Download important facts and handy facts subject : maths class : vi

IMPORTANT FACTS AND HANDY FACTS
SUBJECT : MATHS
CLASS : VI
TOPIC: NUMBERS AND NUMERATION
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The smallest period is ones.
Ones period has 3 places – ones, tens, hundreds.
A comma is put after every period.
In Indian P.V system periods are – ones, thousands, lakhs and crores.
In International P.V system periods are – ones, thousands and millions.
Ones period ( 3 digits ) ( Indian P.V )
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H
T
O
Thousands period ( 2 digits ) ( Indian P.V )
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T thTh
Lakhs period ( 2 digits ) ( Indian P.V )
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TL
L
Crore period ( 2 digits ) ( Indian P.V )
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TC
C
Ones period ( 3 digits ) ( International P.V )
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H
T
O
Thousands period ( 3 digits ) ( International P.V )
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H Th
T ThTh
Millions period ( 3 digits ) ( International P.V )
HM
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TM
M
Largest 6-digit number = 9,99,999
Smallest 7-digit number = 10,00,000 = ten lakh (9,99,999 + 1 )
Largest 7-digit number = 99,99,999
Smallest 8-digit number = 1,00,00,000 = one crore (99,99,999 + 1 )
Largest 8-digit number = 9,99,99,999
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Smallest 9-digit number = 10,00,00,000 = ten crore (9,99,99,999 + 1 )
The face value of a digit is always the number itself.
Example : face value of 2 in 42315 is 2.
The place value of a digit in a number depends upon the place it occupies in PV chart.
Example : place value of 2 in 42315 is 2 thousand or 2000.
Place value and face value of zero is always zero.
Place value = face value x place of a number.
Facts about Roman Numerals
1. Only 7 roman numerals are used to write numbers. These symbols are :I , V , X , L , C , D M.
2. Numerals I, X, C and M can be repeated to form a number. Repetition of these symbols
means addition. These symbols cannot be repeated more than 3 times.
Example :- III = I + I + I = 3
XXX = X + X + X = 10 + 10 + 10 = 30
3. Symbols V, L and D cannot be subtracted or repeated.
4. Romans had no symbol of zero.
5. When a smaller numeral is on the left of a greater numeral, we subtract the smaller one from
the greater one.
Example :- IV = 5 -- 1 = 4
IX = 10 -- 1 = 9
6. When the smaller numeral is on the right of a greater numeral, we add the smallest one to the
greatest one.
Example :- VI = V + I = 5 + 1 = 6
XI = X + 1 = 10 + 1 = 11
TOPIC– OPERATION ON WHOLE NUMBERS
ADDITION
1.
2.
3.
Addition- Addition means putting together.
Addends- The numbers to be added are called as addends.
Sum- The number we get after adding is called the sum
OR
The number of an addition problem is called as the sum.
Example :-434 + 215 = 649
Addends
sum
Facts about addition
1.
2.
4.
3.
On adding two or more numbers in any order, the sum remains the same. This is called as cummutative
property of addition.
Example :- 4 + 2 = 4 + 2 = 6
When we add zero to a number, the answer is the number itself. This is called as additive property of
addition.
Example :- 825 + 0 = 825
Associative property – Even if the groups of the addends is changed, the sum remains the same.
Example – ( 4 + 3 ) + 2 = 7 + 2 = 9
4 + (3 + 2)= 4 + 5 =9
(4 + 2) +3 = 6 + 3 =9
When we add one to a number, we get the next number or the successor of the given number.
Example :- 342 + 1 = 343
Checking for addition
To check if the answer for the addition problem is correct, we subtract anyone number from the
sum and we get the other number.
Example :- 5 2 7 4
+3132
8406
checking :- 8 4 0 6
—3132
5274
or
8 4 0 6
—
5 2 7 4
3 1 3 2
SUBTRACTION
3. Subtraction – Taking away one number from another.
4. Difference – The answer or result of a subtraction problem is called difference.
5. In subtraction bigger number is always written on the top.
Facts about subtraction
1.
When 1 is subtracted from a number, we get the predecessor of the given number.
Example :- 2435 -- 1 = 2434
2.
When 0 is subtracted from a number, the difference is the number itself.
Example :- 4561 -- 0 = 4561
3.
When we subtract a number from itself, the difference is always 0.
Example :- 5678 -- 5678 = 0
4.Additive inverse:- The additive inverse of a number a is the number that, when added to a, yields zero.The
additive inverse of a is denoted by : −a. For example, the additive inverse of 7 is −7, because 7 + (−7) = 0
5.
Commutative and Associative property does not exit for subtraction.
6.
Order of numbers involved in subtraction cannot be changed.
7.
Bigger number is called minuend.
8.
Smaller number is called subtrahend.
Checking for subtraction
To check if the answer for the subtraction problem is correct, we add the difference to the smaller number and
we get the larger number.
Example :- 5 2 7 4
—3132
2142
checking :- 2 1 4 2
+ 3132
5274
Relation between addition and subtraction
Addition and subtraction are inverse operation. It means that when two numbers are added, we get a sum and if
we subtract any one number from the sum, we get the other number.
