Virtual teaching phase #1
Class: 7
Mathematics
Week #1
lesson # 1(7M01)
Topic: Rational numbers
Let’s Revise Numbers
Natural Numbers : All counting numbers are known as natural
numbers. e.g. : 1,2,3,…
Whole numbers: All counting numbers including zero, are known
as Whole numbers. e.g.: 0,1,2,3,…
Opposite of Natural numbers : -1,-2,-3 , …
Integers: A collection of Whole numbers and the opposite of
Natural numbers is known as Integers. e.g …,-2,-1,0,1,2,...
Fractions & its types
Number
Place value chart of decimal
104 103 102 101 100 10-1 10-2 10-3 10-4
Whole part Decimal part
Write the place value of 13546.789 in
base 10.
.
1 3 5 4 6 .7 8 9
104 103 102 101 100 10-1 10-2 10-3
1 1 1
13546.789 = 1× 10,000 + 3× 1,000+ 5 × 100+ 4× 10+ 6× 1+ 7× + 8× +9×
10 100 1000
13546.789 = 1× 104 + 3× 103+ 5 × 102+ 4× 101+ 6× 100+ 7× 10-1 + 8 × 10-2 + 9 × 10 -3
Types of decimals
Decimal
Do the decimal digits go forever?
No Yes
Non Terminating decimal
It has infinite / uncountable number
Terminating decimal of digits after decimal point .
It has finite number e.g. 3.14159… , 3.3333…..
of digits after decimal 3.142857142857…
point . Is there a repeating pattern after decimal point?
e.g. 3.5 , 12. 9678 NO
Yes
Non Recurring decimal
Recurring decimal If no digit or block of digits
If a digit or block of digits are repeating itself infinite
are repeating itself infinite number of times after the
number of times after the decimal point .e.g. 3.14159…
decimal point.e.g. 3.333…. ,
,𝟐 𝟐 , 𝝅
3.142857142857… , 2. 𝟕𝟑
Let’s answer following questions ..
Is sum of any two integers is always an integer ?
Yes ! e.g. ( -5) + (- 6) = (-11) which is an integer .
Is difference of two integers is an integer ?
Yes! E.g. ( 9) –(-5) = 9+ 5 = 14 which is an integer.
Is product of two integers is always an integer?
Yes , e.g ( -3) ( +2) = -6 which is an integer .
Is Quotient of two integers is always an integer ?
It may or may not be an integer. e.g. ( -4) ÷(-2) = +2
But (-2)÷(-4) = + ½ which is not an integer number ,it is
expressed as a fraction it is known as rational number .
What kind of numbers are these ??
−1
2
−1
−2
+1
−2
Quotient of an integer and a non zero integer is known
as Rational number .
Rational numbers can be expressed as fraction .
The numbers which can be expressed as
𝒂
𝒃
, 𝐰𝐡𝐞𝐫 𝐚 & 𝐛 𝐚𝐫𝐞 𝐢𝐧𝐭𝐞𝐠𝐞𝐫𝐬 𝐚𝐧𝐝 𝐛 𝐜𝐚𝐧 𝐧𝐞𝐯𝐞𝐫 𝐛𝐞 𝐳𝐞𝐫𝐨 .
Venn diagram
Rational numbers
𝟐 −𝟐
𝟏𝟔 𝟑 𝟑
𝟖
3.𝟒𝟐𝟏 Integers
0.564
… , -3, -2, -1, …
Whole numbers
0
Natural numbers
1,2,3,…
Activity Time !!!!(check your self)
-1 12 𝟐
𝟓
0 2.678812 𝝅
𝟒
2 𝟓
𝟐 −𝟐
𝟒 𝟑
0.33…
3.125
7 𝟐 𝟒
𝟗
Express the following rational as decimal
𝟑
.
0 6
𝟓
5 3 .00000
= 0. 6 -0
30
30
0
Express the following rational to the number of
decimal places given in brackets .
𝟏𝟕
𝟐𝒅𝒆𝒄𝒊𝒎𝒂𝒍 𝒑𝒍𝒂𝒄𝒆𝒔
.
0 32
𝟓𝟑
53 17.00000
= 0.32 -0
17 0
-159
11 0
-106
4
Points to Remember
All integers are Rational numbers.
Zero is also a Rational numbers.
All terminating decimals are Rational numbers as they can
be expressed as fraction .
