Fractions in your head, is that even possible? Yes it is. And we will show you how in this little book.
There are 42 lessons in this book. Just do one lesson per day, and you will see magic happen in just 40 days or maybe even sooner.
Fractions is the first topic where the education system first fails the students in math education. Children who for some reason don’t “get” fractions, are forever left behind. School systems do not pay adequate attention to making sure that each and every student is completely proficient in Fractions. Hence your student may have moved on without a total understanding or mastery of fractions as a topic. This is not good at all, as this little misstep dooms the child to forever fall behind in math.
If your student is about to enter sixth grade or is in higher grades but seems to have trouble with math, you must make sure that she/he has mastered fractions. If your student is about to take PSAT or the SAT exams and is unsure about his or her math skills, this book will help her to feel confident and be able to do tricky-looking word problems quickly in her head.
Majority of the SAT problems involve fraction manipulations. Your child has probably been taught other slower methods of doing fractions in school, we will teach him faster methods of doing these types of problems. Time is of the essence for Math part of the SAT, and doing problems the long drawn out, algorithmic way, as taught in schools, just takes too long.
In this book, we give you a time-proven and superior method for giving your student a head-start, an advantage that she or he will retain for the rest of his/her life. She will develop confidence in her ability to understand and do complex looking problems, such as the one given below, quickly and in her head.
The distance from Paoli to Christiana is 24 miles, and (2/3) of this distance is (4/5) of the distance from Christiana to Lancaster. What is the distance to Lancaster?
The book comes in two versions, the teacher version, contains the questions and the answers. This version is for you, the teacher. The student version has only the questions and no answers, and this is for your student. Both are included in this pdf version.
1. You must start this course at lesson one, even if the problems seem very simple to your child.
2. This course requires a teacher or parent to work with the student. Problems must be read to the student. You may need to guide the student, helping as needed with difficult problems, and using the solutions and methods given in the book. The answers are there just for you. (If you feel it necessary to give your student a copy of the problems, this book-without the answers-is available for purchase in eBook form at our website or at Amazon.com.)
3. All of these problems can be done mentally. When you read the problem to the child, he or she may write down the numbers but all calculations should be done mentally.
4. Follow the method that is given at the beginning of each lesson. The solutions given should be explained to the student if she has difficulty.
5. Most students can easily do half a lesson a day. Some longer lessons can be spread over a week. The problems do appear more difficult towards the end of the book, but are not if previous lessons are completed diligently.
6. Subordinate speed to accuracy, but do not neglect speed. The ability to answer these problems quickly results in mastery of the concepts. Always pay attention to how quickly the student can answer the question.
7. The course is suitable for students in 4th-6th grades and above depending on the child’s ability with arithmetic.
8. Older students who are not confident with fractions or weak in algebra will benefit from this course as well. College entrance exams often have problems of this type on the tests. This book is an excellent refresher course for boosting math scores in standardized tests.
9. This course is also excellent for an older adult who may be suffering from cognitive decline or feels that his/her mental calculation skills have weakened.
10. If your student has difficulty with understanding or retaining these problem by just listening to the numbers, please consider buying the Verbal Fractions Student Copy, without the answers. The student can then have his own copy but of course without the answers or the solutions. It is available both in PDF and eBook formats. For pdf version, go to our website.
11. After you have done approximately two-thirds of this book, please consider starting the companion book on Percents.
12. Last two chapters are indeed difficult for many students and are not necessary for proficiency.
See sample file on this page.
Table of Contents
Lesson one-Halves, Thirds, and Fourths
Lesson 2 - Fifth, Sixth, and Seventh
Lesson 3 - Eighths and Ninths
Lesson 4 - Addition, Subtraction
Lesson 5 - Rates
Lesson 6 - Rates to Fractions
Lesson 7 - Reducing Fractions
Lesson 8 - Number Analysis
Lesson 9 - Arithmetic Analysis
Lesson 10 - Relationship of Numbers
Lesson 11 - Fraction as Part of a Number
Lesson 12 - Properties of Numbers
Lesson 13 - Unit Values
Lesson 14 - Numbers to Fractions
Lesson 15 - Fractions to Numbers
Lesson 16 - Reduction to Higher Terms
Lesson 17 - Reduction to Lower Terms
Lesson 18 - Simple and Mixed Fractions
Lesson 19 - Addition of Fractions
Lesson 20 - Subtraction of Fractions
Lesson 21 - Product of Fractions and Numbers
Lesson 22 - Multiplication of Fractions
Lesson 23 - Multiplication of Numbers and Fractions
Lesson 24 - Division of Fractions
Lesson 25 - Proportions and Fractions
Lesson 26 - Fraction Operations
Lesson 27 - Given the Sum of Parts
Lesson 28 - Difference of Parts
Lesson 29 - Increasing or Reducing by a Fraction
Lesson 30 - One Part More or Less Than Another
Lesson 31 - One Part a Number of Times Another
Lesson 32 - One Part a Given Number More Than Another
Lesson 33 - Multiple of Fractions
Lesson 34 - The Proportional Parts
Lesson 35 - Compound Proportions
Lesson 36 - Sharing Problems
Lesson 37 - Bigger and Equal Number
Lesson 38 - Rate Problems
Lesson 39 - Combination Problems
Lesson 40 - Mixed Problems
Lesson 41 - Time Problems
Lesson 42 - Age Problems