Math Mammoth Rational Numbers

77 pages
(includes answers)

Sample pages (PDF)
Contents
Rational Numbers
Multiply & Divide Rational Numbers 1
Equations with Fractions

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Este libro en español

In Math Mammoth Rational Numbers we study rational numbers, which are numbers that can be written as a ratio of two integers. All fractions and whole numbers are rational numbers, and so are percents and decimals (except non-ending non-repeating decimals). Obviously, students already know a lot about rational numbers and how to calculate with them, from all their schooling thus far. Our focus in this book is to extend that knowledge to negative fractions and negative decimals. Then in 8th grade and in high school, students will learn about irrational numbers, including square roots and other roots, and how to do calculations with them.

The first lesson presents the definition of a rational number as a ratio of two integers, and students practice plotting rational numbers on number lines and comparing them. In the next lesson, they learn about repeating decimals and how all rational numbers are either terminating or repeating decimals when written in their decimal form.

Then we turn our attention to calculations. Adding, subtracting, multiplying and dividing with negative and positive rational numbers happens the same way as doing those calculations with integers.

Students first practice adding and subtracting rational numbers, with an emphasis on adding and subtracting negative fractions and decimals. The next two lessons are about multiplying and dividing rational numbers. The first of the two focuses on basic multiplication and division with negative fractions and decimals. The second of the two presents complex fractions (fractions that contain another fraction, either in the numerator, in the denominator, or in both), and problems that mix decimals, fractions, and percents.

Then students continue on to practice more complex calculations with rational numbers, dealing with real-life contexts for products and quotients of rational numbers, and learning the importance of pre-estimating what a reasonable answer would be.

The book concludes with two lessons on solving simple equations that involve fractions and decimals.

The PDF version of this book can be filled in on a computer, phone, or tablet, using the annotation tools found in many PDF apps. See more.

I have made a set of videos to match the lessons of this book. You can access the videos here (free).