pizzas and 7 friends, how much of a whole pizza will each friend get?
Of the 88 keys on a piano 36 are black. What fraction of the keys are not black?
You answered 43 questions correctly on an exam of 50 questions. What fraction of the questions did you
answer correctly?
Accurately shade the following: You Tube Video
1
2
2
4
3
6
We call the previous fractions__________________________________________________.
1
2
1
2
1
2
1
3
1
3
1
3
4
8
Practice problems:
1) Find the matching equivalent fractions.
𝑎)
2
=
5 10
𝑏)
2) Find three equivalent fractions for
3) Find three equivalent fractions for
6 36
=
7
𝑐)
10
=
35 7
3
.
8
24
.
36
4) Circle the fractions that are equivalent to
2
5
.
6
12
18
40
14
35
7) Costco slices it's pizza in to 6 slices. Each slice is to large for a normal person to consume.
a) What fractional size is each slice?
b) If you purchased a 6 slice pizza, then each slice is _______. If you ask for a knife and start slicing the pizza
again into equal size slices, then name two more fractional size slices you could create with your plastic knife.
1) find
15
8
inches,
1
inches,
4
Equivalent fractions
4
16
inches,
20
16
inches,
7
2
inches
Reducing fractions You Tube Video
24
60
Try:
1)
25
75
2)
151
6
3)
36
16
24 x 2
60 x3
24 x 2
60 x3
=
24 x 2
2
2
and
are called equivalent fractions.
is the reduced form
3
5x
5x
60 x
SECTION 4.2
Multiplying Fractions You Tube Video
MULTIPLYING FRACTIONS
1. Reduce (cancel top to bottom)
34
 
86
2. Multiply
3
2
5
32  5 
 
15  12 
3
x

8x 3 6
𝟏 𝟏𝟒

Multiplying with mixed numbers 𝟑 ( )
𝟕 𝟑
3
1. Convert all Mixed numbers to improper fractions
2. Reduce (cancel top to bottom)
∙
3. Multiply
1 7
3
7 2
 1
3 1 
 5

1 7  3  1 22


7
7
7
Multiplying Fractions You Tube Video
Fractions as part of a whole:
You will need two colors for the following. Draw a picture of the answer:
1 of
2
5
6
Jim mowed 1/3 of the lawn. If the lawn is 300 square feet. How many square feet did Jim mow?
If
2
of the 30 students in this class love math, then how many students in this class love math.
3
𝟏
What does 𝟐 ∙ 𝟓 really mean?
Fractions in repeated addition:
𝟏
𝟐∙𝟒
𝟐
𝟔∙𝟑
If Jenny is left with 7 pizza boxes, each with 1/3 of a pizza in them, then how many whole pizzas does Jenny
have?
𝟏
What does 𝟓 ∙ 𝟐 really mean?
SECTION 4.3
Dividing Fractions You Tube Video
1. Flip the divisor (the second number) and change the sign to multiply.
3 6

8 4
2. Multiply the fractions as in MULTIPLYING FRACTIONS.
a)
14
5
÷
7
25
b) −
𝟏
26
9
5
6
c)
3
12
2
÷ (− )
3
𝟑
Dividing with mixed numbers 𝟑 ÷ ( )
𝟕
𝟏𝟒
1. Convert all Mixed numbers to improper fractions
2. Flip the divisor (the second number) and change the sign to multiply.
2. Reduce (cancel top to bottom)
∙
3. Multiply
a)
4
2
1
3
3
b) 1
2
6
3
÷
Dividing Fractions - Word problems You Tube Video
3
6
=
2
2 groups of 3
Divided into groups of 3
4
 1
=
2
Divided into groups of
8
1
2
8 groups of
1
2
2
1
=
3
Divided into groups of
1
3
Use pictures for the following, then use the algorithm.
𝟏
𝟏÷𝟑
𝟏
𝟐÷𝟒
6
3
4
6
6 groups
1
3
Now perform the operations::
a) It takes
2
of a pizza to feed one person. How many people will 4 pizzas feed?
3
b) It takes
2
pounds of mud to fill a belly. How many bellies can 10 pounds of mud fill?
5
c) A highway is 8 𝑚𝑖𝑙𝑒𝑠 𝑙𝑜𝑛𝑔. 𝐼𝑓 𝑦𝑜𝑢 𝑤𝑎𝑙𝑘
3
4
..
d) Jim has 2/3 times as many cookies as Bob. If Jim has 4 cookies, how many cookies does Bob have?
SECTION 4.4
LCM
Least Common Multiple You Tube Video
superfluous buns
LCM is the smallest multiple that two or more numbers share.
1
2
3
4
5
6
8
The LCM is____ here
12
Warm up:
Grocery List 1
Grocery List 2
LCM:
Finding the LCM using a factor tree:
60
168
Ladder Method:
60
168
LCM= All of the outside numbers =
Find the LCM.
18
8
36
64
18
45
8
9
7
3 apples plus 5 apples is 8 apples.
3
+ 5
You Tube Video
= 8
1 fifth plus 2 fifths is 3 fifths
2
1
+
=
5
5
5
7
3 7

