# Chapter 2: Using Rational Numbers

## Introduction

Here you will review rational numbers. You will start by reviewing decimals and decimal operations. Next, you will review fractions and mixed numbers. Then, you will learn about integers and how to use integer equations to help solve real-world problems. Finally, you will learn how to represent the same rational number in multiple ways, and how to compare and order rational numbers written in different representations.

## Chapter Outline

- 2.1. Add and Subtract Decimals
- 2.2. Estimate Decimal Sums and Differences Using Front-End Estimation
- 2.3. Multiply and Divide Decimals with and without Rounding
- 2.4. Estimate Decimal Products and Quotients Using Leading Digits
- 2.5. Identify and Apply Number Properties in Decimal Operations
- 2.6. Add and Subtract Fractions and Mixed Numbers
- 2.7. Estimate Sums and Differences of Fractions and Mixed Numbers
- 2.8. Multiply and Divide Fractions and Mixed Numbers
- 2.9. Estimate Products and Quotients of Fractions and Mixed Numbers
- 2.10. Identify and Apply Number Properties in Fraction Operations
- 2.11. Add and Subtract Integers
- 2.12. Multiply and Divide Integers
- 2.13. Identify and Apply Number Properties in Integer Operations
- 2.14. Use Simple Integer Equations to Solve Real-World Problems
- 2.15. Find Equivalent Forms of Rational Numbers
- 2.16. Compare and Order Rational Numbers
- 2.17. Solve Real-World Problems by Using Rational Numbers and Simple Equations

### Chapter Summary

## Summary

You started by learning all about decimals. You learned how to use place value to help you to add and subtract numbers with decimals accurately. You learned that sometimes it is appropriate to just estimate an answer, and with decimals you can use front-end estimation. You also learned how to multiply and divide decimals, and round answers appropriately.

Next, you learned all about fractions. You saw both regular fractions and mixed numbers. You learned that to add or subtract fractions you need a common denominator, and that a dividing fractions problem can be turned into a multiplying fractions problem. Just like with decimals, it is sometimes appropriate to estimate when dealing with fractions, so it is important to have a sense for where a fraction is in relation to whole numbers.

Then, you learned about integers. Integers include both positive and negative whole numbers as well as the number 0. When adding and subtracting integers, it is helpful to think about losses and gains. When multiplying and dividing integers, you learned the rule that "when signs are the same, the answer is positive; when signs are different, the answer is negative."

Finally, you learned that a rational number is a number that can be written as a ratio of two other numbers (a fraction). You learned how to represent rational numbers as fractions, decimals, and percents. You learned how to compare rational numbers given in different representations by first converting them all to the same representation.