Download Class VII - Senior Section

CLASS VII New
Integers
A
1.
2.
3.
4.
5.
6.
The integer consist of ___, ____ and ____ numbers
The numbers less than zero are called _______ integer.
All the numbers which are less than zero have ____ sign.
Zero is greater than _____ integer.
The natural numbers are ____ integers.
On the number line of integers , the value increases as we move from left side to the
___ side.
7. ____ is the largest negative integer.
8. ____ is the smallest positive integer.
9. ____ is neither positive nor negative.
B
1. Represent the following on the number line
a) 2 +-3
b) -4 + ( -5) c) - 6 - 3
d) 2 - ( -2)
f) 7– 5 + 2
Predecessor: one less than a given integer.
To find the predecessor --- subtract 1 from the given number or add -1 to the
number. Predecessor of “a” is “a -1”
2. Write the predecessor of the following integers
10,
- 10 ,
100,
-100,
0,
-1,
1,
Successor—one more than a given integer.
To find the successor of a integer--- Add 1 to a given number. Successor of “a”
is “a + 1”
3. Write the successor of the following integers
9, - 9 ,
-11, 11, -99, -40, 101,
1000, -999
4. Arrange in the ascending order:
a) o, -3,
5, -1
b) 10, -10, 5, -5, 0 , -1, 1
1
5. Arrange in the descending order:
a) -20, -30, - 7, -16, - 9
b)
100, -100, 0, 97, - 99
When we add or subtract two integers---1) If two integers have same (like ) sign --- Write the common sign and Add the
two numbers without looking at the sign. Example -3 - 9 = - ( 3 + 9) = - 12
2) If two integers have different( unlike) sign—Write the sign of larger number (
absolute value) and subtract the smaller from the larger.
Example: - 10 + 7 = - (10 – 7 )
(Here 10 is greater therefore write the sign of 10)
= -3
6.
Simplify the following
a) 17 – 8
b)
-7 + 11 c)
-25 - 10
d) -20 + 17
e) 31 – 33
When we solve problems having sign before the integer. First remove the
bracket and then solve. Example: -3 – (-10)
-3 –( -10) --- We have - sign, so write the additive inverse of the number inside
the bracket or write the opposite of the number inside the bracket. Inverse or
opposite of -10 is +10
-3 – (-10) = -3 + 10 = 7
Example -3 + (-10) --- + sign is there before the bracket, just copy the number
inside the bracket and remove the + sign which is before the bracket.
-3 + (-10) = -3 -10 = -13
7.
Simplify
a)
-8 - ( -8 )
b) 100 – (- 90 )
c) - 20 + ( - 15)
d) 17 + ( -20)
7. Subtract the first from the second
a) 34, 25
b) - 30 , -35
c)
50 , -45
8. Subtract -39 from -40
9 . Subtract 28 from -28
2
d) -90, -90
10 . Insert <,> or = sign
a) -10 ____ -11 b) 0 _____ (-2)
e)
- 7 - (-7)
_____ -7 + 7
g) -20 + ( - 30) ___
7 ( -2)
c)
f)
-90 ______ -89
d) -40 ____ 40
10 – ( - 10) _____ 2 x 10
h) -100 ÷ 5 ___ -6 (-5)
13. Fill in the blanks.
a) - 3 + ____ = -10
b)
7 - _____ = 10
c) 12 + _____ = 10
d)
e)
-3 + ____ = - 18
f)
-18 - ______ = 10
g) 45 - ( ___) = - 5
h)
___ + (-9) = 27
- 45 – ( ___) = - 9
14. Find the number which is___
a) 6 more than -5
b) 5 less than -6
c) the predecessor of -20
d) the successor of -100
e) 10 more than ( -3 – 7)
Playing with numbers
1. 6 x 7 = 42--___and ___ are factors of ____ .
____ is multiple of ____and ___ .
2. Find all the factors of the following numbers.
24, 28, 27, 32, 36, 45, 48
3. How many factors are there for 18?
4. Pick out all the common factors of 12 and 24.
5. Write first four multiples of each of the following given numbers.
3,
8 and 10
6. Fill in the blanks
a.
____ is factor of every numbers.
3
b. The largest factor of the given number is ____
c. The smallest multiple of the natural number is the number ______
d. The smallest factor of 25 is _______ .
e. The smallest multiple of 6 is _____ .
f. All the numbers which are divisible by 2 are called _____.
g. The composite numbers have more than _____ factors.
h. Numbers which have only two factors are called ______
Prime Numbers: Numbers which have only two factors 1 and the number itself.
Composite numbers: Numbers which have more than two factors.
1 is neither prime nor composite number as it has only one factor.
7. Write all the prime numbers between 1 -20
8. 21 is not a prime number. Why?
Even Numbers : Numbers which are divisible by 2. If the unit digit of a number is
of 0, 2, 4, 6, 8—The number is even number.
Odd Numbers: Numbers which are not divisible by 2. If the unit digit of a number
is of 1, 3, 5, 7, 9—The number is odd number.
