Types of Fractions
The fraction whose numerator is smaller than the denominator is called proper fraction. The fractions 
are proper fractions 
The fractions whose numeratoris greater than the denominator is called improper fractions. The fractions,
are improper. A mixed Fraction has both whole and fractional parts. The fraction 
is a mixed fraction. 3 is the whole part and 
is the fractional part of the mixed fraction 
Express the shaded parts of the following figures in its equivalent mixed fractions.
(a) 
(b) 
(c) 
(d) All of these
(e) None of these
Answer (b)
Explanation:
A whole figure is completely shaded and represented by 1and another same figure is divided into four parts and its three parts areshaded. Hence theshaded parts is represented by 
Thus, their sum 
Half of a whole
When a whole number or object is divided into two equal parts, each part is called half of the whole part. The half of a whole number is obtained by multiplying the number by 
and the half of a figure is obtained by dividing the figure into two equal parts. In the figure given below, the shaded part of the figure is same as theunshaded part of the figure. Therefore, the shaded part of the figure is exactly half of unshaded part of the figure. One half of a figure covers completely to the otherhalf of the same figure.
Quarter of a Whole
When a number or figure is divided into four equal parts each one part is called quarter of the number and it is written as 
The quarter part of a number 56 is obtained by multiplying the number by 
Therefore, the quarter of 
In the figure given below there are four same figures made by cutting a paper. One of them is shaded therefore, one of 4 figures is shaded and written as the shaded part of the figure is
Three Quarter or Three - Fourths
If a number or a figure is divided into four equal parts then three parts out of fourhree quarter of the number or figure. Three quarter of a number is more... 
Introduction
The Latin name of fraction is fractious. It means broken. Fractions are always in ratio form and it has two parts upper and lower part. The upper part is called numeratorand the lower part is denominator. Lower part represents the whole which is divided into. Upper part represents a part of whole. In this chapter we will learn about thefractions and its type.
Numerator and Denominator of A Fraction
A fraction has two parts, upper part is known as NUMERATOR and lower part is known as DENOMINATOR and they are separated by a line known as DIVISION
LINE. Denominator states the total number of parts in which whole is divided. Numerator states that number of part which is taken from whole. In the fraction given below 3 is numerator and 5 is denominator.
Hence, the fraction is a part of a whole. It is represented by
division line between a and b separate it into two parts.
Look at the following figures of whole:
In the above figures both the figures are in whole because there are no division line across the figure.
Look at the folio wing figures of fractional parts of whole figure:
In the figures above both the figures are divided into two different parts. The shaded part of the figure is exactly half of the whole and said to be shaded part of the figure is
of the whole figure. In the fraction 
represents the number of parts in which the whole figure is divided into and 1 represents the shaded part or one part of the figure. Another figure is divided into four equal parts and its one part is shaded. Therefore, the shaded part of the figure is 
In the fraction 
represents the number of parts in which whole figure is divided and 1 represents the shaded or one part of the figure.
In the figure given below find the shaded parts of the whole figure.
(a) 
(b) 
(c)
(d) All of these
(e) None of these
Answer: (a)
Explanations Given figure is divided into five equal parts, its three parts are shaded. 
Division by Forming Groups
There are 24 scissors given below. 24 scissors are arranged in such a way that each group contains 8 scissors. Therefore, 3 groups of scissors containing 8 scissors each will form as shown below.
Hence, 
is defined as if 24 scissors are arranged in 3 groups then each one group will contain 8 scissors.
Arrange the following pencils in groups in such a way that each group can contain 5 pencils. How many groups will form?
(a) 4
(b) 5
(c) 7
(d) 3
(e) None of these
Answer (a)
Explanation
20 - 5 = 4. Hence, 4 groups of 5 pencils in each group will form.
Division on Number Line
Division of 24 by 8 on number line is performed by the following steps:
Step 1: Draw a line and divide it into 24 equal parts.
Step 2: Write numbers on each division.
Step 3: Start counting for each 8 from right and count how many 8 are there on the number line.
Step 3: Therefore 3 is the division of 24 by 8.
Which one of the following options is correct for the division of 6 by 2 on number line?