Example :- 2 3 6
+123
359
MULTIPLICATION
359
—1 2 3
236
359
—236
123
Multiplication is repeated addition.
Example : 4 × 3 = 12
or 3 × 4 = 12
4 + 4 + 4 = 12
or
3 + 3 + 3 + 3 = 12
PRODUCT– The answer of a multiplication problem is called as the product.
MULTIPLICAND – The number to be multiplied is called as the multiplicand.
MULTIPLIER – The number by which the multiplicand is multiplied is called as the multiplier.
Example : 6 × 4 = 24
product
multiplier multiplicand
FACTS OF MULTIPLICATION
1. When any number is multiplied by 1, the product is the number itself.
Example : 451 X 1 = 451
2. When any number is multiplied by 0, the product is always 0.
Example : 243 X 0 = 0 or 0 X 32 = 0
3. Two numbers multiplied in any order give the same product. This is called as commutative
property of multiplication.
Example : 24 X 2 = 48 or 2 X 24 = 48
So, 2 X 24 = 24 X 2 = 48
4. Even if the grouping of numbers is changed , the product remains the same. This is called as the
associative property of multiplication.
Example : ( 7 x 4 ) x 3 = 7 x ( 4 x 3 ) = ( 7 x 3 ) x 4
MULTIPLICATION WITH 10– To multiply a given number by 10, we simply put a zero to the right
of the number.
Example : 28 X 10 = 280
MULTIPLICATION WITH 100 – To multiply a given number by 100, we simply put two zeroes to
the right of the number.
Example :76 X 100 = 7600
MULTIPLICATION WITH 1000 – To multiply a given number by 1000, we simply put three zeroes
to the right of the number.
Example : 8 X 1000 = 8000
MULTIPLICATION WITH 10, 20, 30 ,40, 50, 60, 70, 80 AND 90– To multiply a given number by
10, 20, 30……..90 we simply multiply it by 1, 2, 3…….9 and add a zero to the right of the product.
DIVISION is the equal distribution of a given quantity.
1. DIVIDEND -The number to be divided is called as the dividend.
2. DIVISOR -The number which divides the another number is called as the divisor.
3. QUOTIENT -The answer of a division problem is called as the quotient.
4. REMAINDER -The number left after division is called as the remainder.
5. Dividend = divisor x quotient + remainder.
FACTS ABOUT DIVISION
1. When a number is divided by itself, the quotient is always 1.
Example : 4567 ÷ 4567 = 1
2. When a number is divided by 1, the quotient is the number itself.
Example : 2341 ÷ 1 = 2341
3. When zero is divided by any number, the quotient is zero.
Example : 0 ÷ 4511 = 0
4. When any number is divided by zero, the answer is infinity. (or not possible or meaningless)
Example : 8934 ÷ 0 = infinity
RELATION BETWEEN MULTIPLICATION AND DIVISION
Multiplication and division are inverse operations.
Example :12 × 5 = 60
60 ÷ 5 = 12 and
60 ÷ 12 = 5
1.
DIVISION BY 10, 100 AND 1000
If the divisor is 10, the last digits (right most) of the dividend is the remainder and the number formed
by the remaining digits is the quotient.
Example : 7862 ÷ 10 ,
Q = 786 , R = 2
2.
If the divisor is 100, the number formed by the last two digits of the dividend is the remainder and the
number formed by the remaining digits is the quotient.
Example : 682123 ÷ 100 , Q = 6821 , R = 23
3.
If the divisor is 1000, the number formed by the last three digits of the dividend is the remainder and the
number formed by the remaining digits is the quotient.
Example : 462113 ÷ 1000 ,
Q = 462 , R = 113
TOPIC -FACTORS AND MULTIPLES
Factor – A factor is a number which divides another number without leaving a remainder.
Example :- factors of 12 – 1,2,3,4,6,12.
Properties of factors :• 1 is a factor of every number.
• Every non-zero number is a factor of itself.
• The smallest factor of a number is 1.
• The largest factor of a number is number itself.
• Every factor of a number is non-zero number which is less than or equal to a number.
• There are limited or countable or finite factors of a number.
Multiples – Multiple of a number are exactly divisible by it.
Example :- multiples of 7 – 7,14,21,28,35………
Properties of multiples :• Every number is a multiple of itself.
• Every number is a multiple of 1.
• Multiple of a number are greater than or equal to a number.
• The smallest multiple of a number is the number itself.
• Multiples of an even number are always even.
• Multiples of an odd number is alternatively odd and even.
• There are unlimited or uncountable or infinite multiples of a number.
• Common multiples are those multiples that are common to two ormore numbers.
Prime numbers – Any number greater than 1, which has only 2 factors, 1 and the number itself, is called a
prime number. Example :- 2,3,7…..etc
Composite numbers – A number which has more than two factors is called a composite number.
Example :- 4,8,15…….etc.
• 2 is the smallest even prime number.
• 1 is neither prime nor composite.
• 4 is the smallest even composite number.
• There are 25 composite numbers between 1 and 100.
• There are 24 prime numbers between 1 and 100.
Twin prime – Two prime numbers with difference of 2 are called as twin prime numbers.
