Download File - Mr. Hill`s Class

UNIT 8
Fractions and Ratios
LESSON 8.1
Comparing Fractions
Defining Fractions


Denominator – represents the number of equal
sized pieces something is divided into (bottom
number)
Numerator – indicates the number of those equal
pieces being considered (top number)
Warm-Up (use reference page 399 to help)

Are the following
fractions closer to 0,
½ , 1, 1 ½ , or 2

2/10

6/10

3/10

9/8

15/8

5/3

9/5

8/5
Renaming Fractions as Equivalent
Fractions

Division Rule: Divide both the numerator and
denominator by the same number yields an
equivalent fraction.
Using your fraction sticks

Image from
scimathmn.org
Comparing Fractions

Quick Common Denominator (QCD) – the
product of the denominators or two or more
fractions. (Quick way to get a common
denominator, not the lowest common denominator)
Renaming Fractions as Equivalent
Fractions


Equivalent means having the same solution set
(They are EQUAL to each other)
Multiplication Rule: Multiply both the numerator
and denominator by the same number yields an
equivalent fraction.
LESSON 8.2
Adding Mixed Numbers
Improper Fractions

Improper Fraction: when numerator is greater than
or equal to the denominator

examples:

5/3

39/31
Warm-Up: Rename as a whole, mixed,
or improper fraction

3/3

4 1/8

2½

37/5

3/2

62/5

13/8

11 ¼
Adding fractions with the same
denominator

When the denominators are the same, add the
numerators and keep the common denominator.
What are mixed numbers?

A whole number with a fraction

Written:

Actually:
Adding Mixed Number with the same
denominator




Everyday Math Way
1. Add the whole
numbers
2. Add the fractions
3. Rename in simplest
form
Let’s Practice Together

Problems will be reviewed on the white board
Adding mixed numbers with unlike
denominators

1. find the common denominator for each fraction

2. use the adding mixed number technique


3. simplify
Let’s practice finding the common denominator
Let’s Practice Together

Problems will be reviewed on the white board
LESSON 8.3
Subtracting Mixed Numbers
Warm-Up (Find the QCD for the left
and CD for the right)
QCD








1/2 and 1/3
answer: 6
5/6 and 7/9
answer: 54
4/5 and 7/10
answer: 50
7/10 and 19/20
answer 200
CD








1/2 and 1/3
answer: 6
5/6 and 7/9
answer: 18
4/5 and 7/10
answer: 10
7/10 and 19/20
answer 20
Warm Up- (rename the fractions to
have like denominators)




1/2 and 1/3
answer: 3/6 & 2/6
5/6 and 7/9
answer:15/18 & 14/18

4/5 and 7/10

answer: 8/10 & 7/10
7/10 and 19/20

answer:14/20 & 19/20

Subtracting Mixed Numbers with the
same denominator




1. Rename (if necessary) the fraction on the top
part of the equation larger than the bottom part.
Example:
2. Subtract the fractions
3. Subtract the whole numbers
4. Answer in simplest form : Answer: 1 2/3
Let’s practice renaming fractions to
make the fraction part larger

5¼

answer: 4 5/4
6 2/5

answer: 5 7/5

Let’s Practice Subtracting Mixed Numbers (Complete
the following in your binder)

8 – 3 2/3

answer: 4 1/3

6–¼

answer: 5 ¾

4 3/5 – 1 4/5

answer: 2 4/5

6 5/12 – 3 11/12

answer: 2 ½
Complete Math Journal pg. 254








Answers:
1. 2 ½
2. 2 4/5
3. 5 ½
4. 4
5. 3
6. 23
7. 7






8. 7 2/3
9. 2 2/5
10. 3 ½
11. ¾
12. 1 2/3
13. 4 3/5
Subtracting fractions with unlike
denominators


1. Find the common denominator or quick common
denominator
2. Rename (if necessary) the fraction on the top part of
the equation larger than the bottom part.


3. Subtract the fractions

4. Subtract the whole numbers

5.Answer in simplest form
LESSON 8.5 – 8.8
Fractions of Fractions
Using paper modeling (What is ½ of
½ ?)

Using a standard sheet of paper fold it in half
vertically (the longer dimension)
½ of ½ is ¼

Then fold it in half horizontally (the shorter
dimension)
Lets try some more using paper
modeling

What is 2/3 of 1/2
1st fold the paper in half (vertically) (shade 1 of the
two)
 Then in thirds (horizontally) (shade the 2 of the thirds)
 Write and X on the parts shaded twice
 Your answer should be 2/6 or 1/3

Continued

What is 3/4 of 2/3
1st fold your paper into thirds (vertically) (shade two of
the thirds)
 Then fold your paper into fourths (horizontally) (shade
in three of the fourths)
 Write an X in the parts shaded twice
 Your answer should be 6/12 or ½


Practice with pg. 261 in your Math Journal
Multiplication Algorithm


¾ of ¼ =
Multiplication of Whole Numbers

Multiplication of Mixed Numbers

Multiplication of Mixed Numbers

Partial Products Method





1. Multiply the whole #’s
2. Multiply the 1st fraction and the 2nd whole
number
3. Multiply the 1st whole # and the 2nd fraction
4. Multiply the 1st fraction and the 2nd fraction
5. Add the products
LESSON 8.9
Finding a Percent of a Number
Percent (%)





Definition – Per hundred, for each hundred, or out
of a hundred. 1% = 1/100 = .01
Examples:
20% = 20/100 = .20
60% = 60/100 = .60
33% = 33/100 = .33
Let’s Practice


What is 40% of 320?
1. Make 40% into a fraction.


2. Multiple


40/100 or 4/10 or 2/5
2/5 * 320/1
3. Simplify for your final answer
Discounts


Definition – The amount by which a price of an
item is reduced in sale, usually given as a fraction
or percent of the original price or as a percent off.
Example: An item that originally cost $10 at 10%
off is now $9.00.

Remember – the discount is the amount to be
subtracted from the original whole.
Let’s Practice





Hill’s Sporting Goods was selling all hockey
equipment at a 25% discount. How much does each
item cost after the discount?
Hockey Stick - $150
Helmet - $120
Philadelphia Flyers Jersey - $170
Goalie Leg Pads - $450
Division (Standard Algorithm)


How many _____ are in _____?
Ex: How many 2’s are in 10? (10

5
How many ½ are in 6? (6



1/2 )
12
How many ¾ are in 5? (5

2)
6 2/3
¾)
Division (Common Denominators
Method)

How many 4/5 are in 4? ( 4


4/5)
5
How many 5/6 are in 1/18? ( 1/18

15
5/6)