2.3 Solving problems with rational numbers in fraction form

What is a rational number? A rational number is a real number that can be expressed in the form of fraction of two integers, $\frac{a}{b}$, where the denominator (b) does not equal to zero.

A rational number can also be represented in decimal form. The decimal form of rational number always ends with a finite number of digits or repeats the same sequence of number again and again. In other words, a finite number of decimals and a repeating sequence of decimals are both indicators of rational numbers.

The following table shows a few examples of rational numbers.

 Number Fraction form Rational or Irrational (R/IR) 3 $\frac{3}{1}$ R 0.2 $\frac{1}{4}$ R 7.5 $\frac{15}{2}$ R ?1.4 -1$\frac{3}{1}$ R $\pi$ (3.141592653…) N/A IR

A number that is not rational is called an irrational number. The difference between rational numbers and irrational numbers is that irrational numbers cannot be expressed as a ratio of two integers; nor have a finite number of decimals or a repeating sequence of decimals.

To begin this chapter, we will first understand the nature of rational numbers and learn how to compare and order rational numbers in both decimal and fraction forms. One way to compare rational numbers is using equivalent fractions. When two rational numbers are in fraction form, we can compare them with their numerators if they are expressed as equivalent fractions with a common denominator. Another way to compare rational numbers is to convert the fractions into decimal numbers.

In the second part of the chapter, we will explore the operations of rational numbers. Adding, subtracting, multiplying and dividing rational numbers in decimal form will be covered. Then, we will also talk about how to solve problems by adding, subtracting, multiplying and dividing rational numbers in fraction form.

Solving problems with rational numbers in fraction form

Similar to the previous section, we will practice adding, subtracting, multiplying, and dividing rational numbers. Rational numbers can be expressed in two forms: fraction form and decimal form. This time, we will deal with rational numbers in fraction form.