Example :- 5 and 7.
Co-prime numbers - Some numbers have only one factor in common, that is, the number 1. Any such pair of
numbers is called co-primes. Example :- 17 and 23 , 1 and 16, etc.
HCF ( Highest Common Factor ) – The largest common factor of two or more numbers is called the
highest common factor (HCF).
LCM ( Lowest Common Multiple ) – The smallest common number that can be divided by the given
numbers without leaving any remainder is called the LCM ( lowest common multiple).it is also called least
common multiple.
TOPIC – BASIC GEOMETRICAL CONCEPTS
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Point : A dot represents a point. A point tells the exact location of an object.
It has no length, breadth and height. It is the smallest shape.
It is represented by a capital letter as :
• A
Point A
Line : A line is a collection of points moving in a straight direction.
It has no end point.
It can be extended on both side.
A
It has no fixed length.
It is represented as
A line can be named using two capital letters. For eg. or
.
B
Line Segment : Line segment is a part of line having two end points.
It has two end points.
It cannot be extended in any of the two directions.
It has a fixed length.
It is represented as
.
A
Ray : It has one end point.
It can be extended on one side only.
It has no fixed length.
It is represented as
.
B
A
B
TYPES OF LINES:
Coplanar Lines : 2 lines lying in the same plane are called coplanar lines.
A
A
B
C
B
C
D
D
and
are coplanar lines.
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Concurrent Lines : Lines that pass through the same point.
Infinite lines can pass through a
single point.
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Collinear Points:: If 3 or more points lie in a straight line, the points are said to be collinear points.
Non-collinear Points : Three points not lying in the sam
samee straight line are called the non-collinear
non
points.
Points A, B are collinear points whereas D, E and F are non
non-collinear
collinear points.
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Plane : A plane is a flat surface that goes on endlessly or extends infinitely in all directions.
A plane is a collection of an infinite point.
A plane contains an unlimited number of lines, line segments and rays.
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Angle : Two rays or line segments with a
common end point form an angle.
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Vertex : The common end point of two rays
(arms) is called vertex of the angle.
ANGLES
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P
arms
vertex
angle
Q
Arms : The two rays or line segments are
arms
called the arms of the angle.
Use capital letters of the English alphabet to name an angle.
The letter denoting vertex of angle is always written in the middle.
R
Interior and Exterior of an angle :
An angle has 2 parts – interior and exterior. The points lying inside the angle form the interior of the
angle. (Points A and B)
The points lying outside the angle form the exterior of the angle.
Points A, D and F are interior points of the angle. Points B and C are exterior points of the angle.
PROTRACTOR:
An angle is measured with a protractor. In the measurement of angles, the unit of measurement used is
called degree. The symbol for degrees is ‘ O’ as in 30 , 45 etc. The number of degrees in an angle is
called its measure. The symbol ∠
is read as the ‘measure of angle AOB.
POLYGONS
A closed figure made up of 3 more line segments that do not cross each other is called a polygon. e.g.
A triangle is a polygon made up of 3 line segments.
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KINDS OF ANGLE
Acute Angle : An angle whose measure is between
0º and 90º is called an acute angle.
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Obtuse Angle : An angle whose measure is greater
than 90º but less than 180º is called
an obtuse angle.
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Right Angle : An angle whose measure is
90º is called an right angle.
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Straight Angle : An angle whose measure is 180º is called a straight angle.
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Reflex Angle : An angle that is greater than 180 but less than 360 is known as reflex angle.
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Whole or Complete Angle : An angle that is 360 is known as a whole or complete angle. It is formed
when the two arms complete a whole rotation to meet again.
TRIANGLE
A triangle is a closed figure having three sides, three vertices and three angles. The
T total measure of all 3
angles of a triangle is equal to 180 . The symbol of a triangle is ∆.
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TYPES OF TRIANGLE (ON THE BASIS OF SIDES)
Equilateral Triangle : It is one in which all the three sides are equal. Equal angle is of 60 .
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ISOSCELES TRAINGLE : It is one in which any of the two sides are equal.
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SCALENE TRIANGLE : It is one in which all the three sides are of different lengths.
TYPES OF TRAINGLES (ON THE BASIS OF ANGLES)
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ACUTE ANGLES TRAINGLE : It is one in which all the three an
angles
gles are acute.
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RIGHT ANGLES TRAINGLE : It is one in which any one of the angles is 90
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OBTUSE ANGLES TRIANGLE : It is one in which any one of the angles is obtuse.
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Properties of Triangles
a. The sum of all the angles of a triangle is equal to 180
b. The sum of any 2 sides of a triangle is always greater than the third side.
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CIRCLE
Circle : Circle is a simple closed curve. It is defined as the path traced out by a moving point which
moves at a fixed distance from a fixed point.
Circumference: It is the
he distance around the circle.
Radius: The distance between the centre and any point on the circumference. Plural of radius is radii,
e.g., XY, XB, etc.
Diameter: The distance from a point of the circumference to another point of the circumference passing
through the centre. It is double the radius, e.g., AXB.
Chord: The distance between one point of the circumference to
another point of the circumference. It may or may not pass
through the centre, e.g., UV.
