UNIT 8Fractions and Ratios

LESSON 8.1Comparing 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 8.2Adding 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

2 ½ 3/2

13/8

4 1/8

37/5

62/5

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)

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

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

QCD CD

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

5 ¼

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

6 – ¼

4 3/5 – 1 4/5

6 5/12 – 3 11/12

answer: 4 1/3

answer: 5 ¾

answer: 2 4/5

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.

40/100 or 4/10 or 2/5 2. Multiple

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 2)

5 How many ½ are in 6? (6 1/2 )

12

How many ¾ are in 5? (5 ¾) 6 2/3

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 5/6) 15