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RS Aggarwal Solutions

RS Aggarwal Solutions Class 8 Chapter-1 Rational Numbers (Ex 1A) Exercise 1.1

RS Aggarwal Solutions Class 8 Chapter-1 Rational Numbers (Ex 1A) Exercise 1.1

Q: 2. What is the correct method to find the multiplicative inverse of a rational number like -13/19, as seen in RS Aggarwal Class 8 Ex 1A?

To find the multiplicative inverse (also known as the reciprocal) of a rational number, you must interchange its numerator and denominator. The sign of the number does not change. For the example -13/19, its multiplicative inverse is 19/-13, which is conventionally written as -19/13. A key property to remember is that the product of any rational number and its multiplicative inverse is always 1.

Q: 4. What is the correct procedure to express a rational number like 33/-55 in its standard form as required in the solutions?

To write a rational number in its standard form, two conditions must be met: the denominator must be positive, and the numerator and denominator must be co-prime (their highest common factor is 1). For 33/-55, the steps are:First, make the denominator positive by multiplying the numerator and denominator by -1: (33 × -1) / (-55 × -1) = -33/55.Next, simplify the fraction by dividing the numerator and denominator by their highest common factor (HCF), which is 11.This gives (-33 ÷ 11) / (55 ÷ 11) = -3/5.Thus, the standard form of 33/-55 is -3/5.

Q: 6. How does using properties like distributivity simplify complex calculations in Chapter 1?

Properties like the distributive property are crucial for simplifying expressions by rearranging and grouping terms. For example, to solve (7/5 × -3/12) + (7/5 × 5/12), instead of multiplying separately, you can use distributivity:Factor out the common term, 7/5: 7/5 × (-3/12 + 5/12).First, solve the operation inside the brackets: -3/12 + 5/12 = 2/12.The expression becomes a much simpler multiplication: 7/5 × 2/12 = 14/60, which simplifies to 7/30.This method reduces calculation steps and minimizes the chances of error.

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RS Aggarwal Solutions Class 8 Chapter-1 Rational Numbers

RS Aggarwal Class 8 Chapter 1 Exercise 1A Solution can be referred by the students to understand the concept of this given topic from the beginning. Experts have prepared the full-length exercise of RS Aggarwal Solutions Class 8 Math ex 1A with utmost precision for the students. It provides a complete exposure to the basic concepts of Rational Numbers as well as other properties of the same in this chapter. By practicing the RS Aggarwal Math Class 8 Exercise 1A, students will gain confidence in solving the Mathematical problem in their examination. Students need to follow the guidelines and syllabus while solving the questions present in the RS Aggarwal textbook. So, students willing to secure good marks in the examination need to follow and practice RS Aggarwal solutions Class 8 Maths ex 1 without failing. You can also download NCERT Solution for Class 8 Math to help you to revise the complete syllabus and score more marks in your examinations.

State the Concepts Discussed in RS Aggarwal Solutions Class 8 Chapter 1 Exercise 1A

RS Aggarwal Class 8 Maths Chapter 1 exercise 1A, deals with the fundamental concepts related to rational numbers. We can say that the chapter focuses on brushing up of the properties that the students have learnt in the exercise. Some of the concepts that are given priority in this RS Aggarwal Maths Class 8 exercise 1A includes the following.

Rational numbers and their properties.
Representation of rational numbers on the real line.
The standard form of the rational number.
Addition of rational numbers.
Subtraction of rational numbers.
Division of rational numbers.
Multiplication of rational numbers.
Word problems related to rational numbers.

At the end of this RS Aggarwal Maths Class 8 exercise 1A solution, objective type questions are provided for students to see how well they have grasped the concepts.

Properties of Rational Numbers:

When we add, multiply or subtract two Rational Numbers, the result is always Rational Number
When we multiply or divide the numerator and denominator of a Rational Number, the result is always the number remaining the same
If we add the Rational Number and zero, the answer is always the same number.