Arc: A part of the circumference of a circle is called an arc. It is
named by 3 points, e.g.
.
Interior and exterior of a circle: The area enclosed by the
circumference is called the interior of the circle. The area outside
the circumference is called the exterior of the circle.
Semicircle: Points A and B divide the circle in two equal arcs.
Each of the arc is called a semicircle.
TOPIC: TIME
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A day has 24 hours.
A clock has an hour hand and a minute hand
hand.
Some watches have a third hand which is known as the second hand.. It is the thinnest and the fastest
needle.
Second hand covers 60 small divisions in one minute. It takes one second to cross one division.
The clock’s face has only 12 numerals and a full day has 24 hours.
There are 2 parts of a clock - 12 hours each. Istpart of the full day
y in which sun rises is known as A.M.
(Anti Meridian) which means before noon or midday. A.M. is the time between midnight and noon.
2nd part of the full day in which moon rises is known as P.M. (Post Meridian) which means afternoon
or midday.
The A.M. of the day starts at 12 o’clock midnight and ends at 12 noon.
The P.M. of the day starts at 12 noon and continues till o’clock midnight.
The hour hand of the clock goes round the dial twice in 24
24-hours.
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
1 hour = 3600 seconds
We use 2 types of clock systems to read time.
1. 12-hour clock – We see this kind of clock in schools and homes. The hour
hour-hand
hand in this clock circles
the clock twice a day. Each round shows a passage of twelve hours we know that a day has 24 hours.
( 12 x 2 = 24 ).
2. 24-hour clock – The Railways, the Airlines and some other organizations work day and night which
means for 24 hours. At such places a 24
24-hour clock is used. Look at the 24-hour
hour clock shown below.
Time in 24-hour
hour clock is written in 4 digits.
The first two digits on the left are for the hours and the two digits on the right are for the minutes.
There is no dot separating the four digits.
12 O’clock midnight is expressed as 0000 hours or 2400 hours.
12 O’clock at noon is expressed as 1200 hours.
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CONVERTING THE 12-HOUR CLOCK TIME TO 24-HOUR CLOCK TIME
For a.m. timings write hours and minutes side by side without separating them (writing hours as a 2digit number).
For p.m. timings, add 12 to the hours and then write hours and minutes together without separating
them.
12-hour clock
24-hour clock
0300 hours
(two digits on the left are for hours and two
3:00 a.m.
digits on the right are for minutes. No dot is
used to separate hours from minutes).
9:30 a.m.
0930 hours
12:00 noon
1200 hours
4:30 p.m.
1630 hours
(since 1200 + 0430 = 1630 hours)
9:00 p.m.
2100 hours
CONVERTING THE 24-HOUR CLOCK TIME TO 12-HOUR CLOCK TIME
1200 hours is subtracted from the 24-hour clock time when more than 1200 hours is shown. Write p.m.
next to it.
Write hours and minutes side by side by separating them with dots when less than 1200 hours or 1200
hours is shown. Write a.m. next to it.
24-hour clock
12-hour clock
1700 hours
5:00 p.m.
( since 1700 -- 1200 = 0500 hours)
0430 hours
4:30 a.m.
LEAP YEAR
If the year number is exactly divisible by 4, then it is said to be a leap year. For eg.1988 , 2004 , 1996.
A month usually has 30 or 31 days but February has 28 days and 29 days in a leap year.
The year number which ends with 2 zeroes will be a leap year, only if the year is exactly divisible by
400.
2000 is a leap year as it is divisible by 400.
2100, 2200 , 2300 will not be a leap years as they have 2 zeroes at the end but they are not exactly
divisible by 400.
12 months = 1 year
52 weeks = 1 year
365 days = 1 year
366 days = 1 leap year
TOPIC: PERIMETER, AREAS AND VOLUMES
• Perimeter : The distance around a figure is the perimeter of the figure.
• Area : The amount of surface covered by a figure is known as the area of the figure.
• Volume : The amount of space taken by a solid is known as its volume.
Formulas:
• Area of a square :
• Perimeter of a square : 4 ×
• Area of a rectangle : " × #
• Perimeter of a rectangle = 2 " + #
&
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Area of a triangle = × '( ' *+ ,ℎ ( '.,'/0"
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Perimeter of a triangle = 1 *+ " /0,ℎ *+ '""
Volume of a cube =
×
×
Volume of a cuboid = " × # × ℎ OR ( ' *+ #'
× ℎ 0ℎ,
TOPIC: MONEY (PROFIT AND LOSS)
Formulas (SP- selling price, CP- cost price, L- loss, G- gain)
• when SP > CP
P = SP – CP
SP = P + CP
CP = SP – P
2
P % = 32 × 100
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when CP > SP
L = CP – SP
CP = L + SP
SP = CP – L
4
L % = 32 × 100
TOPIC : PICTORIAL REPRESENTATION OF DATA
Data :
The information in the form of numerical figures, which is used to find out things and to make
decisions, is called data.
Frequency : The number of times a particular observation occurs in the data is known as frequency. If an
observation occurs 6 times in the data, its frequency, is called data.