(a)
(b)
(c)
Answer (b)
Explanation
In the option (b) a number is divided into 6 equal parts and there are 3 groups of division are there on the number line and each group contains 2 division.
Division by Long Division Method
The following steps are used for the division of 4563 by 7:
Step 1: Arrange the numbers as: 
Step 2: Consider the minimum dividend from 4563 as 45 because 4 is smaller than divisor 7.
Step 3: Recite the table of 7 till equal to 45 or nearest to 45 and write required number of times of 6 as quotient and their product 42 below 45 and subtract them as shown below.
Step 4: Write the next number from dividend after the remainder.
Recite the table of 7 till equal to 36 or nearest to 36 and write required number of times of 5 as quotient and their product 35 below 36 and subtract them shown below.
Step 5: Write the next number from dividend after the remainder.
Recite the table more... 
Properties of Division
Division by Distribution
There are 12 pieces of apples and which are distributed among 4 boys. If each boy gets one piece, then 12 - 4 = 8 pieces of apples will left over and again one piece of apple is distributed among the boys, now each boy gets 2 pieces of apples and 8 – 4 = 4 pieces of apples are left. Now the number of remaining pieces of apples is 4. These apples are again distributed among 4 boys and each gets one apple.
From the above distribution of apples we can say that everyone gets 3 apples.
Hence, 
.
The following cakes are distributed equally among 3 boys. Find the number of cakes which is obtained by every one?
(a) 3
(b) 4
(c) 5
(d) 6
(e) None of these
Answer (c)
Explanation 15 cakes are distributed among 3 boys. Hence, everyone gets
cakes. 
Commutative or Order Property of Multiplication
The numbers can be multiplied in either order or on changing the order of the numbers then the resulting product of the numbers does not change. The product of 56 and 67, 67 x 56 = 3752. The product of the numbers 56 and 67 on changing their order = 56 x 67 = 3752 is same as the product in the previous order. Therefore, multiplication is commutative.
The product of two numbers M and N is same as the product of the numbers A and B. Which one of the following options is correct about the above statement?
(a) M x N = A x B
(b) M x A = N x B
(c) Both A and B
(d) M x B = N x A
(e) None of these
Answer (a)
Explanation
Explications Product of M and N is equal to the product of A and B. Hence,
M x M = A x B.
Associative or Grouping Property of Multiplication
The product of three numbers remains same even if the group of the numbers is changed. The product of the numbers 21, 4 and 25 when written in the order of (21 x 4) x 25 = 84 x 25 = 2100 and the product of the same numbers 21, 4 and 25 is same when written in the order of 21 x (4 x 25) = 21 x 100 = 2100. If three numbers are denoted by a, b and c then their product (a x b) x c = a x (b x c).
The product of group of the numbers A and B with a number C is same as the another group of A and C with B. Which one of the following options is correct about the above statement?
(a)
(b)
(c)
(d) All of these
(e) None of these
Answers (b)
Explanation According to the associative property of multiplication (A x B) x C = (A x C) x B is a true statement.
Multiplicative Property of Zero (Or Null property)
The product of a number and zero is always zero. Therefore, 34 x 0 = 0, 0 x 45 = 0.
For a number N, the product of N by zero is zero or N x 0 = 0, 0 x N = 0.
What should be multiplied with the number 58765 to get zero?
(a) 2
(b) 1
(c) 0
(d) All of these
(e) None of these
more... 
Introduction
Multiplication means repeated addition. The symbol for the notation of multiplication is x. Sometime a dot mark (.) is used for the notation of multiplication. If there is no sign between two or more numbers then the product sign is considered. Two variables x and y when written as 
there is a product sign between x and y. In this chapter we will learn about the multiplication or product of numbers.
Multiplication and its Properties
The multiplication of 3 and 4 is the addition of 4 times 3 = 3 + 3 + 3 + 3 = 12 or it is the addition of 3 times of 4 = 4 + 4 + 4 = 12. The resulting numbers of both the addition are same. In the short form, the multiplication of 3 and 4 is written as 3 x 4 or 4 x 3. In 4 x 3, 4 and 3 are multiplicand and multiplier respectively and their multiplication 12 is called product. Therefore, in a multiplication the number which is multiplied is known as multiplicand, the number by which it is multiplied is known as multiplier and the answer or the result of multiplication is known as product. The multiplication of a number with zero is always zero. e.g. 4252 x 0 = 0 and the product of a number by 1 is the number itself, e.g. 6240 x 1 = 6240.
