Adding and Multiplying Rational Numbers

Study Notes

Adding and Multiplying Rational Numbers

Rational numbers are a subset of real numbers that can be expressed as the ratio of two integers, with the denominator not equal to zero. Examples include integers, fractions, terminating decimals, and non-terminating decimals with repeating patterns. When dealing with rational numbers, we can perform operations such as addition and multiplication.

Addition of Rational Numbers

Addition of rational numbers involves combining two fractions or rational numbers with the same denominator. To add rational numbers, we simply add the numerators and keep the same denominator. For example, to add 1/2 and 3/4, we get (1 + 3)/4 = 4/4 = 1. We can also add fractions with different denominators by finding a common denominator and then converting the fractions to equivalent fractions with the common denominator. For example, to add 1/3 and 2/4, we find the least common multiple of 3 and 4, which is 12. Then, we convert 1/3 to 4/12 and 2/4 to 3/12. Now, we can add the numerators and keep the common denominator: (4 + 3)/12 = 7/12.

Multiplication of Rational Numbers

Multiplication of rational numbers involves multiplying the numerators and denominators of two fractions. For example, to multiply 1/2 and 3/4, we get (1 × 3)/(2 × 4) = 3/8. Similarly, to multiply two decimal numbers, we multiply the decimal parts and keep the same denominator. For example, to multiply 0.5 and 0.2, we get (0.5 × 0.2)/1 = 0.1.

In summary, rational numbers can be added and multiplied by combining the numerators and keeping the same denominator. This allows us to perform various operations with rational numbers, making them a useful part of mathematics.

Description

Learn how to add and multiply rational numbers, which are a subset of real numbers expressed as the ratio of two integers. Understand the processes of combining fractions or decimals by manipulating numerators and denominators. Explore examples and techniques for adding and multiplying rational numbers.