Bar-Graph : A bar graph represents numerical data by a number of rectangular bars of equal width. The
lengths of the bar graph represent the frequency. Bar graph can be horizontal or vertical. Every
bar graph must have the following features :
a) Title of the bar graph.
b) The horizontal and vertical scales used.
c) The labeling of the scales.
Class VIII
QAP Worksheet
SUBJECT : MATHS
GENERAL INSTRUCTIONS:
• These QAP Worksheets will be discussed in July by the respective teachers in the class.
• QAP worksheets to be done in LE Register.
Objective Questions
Q1. How many thousands make a Lakh?
c. 10 thousands
b. 100 thousands
c. 1 thousands
d. 1 hundreds
Q2. A rope of length 10 m has been divided into 8 pieces of same length. What is the length of each
piece?
c. 1m 20 cm
b. 1 m 25 cm
c. 1m 2 cm
d. 1 m 10 cm
Q3. By how much is 5643879 smaller than 1 crore?
c. 4356121
b. 4366121
c. 4356111
Q4. How many does the digit 9 occur between 1 and 100
c. 19
b. 11
c. 21
Q5. 1512 when rounded off to the nearest 100 is:
c. 1600
b. 1510
Q6. Which of the symbols are never repeated?
c. V, X and C
b. V, X and D
d. 20
c. 1500
d. None of these
c. V, L and D
d. L, K and C
Q7. The difference of the successor and predecessor of 999999 is
c. 2
b. 1
c. 999998
Q8. The sum of two odd numbers is:
a. An odd number
c. A prime number
d. 4356122
d. 1000000
b. An even number
d. None of these
Q9. How many whole numbers are there between 1018 and 1203?
c. 185
b. 186
c. 184
d. None of these
Q10. Which of the following is not zero?
c. 0 X 0
b.
c.
d. 2 + 0
Q11. The HCF of 256 and 400 is?
a. 4
b. 8
c. 16
565
d. 32
Q12. If LCM of two numbers is 600 and the numbers are 150 and 200 then find their HCF.
c. 50
b. 60
c. 75
d. 80
Q13. Find the fraction if numerator is 7 and denominator is one fourth of 16.
7
8
8
a.
b.
c.
d.
8
7
8
&
9
&
Q14. The distance travelled by a car in 2 hours is 150 km. Find the speed of the car if
:
the speed remains the same throughout the trip?
a. 82km/hour
b.65km/hour
c. 70km/hour
d. 64.50km/hour
Q15. What least no. should be added to 23.65 so that it becomes 456.32?
a. 432.67
b. 479.97
c. 452.47
d. 477.57
Q16. The area of a rectangle whose length is 1.235m and width is 0.73m.
a. 0.90155
b. 09.0155
c. 090.155
d. 0901.55
Q17. In a rectangle, sum of any two angles is a
a. Right angle
b. acute angle
d. straight angle
c. obtuse angle
Q18. Length of one side of an equilateral triangle is 4.3cm. Find the perimeter of the
triangle.
a. 12.3cm
b. 12.6cm
c. 12.9cm
d. 12.12cm
Q19. Length and breadth of a box is 8cm and 12cm if its volume is 672cm³ then find its
height?
a. 6cm
b. 7cm
c. 8cm
d. 9cm
Q20. Complete the series 2, 9, 18, 29, ______, 57
a. 42
b. 43
c. 41
d. 44
Q21. Estimate the total number of balls in both the box taken together. (Box A = 54 balls
& Box B = 79 balls)
c. 130
b. 180
c. 145
d. 156
Q22. The product of largest 3 digit number and largest 5 digit number is
c. 9989001
b. 998990011
c. 99899001
d. 9899001
Q23. The value of 32277 ÷ (648-39)
c. 53
b. 530
d. 630
c. 63
Q24. Find the number which when divided by 53 gives 8 as quotient and 5 as remainder?
c. 455
b. 450
c. 431
d. 429
Q25. Solve: 587 X 99 =
c. 57213
b. 58513
Q26. The whole number n when; n+35 =101 is
c. 58113
d. 56413
c. 66
b. 67
c. 61
d. 63
Q27. The cost price of 23 TV sets is Rs. 570055. Find the cost of each such set.
c. Rs. 247885
b. Rs. 24785
c. Rs. 27855
d. Rs. 24855
Q28. Solve: LXXXVI + XXIV =
c. CIX
b. CXI
c. CX
d. CC
Q29. The difference of largest and smallest numbers formed using each of the digits 1, 4,
6, 8, 0 only once is?
c. 75942
b. 10468
c. 79541
d. 86410
Q30. If a is a whole number such that a + a = a, then a =?
c. 1
b. 2
c. 3
d. None of these
Q31. The population of a city is 5054. 4/7 of the total population is eligible for voting and
¾ of them voted. How many people cast their vote?
a. 2016
b. 2356
c. 2166
d. 2266
Q32. Lina bought a second hand car for Rs976.75 and her overhead expense was Rs50.25
She sold it for Rs1037.75 what was her gain or loss
a. Rs 10 loss
b. Rs 15 loss
c. Rs 10 gain
d. none of these
Q33. 5.62 x 36.3 x 0.3, find the digit that is at the ten thousandths place in the product
a. 0
b. 8
c. 5
d. 4
Q34. Madhu gets Rs3.75 and Shrinu gets Rs4.25 everyday as pocket money. in 7 days,
how much more money does Shrinu get than Madhu?
