Tweet 

PDF download $5.75
Printed copy $10.20, b&w
Math Mammoth Fractions 2 continues the study of fraction topics after Math Mammoth Fractions 1. I sincerely recommend that the student study the Fractions 1 book prior to studying this book, if he has not already done so.
I have made a set of videos to match many of the lessons in this book. You can access them at
http://www.mathmammoth.com/videos/fractions_2.php
This book is meant for fifth or sixth grade, and deals indepth with the following topics:
We start out by simplifying fractions. Since this process is the opposite of making equivalent fractions, studied in Math Mammoth Fractions 1, it should be relatively simple for students to understand. We also use the same visual model, just backwards: This time the pie pieces are joined together instead of split apart.
Next comes multiplying a fraction by a whole number. Since this can be solved by repeated addition, it is not a difficult concept at all.
Multiplying a fraction by a fraction is first explained as taking a certain part of a fraction, in order to teach the concept. After that, students are shown the usual shortcut for the multiplication of fractions.
Then, we find the area of a rectangle with fractional side lengths, and show that the area is the same as it would be found by multiplying the side lengths. Students multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Simplifying before multiplying is a process that is not absolutely necessary for fifth graders. I have included it here because it prepares students for the same process in future algebra studies and because it makes fraction multiplication easier. I have also tried to include explanations of why we are allowed to simplify before multiplying. These explanations are actually proofs. I feel it is a great advantage for students to get used to mathematical reasoning and proof methods well before they start high school geometry.
Students also multiply mixed numbers, and study how multiplication can be seen as resizing or scaling. This means, for example, that the multiplication (2/3) × 18 km can be thought of as finding twothirds of 18 km.
Next, we study division of fractions in special cases. The first one is seeing fractions as divisions; in other words recognizing that 5/3 is the same as 5 ÷ 3. This of course gives us a means of dividing whole numbers and getting fractional answers (for example, 20 ÷ 6 = 3 2/6).
Then students encounter sharing divisions with fractions. For example, if two people share equally 4/5 of a pizza, how much will each person get? This is represented by the division (4/5) ÷ 2 = 2/5. Another case we study is dividing unit fractions by whole numbers (such as (1/2) ÷ 4). We also divide whole numbers by unit fractions, such as 6 ÷ (1/3). Students will solve these thinking how many times the divisor "fits into" the dividend.
After these types of divisions, students learn the “shortcut” for fraction division, that is, the usual rule for dividing any fraction by any fraction (the rule of “invert and multiply”). We also study dividing mixed numbers.
The lesson on introduction to ratios is optional. Ratios will be studied a lot in 6th and 7th grades, especially in connection with proportions. We are laying the groundwork for that.
The last major topic is converting fractions to decimals. Problems accompanied by a small picture of a calculator are meant to be solved with the help of a calculator. Otherwise, a calculator should not be allowed.
The book Math Mammoth Fractions 1 is a precursor to this book. It teaches the concepts of fractions, mixed numbers, equivalent fractions, addition and subtraction of like fractions and of unlike fractions, addition and subtraction of mixed numbers, and comparing fractions.
The two videos below show how division of fractions is taught in the Fractions 2 book. First, we study divisions that can be done "mentally", without the rule. Then, we study reciprocal numbers and the regular rule or shortcut for fraction division.
Your [Fractions 1, Fractions 2] books have been such a help to us! My son has attended a private school since kindergarten, but we recently found out the school hasn't been teaching to gradelevel standards in math. So, while he has wonderful grades, he is behind his peers from public school. He will be attending public school this fall, so we are using your worktexts to get him caught up this summer. I am not much of a "math person", so we are both benefiting from your series!
Thanks so much,
Robbie
July 2010
I began homeschooling my daughters back in May of 2008. Math Mammoth was one of the first websites that I came across on the internet. I had looked over Maria's site. I began targeting my math homeschool after what she provided as far as course knowledge. I began throwing long division and fractions at my oldest daughter. She totally freaked out. She kept telling me that she was not taught many of these subjects. I began teaching her what I knew about these particular subjects. As time moved forward, I realized that I need to check and see where she was at in her math.
I emailed Maria on this. She suggested many websites that I could test my daughter. I found out that she was a year and half behind. I thank God that I found Maria Miller's website because I have purchased the fraction book to help my daughter. She now has fractions down pat. She also has the long division down as well.
Maria takes these problems down to the basics and explains in excellent detail how to solve a fraction or long division math problem. Without the tools that she has given me, I would not have been able to bring my daughter forward and current on her math skills. Maria teaches it as I was taught many many years ago. She provides the tools to help our children succeed in mathematics. I just wish that there were more websites like hers in the other subjects.
I am currently using the Geometry module for my youngest daughter. She is enjoying that module immensely. It explains it perfectly for her.
Thank Maria for having an incredibly useful website and books. I thank the heavens above for someone like you.