All non terminating recurring decimals are Rational
numbers as they can be expressed as fraction.
All non terminating non recurring decimals are irrational
numbers because that can’t be expressed as fraction .
Square root of an imperfect square will always be an
irrational number .
Points to ponder
Your turn now!!!
Encircle Yes or No for each of the
following by giving a reason .
Yes / No
(1)Is 0.5 a rational number ?
(2)Is -0.5 a irrational number?Yes / No
(3)Is 0.5555…a rational number? Yes / No
(4) Is 3.14 a rational number? Yes / No
22
(5) Is 𝜋 ≈ a rational number ? Yes / No
7
State whether each of the following statement is
True/False.
(a) Every Integer is a Rational number. True
(b) Every rational number is a whole number. False
(c) Every irrational number is a real number. True
(d) π is a rational number. False
(e) Every real number is an irrational number. False
(f) Collection of all rational and irrational
numbers called Real number. True
Ordering of Rational numbers
Put the following rational numbers in descending order:
• The Least multiple of
denominators is 18.
-1 1 1 -2 • Each number needs to
6 3 1 18 9 then be converted so that
𝟑 𝟔 𝟐 all the denominators are
× × × the same.
𝟑 𝟔
-3 6 19 𝟐 -4
• The numerators can then
18 18 18 18 be compared.
19 6 -3 -4
18 > 18
> 18 >
18
1 1 -1 -2
1 > > >
18 3 6 9
𝟏 𝟏 −𝟏 −𝟐
Descending order : 1 , , ,
𝟏𝟖 𝟑 𝟔 𝟗
Ordering of Rational Numbers
Put the following Rational numbers in Ascending order:
• The common denominator
-3 4 -5 -7 is 24.(LCM of
denominators is 24)
𝟔 4 𝟒 6 𝟑 8 𝟐
12
× × × × • Each number needs to
𝟔 𝟒 𝟑 𝟐 then be converted so that
-18 16 -15 -14 all the denominators are
24 24 24 24 the same.
• The numerators can then
be compared.
-3 > -5 > -7 > 4
4 8 12 6
16-06-25 classwork Monday
Topic: Rational numbers
Exercise #1.1
Guided practice :
Q#4. Arrange the following numbers in Ascending order.
𝟏 −𝟏
, −𝟎. 𝟏𝟎, 𝟐𝟓% , ,0
𝟓 𝟒
𝟏 − 𝟏𝟎 𝟐𝟓 −𝟏
, , , ,0
𝟓 𝟏𝟎𝟎 𝟏𝟎𝟎 𝟒
𝟏×𝟐𝟎 − 𝟏𝟎 𝟐𝟓 − 𝟏×𝟐𝟓
, , , ,0
𝟓×𝟐𝟎 𝟏𝟎𝟎 𝟏𝟎𝟎 𝟒×𝟐𝟓
𝟐𝟎 − 𝟏𝟎 𝟐𝟓 − 𝟐𝟓
, , , ,0
𝟏𝟎𝟎 𝟏𝟎𝟎 𝟏𝟎𝟎 𝟏𝟎𝟎
− 𝟐𝟓 − 𝟏𝟎 𝟐𝟎 𝟐𝟓
, ,0 , ,
𝟏𝟎𝟎 𝟏𝟎𝟎 𝟏𝟎𝟎 𝟏𝟎𝟎
16-06-25 classwork Monday
Topic: Rational numbers
Exercise #1.1
Guided practice :
Q#4. The amount of rain received on four consecutive
𝟐 𝟐
days was 0.3cm, 𝒄𝒎, 𝟎. 𝟕𝟓𝒄𝒎 & cm. order it from
𝟓 𝟑
greatest to least. 𝒄𝒐𝒏𝒗𝒆𝒓𝒕 𝒇𝒓𝒂𝒄𝒕𝒊𝒐𝒏 𝒊𝒏𝒕𝒐 𝒅𝒆𝒄𝒊𝒎𝒂𝒍
0.3cm , 𝟎. 𝟒𝒄𝒎 , 0 .75 , 0.6 7
0.75, 0.67, 0.4 , 0.3
𝟐 𝟐
Descending order : 0.75cm , cm, 𝒄𝒎 , 𝟎. 𝟑𝒄𝒎
𝟑 𝟓
google
quiz Time
