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Chapter Analysis
Beginner14 pages • EnglishQuick Summary
The chapter on Rational Numbers introduces the concept of numbers that can be expressed in the form of p/q, where p and q are integers and q is not zero. It explores the properties of rational numbers such as closure, commutativity, associativity, and the existence of additive and multiplicative identities. The text also delves into operations on rational numbers, demonstrating how they behave under addition, subtraction, multiplication, and division, including discussions on common misconceptions.
Key Topics
- •Closure properties of rational numbers
- •Commutative properties
- •Associative properties
- •Additive and multiplicative identities
- •Operation of addition on rational numbers
- •Operation of subtraction on rational numbers
- •Operation of multiplication on rational numbers
- •Division in rational numbers and its conditions
Learning Objectives
- ✓Understand the concept of rational numbers.
- ✓Explore the properties of rational numbers under various mathematical operations.
- ✓Learn how to express numbers in the form of p/q.
- ✓Identify and apply the commutative, associative, and distributive properties.
- ✓Understand the importance of zero and one in the operations involving rational numbers.
- ✓Perform addition, subtraction, multiplication, and division on rational numbers confidently.
Questions in Chapter
Name the property under multiplication used in each of the following.
Page 12
Tell what property allows you to compute (1/3) × (6/4) × (3/1)
Page 12
The product of two rational numbers is always a ___.
Page 12
Additional Practice Questions
What is the sum of (-3/4) and (5/6)?
easyAnswer: To find the sum, convert to a common denominator. The LCM of 4 and 6 is 12. Convert -3/4 to -9/12 and 5/6 to 10/12. Adding them gives (10/12 - 9/12) = 1/12.
Prove that the product of two negative rational numbers is positive.
mediumAnswer: The product of two negative rational numbers is positive because when two negative numbers are multiplied, the negatives cancel out, resulting in a positive product (e.g., (-a/b) × (-c/d) = (a/b) × (c/d)).
Is the division of two rational numbers always a rational number?
mediumAnswer: Division of two rational numbers is a rational number provided the divisor is not zero. For example, (a/b) ÷ (c/d) = (a/b) × (d/c) is a rational number unless c/d = 0.
Is zero a rational number? Justify your answer.
easyAnswer: Yes, zero is a rational number because it can be expressed in the form of 0/q where q is any non-zero integer.
Calculate the difference between 7/8 and 1/3.
easyAnswer: To calculate the difference, find a common denominator. The LCM of 8 and 3 is 24. Convert 7/8 to 21/24 and 1/3 to 8/24. Subtract to get (21/24 - 8/24) = 13/24.