Chapter 9 Overview

Chapter 9 is a focus on adding and subtracting fractions. Here is a link from themathpage.com that explains most of the concepts we will be covering in Chapter 9.

8.5 Fractions, Decimals, and Percents (p.191-193)

I. Types of Decimals
A. Terminating Decimal: A fraction in decimal form that has zero has a remainder when you divide using long division.
ex: 1/2 = 0.5 = 0.50000000 (if you would try to keep dividing you would only get 00000... because there is nothing left to divide out)
B. Repeating Decimal A decimal that has a pattern of repeating numbers (or one number)- shown as a remainder when dividing--> use a horizontal line above repeating digits (called a vinculum)
ex: 1/9 = 0.1.... = 0.1
4/11 = 0.363636363636 = 0.36
**Try turning some of these fractions into decimal to find repeating patterns:
2/3
7/12
1/7
1/81

II. Turning common fractions into decimals
A. Divide the top number by the bottom number
Ex. 4/5 = 4÷ 5 = 0.8

III. Decimals into fractions
A. Decimals can be turned into percentages by moving the decimal point two places to the right (the the hundredths place)- this shows the value out of 100 equal parts (per cent=>per 100) making up the whole.
Ex: 1/4 = 1 ÷ 4 = 0.25 = 25%
Ex2: 1/3 = 1 ÷ 3 = 0.33...repeating = 33.3% (there should be a line over the 3 in the tenths place.

Try this activity from mathgoodies.com to see what you know
Here is an explanation from mathgoodies that might help too.

8.3 Compare and Order Fractions (<,>,or =)

I. Find a common denominator:
-when all fractions have a common denominator you can equally compare the parts of the whole because they are all the same size.

II. Tips
-The bigger the denominator (bottom number) the smaller the pieces of the whole
-The smaller the denominator (bottom number) the larger the pieces of the whole
-If the numerator and denominator are close together, you are more likely to have a larger value
-if the numerator and denominator are not close in value, you are likely to have a smaller part of the whole

III. Reminder
<> is greater than
= is equal to

Check out this video from mathplayground.com that explains how to compare and order fractions.

8.2 Mixed Numbers and Fractions

I. Improper Fraction: a fraction whose numerator is larger than the denominator
ex: 11/5


II. Mixed Number: A fraction with a value larger than a whole that is represented as a whole number in combination with a fraction


III. Rewrite improper fractions as whole or mixed number
ex:7/4 is equal to 1 wholes and 3/4 = 1 3/4 because it takes 4/4 to make one whole and you have 3 more fractional parts left.

IV. Convert mixed numbers to fractions: multiply the denominator by the whole number and then add the numerator.
3 x 8 = 24+1 = 25 --> the new numerator becomes 25

You are converting the whole parts into fractional parts. In this case, there are 3 fractional parts in every whole. So the 8 wholes make 24 parts, plus the one from the beginning is 25. The denominator will stay the same because the number of parts that make up the whole is not changing.

Print a certificate showing what you know after trying a few problems from visualfractions.com

8.1 Simplest Form (p.182-185)

I. Simplest form: when the numerator and denominator of a fraction only share “1” as a factor
II. Use division to reduce the terms in a fraction
-Divide the the numerator and denominator by a shared factor
-A fraction is reduced (in the smallest terms possible) when there are no shared factors other than one between the numerator and denominator)
Example: in the case of 6/8 , they share 2 as a factor. When you divide both 6 and 8 by 2 the fraction is reduced to 3/4 = simplest form because 3 and 4 do not share any factors other than 1.
6 ...3
- = -
8 ...4

FRACTION REVIEW:
Fraction: a number representing part of a whole: a ratio between two numbers --> 6 out of 8 = 6/8
numerator: the dividend – amount you start with;
denominator: divisor of a fraction – how many pieces the whole is divided into.

8.1 Equivalent Fractions (p.182-185)

I. Equivalent fractions: fraction showing the same amount of the whole that are equal in value and show the same part of the whole. They show the ratio of parts.

II. Common Factors: use common factors to change the numerator and denominator in the same way to find equivalent fractions and put fractions in simplest form.

Check out this helpful info. from themathpage.com for answers to common equivalent fractions questions.
Use this tool from Harcourt for finding factors to make equivalent fractions.
Try this game from LearningPlanet.com. It gets faster and faster every round :).

7.5 Prob. Solving: Make an Organized List (p.174-175)

When solving story problems lists can help you:

• recognize patterns
• find common multiples or factors
• solve multistep problems