a. Rs 0.50
b. Rs 3.50
c. Rs 4.50
d. Rs 7.50
Q35. A = 25.36 and B = 32.31. Find the value of 2A + B
a. 83.03
b. 81.03
c. 28.31
d. 30.38
Q36. The least number of four digits which is exactly divisible by 9 is
c. 1018
b. 1026
c. 1009
d. 1008
Q37. The population of a town is 517530. If one out of every 15 is reported to be a
literate, find how many literate persons are there in the town?
c. 35402
b. 30542
c. 34502
d. 32540
Q38. In order to make a shirt a length of 2m 75 cm of cloth is needed. How much length
of the cloth will be required for 16 such shirts?
c. 44 m 15 cm
b. 43 m 75 cm
c. 42 m
d. 44 m
Q39. On dividing 55390 by 299 the remainder is 75. Find the quotient using division
algorithm.
c. 195
b. 185
c. 175
d. 581
Q40. A car moves at uniform speed of 75 km/hr. How much distance will it cover in 98
hrs?
c. 6950 kms
b. 7350 kms
c. 7550 kms
d. 7530 Kms
Subjective Questions
Q41. Write 18635079 in the Indian and international systems, and give the number
systems.
names in both
Q42. Write the expanded form of: i) 2,04,32,456 ii) 3,567,900
Q43. The population of a town is 8,65,052. Round the population to the nearest 1000.
Q44. Write XCIX in the Hindu-Arabic system.
Q45. Arrange in ascending order:
i) 23,45,678 ii)83,45,672 iii)9,87,654 iv) 83,45,589
Q46. Make the smallest 8-digit number using the digits 2, 4, 6, 8, 0 and 5. Repeat the digits if required.
Q47. a) Add 365401, 62109 and 3876.
b) Subtract 356789 from 411111.
Q48. Multiply:
i) 4856 by 74
ii) 2985 by 604
Q49. Divide:
i) 40,120 by 32
ii) 34,678 by 29
Q50. A bus covers a distance of 592 km in 8 hours. What is the distance travelled by it in 3 hours?
Q51. The Sharma family loves mangoes. In a month they spent the following amounts on mangoes.
Week 1: Rs. 370
Week2: Rs. 350
Week3: Rs. 300
Week4: Rs. 400
What was their average weekly expense on mangoes?
Q52. Manjunath bought a scooter for Rs. 23,560. He spent Rs. 8350 in getting it repaired and repainted.
Now he wants to sell it to make a profit of Rs. 5000. At what price should he sell scooter?
Q53. A chocolate factory produces 10,000 chocolates everyday. These are packed in boxes of a dozen
chocolates each. The chocolates left over are distributed to the workers. How many boxes are
needed daily? How many chocolates are distributed daily?
Q54. Find the largest number that divides 16 and 36 without leaving a remainder.
Q55. Find the smallest number which when divided by 12 and 5, leaves no remainder.
Q56. Find the HCF and LCM of 12, 16 and 24.
Q57. The product of the HCF and LCM of two numbers is 300. If one of the numbers is 15, what is the
other number.
Q58. Check if 45,036 is divisible by
i) 2
ii)3 iii)4 iv)5 v) 6
vi) 9 vii) 10
7 ; : &&
Q59. Arrange in ascending order: , , ,
; 79 :
Q60. Arrange in descending order 4.5, 4.05, 4.52, 4.051.
7
;
:
Q61. Add and give answer in proper fractions or mixed numbers, in the lowest terms. + +
; 7 9
Q62. a) Add 11.17, 10.7, 0.234
b) Subtract 4.655 from 5.67
Q63. 1.75m of cloth is cut into 12 equal pieces. What is the length of each piece?
Q64. 8 mangoes cost Rs. 250. What is the price of 6 mangoes?
Q65. A box full of books weighs 15 kg 325 g. A book weighing 2 kg 350 g is put into it. How much
does the box weigh now?
Q66. A mug has capacity of 650 ml. 10 mugs of water are used to fil a bucket of capacity 15 litres 500
ml. How much water does the bucket have? How much more water can be filled in it?
Q67. A dozen pens cost Rs. 252. How much do I have to pay for 8 pens?
Q68. The cost of a flight ticket from Srinagar to cochinis Rs. 9875. Thirty-five children of class 5 of
Adarsh School travelled on the flight. What was the total cost of tickets?
Q69. A furniture dealer bought an old sofa set for Rs. 12,555. He spent Rs. 4545 in getting it repaired.
He sold it for Rs. 16000. Did he make a profit or loss? How much?
Q70. Mr Abdul had seventy-five lakh rupees. He bought a house for Rs. 50,12,250 and a car for Rs.
10,23,500. How much money in all did he spend? How much money is left with him?
Q71. Which has a greater area – a square of side 12 cm or a rectangle of length 10cm and breadth
15cm. What is the difference in the area?