The standard form of a Rational Number: A Rational Number is a real number generally expressed in p/q form where the denominator, i.e., is not equal to zero. Anything divided by zero is infinite and indefinable. All the other real numbers, which can not be expressed in this standard form, are irRational Numbers.

Multiplicative Inverse of a Rational Number: A Rational Number is a subtype of a real number, which can be expressed in p/q form where “p” is not equal to 0. A fraction that does not have zero as a denominator is a Rational Number. The multiplicative inverse of any Rational Number is its reciprocal number. For example, let us say ⅗ is a Rational Number where the denominator is not equal to zero. Then, the multiplicative inverse of this given Rational Number is 5/3. When we multiply the Rational Number with its multiplicative inverse, the product is 1.

Students can practice the given problems in the textbook, reference material, and mock tests to score well and get in-depth knowledge of the subject. Rational Numbers is one of the easiest chapters in the curriculum. It is very basic and also scoring if students have conceptual clarity.

Expression of Rational Number Mentioned in RS Aggarwal Class 8 Maths Chapter 1 Exercise 1A

The expression of a rational number mentioned in RS Aggarwal Maths Class 8 exercise 1A solution is given as follows.

Equality of Two Rational Numbers

Two rational numbers mn and ab are said to be equal if:

m = a and n = b, as well as mb = an.

Order of a Rational Number

A rational number ab is said to be greater than mn if and only if an > bm.

Addition and Subtraction of Rational Numbers

Two rational numbers ab and mn are added as follows:

ab + mn = an + bmbn

Similarly, the subtraction is done as an − bmbn

Multiplication of Rational Numbers

Two rational numbers ab and mn will be multiplied as acmn.

If the rational numbers are represented in their canonical form, their product will be denoted as a reducible fraction.

Division of Rational Numbers

Division of rational numbers is calculated by multiplying one of the rational numbers with the reciprocal of the other.

To divide ab and mn, ab is multiplied by nm

Inverse Numbers

There are two inverses for every rational number – additive inverse and multiplicative inverse.

Additive inverse of rational number ab is – ab while the multiplicative inverse is ba.

Important Questions in RS Aggarwal Maths Class 8 Exercise 1A

Q. Multiply 4/13 by the reciprocal of -8/18

Solution:

Reciprocal of -8/18 = 18/-8 = -18/8

According to the given question,

4/13 × (Reciprocal of -7/16)

4/13 × (-18/8) = -72/104

Show the given value of rational numbers on the number line.

(i) 11/4

(ii) -2/-5

Solution:

(i) 11/4 can also be represented as 2 ¾

The rational number can be represented in the following way.

(image will be uploaded soon)

(ii) -2/-5

= (– 2 × - 1) / (– 5 × - 1)

= 2 / 5

The rational number can be represented in the following way.

(image will be uploaded soon)

Q. In an election of society, there are 50 voters. Each of them cast their vote. Three persons A, B and C are contesting for the post of Secretary. If Mr A got 3 / 5 of the total votes and Mr C got 1 / 5 of the total votes, then find the number of votes which Mr Y got.

Solution:

Number of votes = 50

Number of person for standing in election election = A,B,C

A got (3 / 5) of total votes = (3 / 5) of 50

= (3 / 5) × 50

= 30

C got 1 / 5 of total votes = 1 / 5 of 50

= (1 / 5) × 10

= 10

Calculation of remaining votes is shown as below

= 50 – (30 + 10)

= 50 – 40

We get,

= 10

Hence, Mr B got 10 votes.

Did You Know?

A rational number is a number that can be written in the form of a ratio. It can also be written into a fraction in which both the numerator and denominator are represented as a whole number. Every whole number is also a rational number as they can be as a fraction.

