CLASS-VII MATHEMATICS

TOPIC:- RATIONAL

NUMBERS

GENERAL INSTRUCTIONS

This presentation is based on chapter 9 of your

book.

Chapter is Rational Numbers.

Go through the presentation thoroughly.

After you have understood the topic, try to solve the worksheets.

Use your previous year notebooks or A4 sizedsheets to solve the worksheets.

Do not copy the general intructions.

TOPICS TO BE

COVERED

Positive and Negativerational

numbers.

Equivalentrational numbers.

Representing rational

numbers on number line.

Rationalnumbers

in standard form.

Comparision ofrational

numbers.

Rational numbers

between two rational numbers.

Addition of rational

numbers

Subtraction of rational

numbers

Multiplication of rationalnumbers

Division ofrational numbers

• A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a boldface Q.

• Or

• Rational numbers are numbers that can be expressed in the form p/q, where p and q are integers and q ≠0.

p q p/qRational/Irration

al Number

10 2 10/2 =5 Rational

1 1000 1/1000 = 0.001 Rational

50 10 50/10 = 5 Rational

7 0 7/0 Not defined(because

q=0)

How to identify rational numbers?

To identify if a number is rational or not, check the below conditions.

•It is represented in the form of p/q, where q≠0.

•The ratio p/q can be further simplified and represented in decimal form.

The set of rational numerals:

1.Includes positive, negative numbers, and zero

2.Can be expressed as a fraction

Examples of Rational Numbers:

Positive and NegativeRational Numbers

Positive RationalNumbers Negative RationalNumbers

If both the numerator and denominator are

of same signs.

If numerator and denominator are of

opposite signs.

All are greater than 0 All are less than 0

Example: 12/17, 9/11 and 3/5 are positive

rational numbers

Example: -2/17, 9/-11 and -1/5 are negative

rational numbers

Equivalent Rational Numbers

• 1. To obtain an equivalent rational number of the given rational number we have to multiply the numerator and denominator of a given rational number by the same nonzero number.

• 2. To obtain a rational number equivalent to the given rational number we have to divide the numerator and denominator of a given rational number by a common divisor.

Click on the following link to know more aboutEquivalent rational numbers

https://www.youtube.com/watch?v=WUr6JpHQbx4

Worksheet1

(1) Write four rational numbersequivalent to −3/5.

(2)Write six rational numbers equivalent to -7/6.

(3)Write five rational numbers equivalent to 8/9.

(4)Write four rational numbersequivalent to 21/3.

(5)Write five rational numbers equivalentto 1.2.

Worksheet2

Representingrational numbers on number line

•Click the following link:-

https://www.youtube.com/watch?time

_continue=79&v=ggipqKQ6WDs&featur e=emb_logo

Standard Form of Rational

Numbers

The standard form of a rational number can

be defined if it’s no common factors aside

from one between the dividend and divisor

and therefore the divisor is positive.

For Example, 12/36 is a rational number.

But it can be simplified as 1/3; common

factors between the divisor and dividend is

only one. So we can say that rational

number ⅓ is in standard form.

Comparison ofRational Numbers

• In order to compare any two rational numbers, we can use the following steps:

• Step I: Obtain the given rationalnumbers.

• Step II: Write the given rational numbers so that their denominators are positive.

• Step III: Find the LCM of the positive denominators of the rationalnumbers obtained in step II.

• Step IV: Express each rational number (obtained in step II) with theLCM (obtained in step III) as common denominator.

• Step V: Compare the numerators of rational numbers obtained instep having greater numerator is the greater rational number.

SOME SOLVED

EXAMPLES

Rational Numbers between Two rational click:-

https://www.youtube.com/watch?time_continue=164&v=VlKWQdRanb8&feature=emb_logo

Let ‘a’ and ‘b’ be two rationalnumbers.

(i) Convert the denominator of both the fractions into the same denominator by taking LCM. Now, if there is a number between numerators there is a rational number between them.

(ii) If there is no number between their numerators, then multiply their numerators and denominators by 10 to get rational numbers betweenthem.

To get more rational numbers, multiply by 100, 1000 and so on.

Additionof RationalNumbersclick:-https://www.youtube.com/watch?time_continue=76&v=YVerO8RvBGI&feature=em b_logo

(*)Addition of rational numbers with same denominators:

Consider two rational numbers , here both have different numerators but same denominators. To add these, we add both the numerators keeping common denominator.

Addition of two rational number

• (*)Addition of rational numbers with different denominators:

• To add rational numbers with different denominators convert them to rational numbers with same denominators and then add.

• In order to convert rational numbers to numbers with same denominators take the LCM of the denominators. Then multiply both rational numbers by this LCM and we will get equivalent rational numbers with this LCM as the denominator.

Subtraction of rationalnumbers• Subtraction of rational numbers with same

and/or different denominators can be done like addition. Subtraction of rational numbers will be easy by transforming subtraction problem into addition problem. This can be done in two steps;

• Change the subtraction sign (-) into additionsign (+)

• Take the additive inverse of the rationalnumber come after the sign.

• Simply, take the additive inverse of the numberafter the sign and add them.

CLICK:-

https://www.youtube.com/watch?v=fo

GeJtPGY08

• Multiplication of rational numbers is as simple as multiplication of integers. In general, product of two rational numbers will equal to the product of the numerators divided by the product of the denominators.

• To find the product of a rational number and an integer, keep the denominator unchanged and multiply the numerators. To find the product of rational numbers, multiply the numerators and multiply denominators

Multiplication ofrational numbers

Click:-

https://www.youtube.com/watch?v=sy0YSJHIvtk

Division of Rational Numbers

• Divisions of rational numbers are similar to the divisions of fractions. To find the quotient of rational numbers, we need to recollect the concept of reciprocal of a rational number. Reciprocal of a rational number is nothing but the swapping of the numerator and denominator of that rational number i.e. invert the given the rational number will give you the reciprocal of that rational number. For example, 7/6 is the reciprocal of 6/7 . The product of a number and its reciprocal will always be 1.

• In order to divide rational number, first change the division sign ÷ to x. Then take the reciprocal of the number after the sign and multiply.

Some solved

examples

Worksheet3

Worksheet4

Worksheet5

Worksheet6

Worksheet7

Worksheet 8

Worksheet 9

Worksheet

10