Sincerely,
Amy K. Burt
November 30, 2008
I recently bought two of your books [Fractions 1 and 2]. I am a public school 8th grade math teacher. I use your materials to go back and fill in the "gaps" for children who have missed important concepts in their past education. Your products have worked wonders!!!!! I can't get over how complete and rigorous they are.
I plan to homeschool my daughter when she is old enough and I can't wait to use these materials with her...
thanks!!!!!
Jill Gaspard
The workbooks are WONDERFUL and I love how fractions are explained so simply and attractively, my 13 yo daughter is sure to understand fractions now. Thank you for a great teaching product!
Shannon
The students and myself liked the pictures and the step by step breakdown in all of the lessons.
Tia Kline
These books fill the gap between using manipulatives (concrete level) and abstract (symbolic) level. Too often students are expected to make that leap from the concrete level without spending time at the representational level.
Paula Listzwan
I like the clear explanations. The fractions 2 book had the best explanation of why dividing by a fraction works like it does of any I found anywhere.
Jennifer Wheelock
I am amazed at how effective these lessons are. I think what makes them interesting to my student is that the problems are often interesting to solve, with an interesting word problem or just the mathematical reasoning interests her in a way that I've never seen with her.
Cyndi Kane
Better Yet  Bundle Deals!Blue Series  $110 (download) or $115 (CD)
Blue Series for grades 13  $45 (download)
Blue Series for grades 46  $69 (download)
Light Blue Series  $150 (download) or $155 (CD)
Light Blue Series for grades 13  $75 (download)
Light Blue Series for grades 46  $75 (download)
Golden/Green Series  $65 (download) or $70 (CD)
All Inclusive  $211 (download) or $216 (CD)
"Everything" Bundle  $276 (download only)
Learn more about these Math Mammoth bundles!
*BONUS*: Buy any bundle listed above, and get the fully upgraded SoftPak software with more features and options for FREE (includes 4 math, 1 language arts, 2 testing programs).
How and where to order
You can buy Math Mammoth books at:
 Kagi store  all of the downloads and CDs. I maintain several order pages at Kagi:
 The Blue Series
 Golden and Green Series
 Light Blue Series, US version
 Light Blue Series, South African version
 Review workbooks by grade levels
 Make It Real Learning workbooks
 discounted bundles (CDs and downloads)
Kagi accepts all major credit cards, Paypal (USD), checks, cash, money orders, purchase orders, wire transfers, TrialPay, and even cash. Read more about the payment methods here. Please see Kagi Shopper Help for any other questions about the ordering process.
After completing the order at Kagi, you will see the download links on the receipt page. You will also receive an email with download links for each book you bought, or for a zip file for the packages. You click on the links and download the books to your computer's hard drive.
In case of any problems with the download, you can always email me, and I can email the books to you directly. My contact info will be in the email you receive.
 CurrClick.com carries all Blue, Golden, and Light Blue series books as downloads. They accept credit cards and Paypal. You will be able to download the products immediately upon the purchase, and also return to your account at CurrClick to redownload.
 Lulu offers printed copies for the Blue, Golden, and Light Blue series books.
 Rainbow Resource carries printed copies for the Light Blue series books, plus Light Blue CDs. You can also find links to Rainbow Resource on the individual product pages on this site.
By purchasing any of the books, permission IS granted for the teacher (or parent) to reproduce this material to be used with his/her students in a teaching situation; not for commercial resale. However, you are not permitted to share the material with another teacher.
In other words, you are permitted to make copies for the students/children you are teaching, but not for other teachers' usage.
Math Mammoth books are PDF files. You will need Adobe Reader to view them, including if you use a Mac or Linux. You can try other PDF viewers, but they seem to either omit or mess up some of the images.
Maria's Math NewsThis is my newsletter that comes out about once or twice a month. Peek at the previous volumes here. You will receive: An initial email to download a GIFT of over 350 free worksheets and sample pages from my books; Maria's Math News: my newsletter filled with math teaching resources, news, downloads, humor, and giveaways. The content is equally good for all of us who teach math. 
Math Mammoth TourConfused about the different options? Take a 7day virtual email tour around Math Mammoth! You'll receive: An initial email to download your GIFT of over 350 free worksheets and sample pages from my books; 6 other emails on 6 subsequent days that describe the different series of Math Mammoth products, answering the most commonly asked questions, including "What is the difference between all these differentcolored series?"This way, you'll have time to digest the information over one week, plus an opportunity to ask me personally which book would be right for your child or students. Note: You will FIRST get an email that asks you to confirm your email address. If you cannot find this confirmation email, please check your SPAM/JUNK folder. 
"Mini" Math Teaching CourseThis is a little "virtual" email course. You will receive: An initial email to download your GIFT of over 350 free worksheets and sample pages from my books; 7 articles on important topics on mathematics education, including: multiplication tables, fractions, how to help a student who is behind, and the value of mistakes; 1 email about Math Mammoth books.Note: You will FIRST get an email that asks you to confirm your email address. If you cannot find this confirmation email, please check your SPAM/JUNK folder. 
Search MathMammoth.com: 
© 20062014 MathMammoth.com