5 5
a)
b)
=
5 3

2 2
d) 6  3
c) 4  8
7
15 15
4 apples plus 2 pears is not 6 applars
4
4
7
-
+

2
7
3 fifths plus 2 eights is not 5 fieghts
3
5
6?
2
8

5
?

Adding fractions you need a common denominator ( a like term)
ADDING AND SUBTRACTING FRACTIONS WITH DIFFERENT DENOMINATORS


5
6
+
2
3
a. Find the LCD
6
LCD=
3
=
.
b.
Convert the denominators into the LCD by multiplying each fraction by 1 as follow.(enlarge the fractions)
5
2
5
 •
 
 •
6
3
6
or
+
2
•
3
+
c. Reduce the answer if possible.

Fractions - Adding and subtracting word problems You Tube Video
𝟏
After a party there are 3 cartons of pizza left. In one carton there is of a pizza left. In the second
𝟏
𝟓
𝟑
carton there is 𝟔 of a pizza left. In the third carton there is 𝟏𝟐 of a pizza left. If we put all of the pizza in
one box, then what fraction of a whole pizza would all of the pieces add up to?
Jimbo decides to make a coat for his pet monkey. He buys 1 linear yard of fabric. He cuts
𝟏
𝟏
𝟏
𝟔
of a yard
for each sleeve. He then cuts 𝟒 of a yard for the front of the coat and 𝟒 of a yard for the rear of the coat.
How much fabric does he have left after all 4 cuts?
1 linear yard
SECTION 4.5
Mixed Numbers You Tube Video
Improper to mixed
7
5
57
divide
Mixed to improper
2
1
5
2
1
5
5 1  2
5
Mixed Numbers - Why?
Mixed
Number
Fraction
1/4
3/4
5/4
7/4
15/4
What is 11/4 in mixed form? Why do we divide?
Fraction
1
1
3
1
2
3
2
1
3
2
2
3
What is 4
1
3
in improper form? Why do we multiply the 4 by the 3?
Improper
Fraction
Expanded
Form
SECTION 4.6
Adding and subtracting Mixed numbers You Tube Video
3 apples plus 5 apples is 8 apples
3
+ 5
2
5
4
3
5
1
Borrowing
1
3
2
3
3
5
3
8
3
3
4
5
Special
2  4
 3   1 
3  5
1 fifth plus 2 fifths is ______fifths
1
5
= 8
2
5
1
3
5
7
1
3
+
2
5
=
2
3
4
3
15
5
4
5
SECTION 4.7
Give Every Mom Or Dad Aspirin Or Sleep You Tube Video
Order of operations
1. Symbols of Grouping. (
2.
3.
4.
), [
], {
}, √
,
Exponents
Multiplication Or Division from LEFT TO RIGHT.
Addition Or Subtraction from LEFT TO RIGHT.
1
1 5 3
  
3 92
2
2
Try:
 1
2 
 2
Special (Trick!)
3
4 6 5 
   
3 5  12 
1 1

5 7
1 1

5 7
5 4 3 
  
3  5 10 
2
7
9
5

27