Q72. Every morning I walk twice around a rectangular field of length 100 m and breadth 75 m. What
distance do I walk?
Q73. How many cubes of side 2 cm can be fitted inside a box of length 20cm, breadth 20cm and height
10cm?
Q74. Ramya starts studying at 6:25 pm. She studies for 2hrs and 35 minute. In between she takes a
break of 15 minutes. At what time does she stops studying?
Q75. How many bricks
cks of length 10cm, breadth 5cm and height 5cm will be required to build a wall of
length 100cm, breadth 50 cm and height 50 cm?
Q76. A refrigerator has a capacity of 2 cu m. Its width and depth are 1m each. What is its height?
Q77. The price of a box of 6 erasers is Rs. 27. How much do I have to pay for 1224 erasers?
Q78. Rs.100 was equally distributed amongst 8 children. How much money did each child get?
Q79. Find the greatest number that divides 56 and 84 exactly.
Q80. Find the greatest number that divides 28 and 49 without leaving a remainder.
Q81. How many millions make a crore?
Q82. Find the difference between the place values of 9 and 5 in 98456774 .
Q83. Find first two common multiples of 8 and 12, and hence find the LCM.
Q84. Make the greatest and the smallest 66-digit numbers using thee digits 3,8,0,6,5 with the condition
given below (digits can be repeated):
(a) digit 5 is always in the thousands place.
(b) digit 6 is always in the tens place.
Q85. A shopkeeper had 12,00,000 with him. He placed an order for 15 tables at 2825 each and 14
cabinets for 4485 each. What will be the amount lleft
eft with him after the purchase?
Q86. Arrange the following fractions in ascending order.
&9
8
,
&9
:
,
&9
&8
,
&9
&5
= __________________________________________________
Q87. Write all the factors of 81.
Q88. Find first two common multiples of 8 and 12, and hence find the LCM.
Q89. What number is Ten crore more than the largest 88-digit number ?
Q90. Subtract 38, 24,748 from the sum of 54,180; 34,788 and 67,92,354.
Q91. The HCF and LCM of 2 numbers are 173 and 6055 respectively. If one of the numbers is 1211,
find the other number.
Q92. Tea is to be packed in 100, 200, 250 or 500 gm packets. Find the least quantity of tea required so
that the exact number of any kind of packets can be made from it.
Q93. Ravi bought a radio for 480 and sold it for 500. Find his profit
rofit or loss percentage.
Q94. The heights of 4 boys in a class are 150 cm, 154 cm, 158 cm and 152 cm. Find the average height
heigh
of a boy in the group.
Q95. SIMPLIFY
a)
b)
c)
d)
(-13) + (-9) – (-12)
34 – (-12) – 5 – 14
(-544) + (-721) – (-539)
(-401) + (-34) + (+513)
Q96. SIMPLIFY
a)
80 + [20 × { 20 – (10 ÷ 5 )}]
b)
[18 ÷ 6 + {2 x (8-77 of 3) + 17x5}]
c)
1 ÷ [ 1 + 1 ÷ {1 + 1 ÷ (1 + 1 ÷2)}]
d)
4
e)
(
&
:
;
&8
&
9
9
–{
×
8
&: &
- (5 ×
2
&
)}
:
)÷27
Q97. Do the following conversion
a. 56 kl 250 l into litres.
b. 212 km 84 m into km.
c. 2 ml into litres
d. 24 cm into metres
e. 74 cm 545 mm into cm
Q98. The perimeter of a rectangular park is 560 m. Its breadth is 100 m. Find the lengthof the park.
Q99. Find the number which is CDXLVI less than <==DCCXXV.
Q100. The average of five consecutive odd numbers is 61. The difference of the highest and lowest numbers is
_____________.
Q101. Write
a) 28 paise as a percentage of Rs. 1 ;
b) Rs 7 as a percentage of Rs. 35 ;
c) 46 paise as a percentage of Rs. 1.84 ;
d) 8mm as a percentage of 1 cm;
e) 75 m as a percentage of Rs. 1 km ;
f) 7m 25 cm as a percentage of 58 m
Q102. If Seema burns about 304.15 calories while walking fast on her treadmill for 38.5 minutes. About how
many calories does she burn per minute?
Q103. Johar had 5000 in his wallet. He bought petrol for Rs. 1152.90, a pack of chips for 85.45 and a candy
bar for Rs. 0.80. How much money is left with him?
Q104. 24.Manit works Monday through Friday each week. His bus fare to and from work is
How much does Manitspend on bus fare for each week?
3.70 each way.
Q105. There are 100 fruit trees on a farm. 7off them are mango threes. How many mango trees are there?
:
Q106. Sam has 84 book. of them are fiction books. of the fictions are on science fiction. How many science
9
:
fiction books are there ?
9
&
8
&9
Q107. Peter mixed 3 kg of sand to 5
kg of cement. What is the weight of the mixture?
Q108. The cost of a table is the cost of 10 chairs. Find the cost of the table if 1 chair costs Rs. 15?
:
Q109. Find the simple interest on Rs. 4200 for 3 years at 4½% per annum .