9. Classify into even and odd numbers.
998, 598, 735, 2111, 34857, 34856
10. What is the number which is even and also a prime .
11. What can you say about the units digit of odd numbers?
12. Find out the numbers divisible by2
362,
731,
895,
8246,
13. Find out the numbers which is divisible by 5
1003, 345,
1230, 3909
14. Find out the numbers which is divisible by both 2 and 5.
235, 1090, 2000, 2402
4
15. Find the HCF of the following numbers.
a) 36 and 42
b) 15 and 50 c) 24 and 48
16. Find the LCM
a) 12 and 16
b) 25 and 50 c) 18 and 27
17. Fill in the blanks
1
2
3
4
5
6
7
8
Numbers
6 and 10
25 and 80
12 and 30
18 and 36
45 and 27
48 and 60
6and 15
15 and 30
HCF
Fraction
1. Write the fractions representing the shaded portion:
2. Colour the part according to the given fraction:
+
3. What part of your family is male?
5
LCM
Types of fractions
Proper fractions: Fractions, where the numerator is less than the denominator.
Improper fractions: If the numerator is greater than the denominator, the fractions
are improper fraction.
Mixed fractions: An improper fraction can be written as combination of a whole
and a part, and such fraction then called mixed fraction.
1 ¾
4/4
3/2 1/10
5/6
1
5. Pick out all the proper fractions
6. Why
is not a proper fraction?
To convert improper fraction into mixed fraction. Divide the numerator by the
denominator and express the answer as Improper fraction = Quotient
3
4
Example
13
12
1
= 3
7. Change the following improper fractions into mixed numeral
7/5
To convert mixed fraction into improper fractions--Example
=
=
8. Express in the improper fraction
To Find Equivalent Fractions—Either multiply or divide both numerator and
denominator by the same number. It is easier by multiplying.
6
Example: Find three equivalent fractions of
Sol Three equivalent fractions of
are
=
=
=
=
=
9. Find three equivalent fractions of 6/5.
10. Fill up the empty boxes.
=
2=
To reduce into simplest form : Find the HCF of the numerator and denominator.
Example
Sol HCF of 30 and 45 is 15 ( 15 x 2 =30 and 15 x 3 = 45
=
=
11. Reduce the following fractions to simplest ( lowest) form.
12. How many 1/8th are there in a whole?
!3. Put <, > or = signs.
a)
__
b)
c)
d)
e)1
f)
14. Find the sum
a)
d)
b)
e)
c) 4
f)
d)
g)1
h)
i)3
15. Find the difference.
a)
b)
c)
d)
7
e)
f)
g)
h)
i) 2
j)
Decimal
1. Determine the whole and decimal part.
a) 3.2
b) 12.0212
2. Write in words.
a) 1.2
b) 0.35
c) 12.06
d) 178.34
e) 0.123
3. Write each of the following as decimals.
a) Five tenth
b) Three tens and three tenths
c) Sixteen point three.
d) Four hundreds four ones and four hundredths
e) Nine thousand nine hundred point five
To convert fraction into decimal---
Divide the numerator by denominator
Example
1) In
2
denominator 2 is a factor of 10
=
=
0.5
1
0
or
10
10
= 0.5
0
4. Write each of the following as decimals:
a)
f)
b)
c) 200 + 50 + 5 +
g)
h)
d)
e)
i) 3
To change decimal into fraction
Separate the whole and decimal parts. Count the number of digits in the decimal
part. Divide the number by 10,100 or 1000 accordingly with the number of digits in
the decimal parts or the number of digits after the decimal point
8
Example 21.3 =
,
0.17 =
(note the answer must be in the simplest
form)
5. Write the following decimals as fractions:
a) 0.7
b) 0.23
c) 1.5
d) 28. 5
e) 0.125
6. Which is greater?
a) 0.4 or 0.5 b) 0.07 or 0.7 c) 7.7 or 7.07
d) 12.3 or 1.23
e) 1.432 or 1.43
7. Calculate
a) 3.2 + 1.7
b) 12.08 + 13.88
c) 1.893 + 0.68
d) 0.9 + 1.34
e) 10 - 9.7
f) 11.67 – 9. 95
g) 102.09 – 77. 345
h) 9.5 – 6.606
8. Subtract ;
a) Rs 28.55 from Rs 30.6 b) 0.512m from 1m
c) 103.3 km from 150km.
UNDERSTANGING ELEMENTARY SHAPES
1.
Measure the sides of the figure given below using scale.
A
B
D
C
2. Draw line segment of the following measure:
a) 4cm
b) 3.5 cm
3. Match the following:
1) Reflex angle
2) Obtuse angle
c) 10cm
a) less than 90
d) 6.3 cm
0
b) equals to 180
9
0
0
0
3) Acute angle
c) more than 90 and less than 180
4) Right angle
d) equal to 360
5) Straight angle
e) greater than 180 and less than 360
6) Complete angle
f) equal to 90
0
0
0
0
4. Classify the following angles as zero, acute, obtuse, reflex, right and complete
angle:
0
0
0
0
0
0
0
0
52 , 103 , 89 , 90 , 359 , 180.5 , 89 , 360 , 00, 2
5. Classify the following angles.
10
0