FAQs on RS Aggarwal Solutions Class 8 Chapter-1 Rational Numbers (Ex 1A) Exercise 1.1

1. How do you identify a rational number as per the definition in RS Aggarwal Class 8 Maths Chapter 1?

According to the solutions for Chapter 1, a number is identified as a rational number if it can be expressed in the form p/q, where 'p' and 'q' are integers and the denominator 'q' is not equal to zero. For instance, 4/7, -8/3, and even the integer 5 (which can be written as 5/1) are all rational numbers. The first step in solving any problem is to confirm that the number fits this definition.

2. What is the correct method to find the multiplicative inverse of a rational number like -13/19, as seen in RS Aggarwal Class 8 Ex 1A?

To find the multiplicative inverse (also known as the reciprocal) of a rational number, you must interchange its numerator and denominator. The sign of the number does not change. For the example -13/19, its multiplicative inverse is 19/-13, which is conventionally written as -19/13. A key property to remember is that the product of any rational number and its multiplicative inverse is always 1.

3. What are the steps to find five rational numbers between -3/2 and 5/3, a common problem type in RS Aggarwal Class 8 Chapter 1?

To find a specific quantity of rational numbers between two given rational numbers, the standard method is as follows:

Step 1: Find a common denominator for the given numbers. For -3/2 and 5/3, the least common multiple (LCM) of the denominators (2 and 3) is 6.
Step 2: Convert both rational numbers into equivalent fractions with this common denominator. So, -3/2 becomes -9/6 and 5/3 becomes 10/6.
Step 3: Identify integers between the new numerators (-9 and 10). You can choose any integers like -8, -5, 0, 2, and 9.
Step 4: Place these integers over the common denominator to get the required rational numbers: -8/6, -5/6, 0/6, 2/6, and 9/6.

4. What is the correct procedure to express a rational number like 33/-55 in its standard form as required in the solutions?

To write a rational number in its standard form, two conditions must be met: the denominator must be positive, and the numerator and denominator must be co-prime (their highest common factor is 1). For 33/-55, the steps are:

First, make the denominator positive by multiplying the numerator and denominator by -1: (33 × -1) / (-55 × -1) = -33/55.
Next, simplify the fraction by dividing the numerator and denominator by their highest common factor (HCF), which is 11.
This gives (-33 ÷ 11) / (55 ÷ 11) = -3/5.

Thus, the standard form of 33/-55 is -3/5.

5. Why is the additive inverse of a rational number different from its multiplicative inverse?

The additive inverse and multiplicative inverse are different because they are defined by different mathematical goals. The additive inverse of a number 'x' is '-x', designed to result in the additive identity, zero (since x + (-x) = 0). For example, the additive inverse of 4/9 is -4/9. In contrast, the multiplicative inverse of 'x' is '1/x', designed to result in the multiplicative identity, one (since x × (1/x) = 1). For 4/9, this would be 9/4. One negates the number to reach zero, while the other inverts it to reach one.

6. How does using properties like distributivity simplify complex calculations in Chapter 1?

Properties like the distributive property are crucial for simplifying expressions by rearranging and grouping terms. For example, to solve (7/5 × -3/12) + (7/5 × 5/12), instead of multiplying separately, you can use distributivity:

Factor out the common term, 7/5: 7/5 × (-3/12 + 5/12).
First, solve the operation inside the brackets: -3/12 + 5/12 = 2/12.
The expression becomes a much simpler multiplication: 7/5 × 2/12 = 14/60, which simplifies to 7/30.

This method reduces calculation steps and minimizes the chances of error.

7. In the context of RS Aggarwal Class 8 solutions, why is an expression like 5/0 not considered a rational number?

An expression like 5/0 is not a rational number because the fundamental definition of a rational number (p/q) strictly requires the denominator 'q' to be a non-zero integer. Division by zero is mathematically undefined. There is no number that, when multiplied by 0, results in 5. Since this operation is impossible, any fraction with a zero in the denominator falls outside the set of rational numbers and cannot be used in the calculations covered in this chapter.