Q110. Find the HCF of 513 , 1134 and 1215 by long division method.
Q111. A sum of money at a rate of interest doubles itself in 8 years. In how many years will the same sum
become three times?
Q112. State true or false:
a) Twice of a right angle is an obtuse angle
b) Half of an obtuse angle is always an acute angle
c) The measure of reflex angle of 108 º is 252 º.
Q113. Total number of students of a school in different years is shown in the following table. Draw a
pictograph for this data using 1
Year
2012
Number of students
400
= 100 students.
2013
2014
2015
2016
450
600
800
500
Q114. The following table gives sale figures of cars in a company. Draw a bar graph for it.
Year
2003-04
2004-05
2005-06
2006-07
2007-08
800
1000
1250
1450
1350
Cars sold
2008 - 09
1400
Q115. The length of a rectangle is 1.5m and the breadth is 20cm. Find the area?
Q116. A square garden has a length of 10m.What is the perimeter of the garden?
Q117. The area of a rectangle is 300m2. If its length is 20cm, find its
a) Breadth b) Perimeter
Q118. A play ground has length 40m and width 30m. A boy runs along the boundary of the ground. Find the
distance he runs in while taking one complete round of the ground?
Q119. An agricultural field is rectangular in shape. Its length is 200m and breadth is 125m. Find
a. its area
b. the cost of ploughing the field at the rate of rupees 60 per sqmetre.
Q120. One side of a square is 6cm.Find its a) area b) perimeter
Q121. What is the area of the rectangle drawn on a centimeter grid?
Q122. Write the number name in Indian Number System. - 497666012
Q123. Write the number name in International Number System. – 404811092
Q124. Find the difference between the largest 6-digit number and the smallest 8-digit number.
Q125. If the cost of 24 oranges is
33.60, find the cost of 4 dozens oranges.
Q126. If 48 boxes contain 6000 pens, then how many such boxes will be needed for 1875 pens?
Q127. Write the Hindu Arabic numeral:
(i) MDCCLXVI
(ii) MMMCDXIV
Q128. Write the Roman numeral:
(i) 3291
(ii) 1596
(iii) MMCMLVIII
(iii) 2784
Q129. Write the greatest and the smallest numbers using the digits 5,9,0,3,8,2 and 7.
Q130. Simplify: (i) 16 x 2 - 54 ÷3
(ii) 36 ÷ 4 + 42 – 36 ÷ 3
Q131. Subtract: (i) 756.24 from 10011.344
(iii) 2rupees 5paise from 20rupees
Q132. Arrange in ascending order:
(ii) 234litres 6ml from 2101litres
141.75, 41.989, 0.141, 0.014, 41.75
Q133. A shopkeeper bought 67.2 kg rice from India and 99.34kg rice from China. He mixes the two types of
rice and sold them at a price of $12 per kg. What amount did he earn by selling the rice?
Q134. Divide: (i) 3.2 by 0.005
(ii) 3.24 by 0.0016 (iii) 5.628 by 12
Q135. The length of 15 metal rods is 160.2m, find the length of each rod.
Q136. Rohit bought three pens for $7.55 each, five books for $25 each and a suitcase for $89.35. If he gave
five $50 notes to the shopkeeper, then how much balance will he get back?
Q137. Multiply:
(i) 489.12 x 78
(ii) 12.082 x 0.007
Q138. Following are the number of students in class VI in different years in a school.
Year 2010- 50,
Year 2011- 150,
Year 2012- 100,
Year 2013- 250,
a) Express the given data in tabular form.
b) Represent the above data by a bar graph .
Q139. If two angles of a triangle measure 63°and 74°, then find the third angle.
Year 2014- 200
Q140. Can a triangle have the following measures of angles? Give reason.
43°, 73°, 74°
Q141. Mr. Rao regularly travels 100 km to reach his office. Out of this, he travels 67.09 km by train, 29.98 km
by bus and the remaining distance he needs to walk. Find the distance he walks.
Q142. Following are the number of Mathematics books sold by a shop during the five months in year 2013.
April- 900,
May- 300,
June- 500,
July- 800,
August- 350
a) Express the given data in tabular form.
b) Represent the above data by a bar graph.
Q143. Convert in decimal form as given in bracket:
(i) 50 rupees 5 paise (in rupees)
(ii) 45.378 centilitre (into kilolitre)
(iii) 456mm (into hm)
Q144. Rakesh is 1.35 m tall. Mahesh is 130 cm tall. Who is taller?By how much?
Q145. Salma travelled 15.5 km by metro and 750 m by rickshaw. How many km did she travel in all?
Q146. A play started at 5:45 p. m. and ended at 8:20 p. m. what was the duration of the play?
Q147. Vinay’s exam began on 15 March and ended on 2 April. How long did his exams last?
Q148. Gurpreet runs 1500 m in 5 mins 43 seconds. How many seconds is that?
Q149. The All India School Badminton Championship started at Nagpur on 25 Feb 2012. It lasted for 18 days.
When did it end?
Q150. Find the time or date?
a. 40 mins after 11:40 p.m.
b. 3h 45 min before 23:45 hours
c. 25 days before 15 August
d. 75 days after 1 December