Multiplication of a Number by 10, 100 and 1000
The product of 7456 by 10 is obtained by placing one zero after the multiplicand or 7456 = 7456 x 10 = 74560. The product of a number by 100 is obtained by simply placing 2 zeroes after the number. Therefore, the product of the number 8765 by 100 = 8765 x 100 = 876500. The product of a number by 1000 is obtained by simply placing 3 zeroes after the number. Therefore, the product of the number 56438 by 1000 = 56438 x 1000 = 56438000. So, in order to multiply the number by 1,000, 2,000, 5,000, etc. The given number of thousands (i.e. by 1, 2, 5, etc.) should be multiplied to the number and then put three zeroes at the end from left, i.e.
and put 3 zeroes = 35000.
A train travels a distance of 90 kilometres in 1 hour. The distance covered by the train in 10 hours is:
(a) 900km
(b) 1000km
(c) 1090km
(d) All of these
(e) None of these
Answer (a)
Explanation 90 x 10 = 900 km (Multiplying 90 and I and putting the number of zeroes that multiplier containing).
Multiplication of Three Digit Numbers more... 
Subtraction of Decimal Numbers
The following steps are used for the subtraction of decimal numbers (324.567 -187.793);
Step 1: Arrange the numbers in column, whole parts of the subtrahend under the whole part of minuend and decimal part of the subtrahend under decimal part of minuend.
Step 2: Subtract the numbers starting from right or ones.
Step 3: Take borrow from the minuend if required.
Step 4: The resulting number is the difference of the decimal numbers.
Area of a rectangular field is 56.80 sq. metres and a square shaped flower park is exactly at the centre of the rectangular field whose area is 36.45 sq. metres.
The area of rectangular field excluding the area of squared flower park is:
(a) 16.25 square metre
(b) 26.149 square metre
(c) 20.35 square metre
(d) All of these
(e) None of these
Answer (c)
Explanation
Whole pare Decimal point Decimal part
T O Tenths Hundredths
5 6 . 
0
- 3 6 . 4 5
2 0 . 3 5
There are 45 number of chairs and 56 number of tables in a furniture shop.
Punit wants to buy 4 more pieces of chairs and 5 more Pieces of tables. The total number of chairs and tables bought by Punit is:
(a) 49 chairs and 61 tables
(b) 26 chairs 49 tables
(c) 49 chairs and 60 tables
(d) All of these
(e) None of these
Answer (a)
Explanations Total number of chairs is bought by Punit = 45 + 4 = 49 and total number of tables is bought by Punit = 56 + 5 = 61.
The number of children in a school is 4500. School management provides dresses to all of them except 234 girls. The total number of dresses provided by the management is:
(a) 4266
(b) 4431
(c) 4341
(d) 4231
(e) None of these
Answer (a)
Explanations Total number of dresses provided by school management =
Total number of students - Total number of girls students = 4500 - 234 = 4266.
Subtract the following: 7x - x.
(a) 5x
(b) 6x
(c) 3x
(d) 7x
(e) None of these
Answer (b)
Explanation
more... 
Introduction
Numbers are useful in counting quantities that we see around us in our daily life. The numbers that we use our country is the Hindu - Arabic numerals. Aryabhatta developed the place value of Hindu Arabic numerals and Brahmagupta introduced the symbol for zero. Hindu Arabic numerals were basically developed in India and laterally accepted by Arabians so called Hindu Arabic numerals. In this chapter we will learn about Hindu - Arabic numbers and their comparison with Roman and International number system. Natural Numbers Counting numbers are known as natural numbers. There are infinite natural numbers starting from 1. Natural number is denoted by N. 
Which one of the following numbers is not a natural number? (a) -3 (b) 3 (c) 2 (d) 50 (e) None of these Answer (a) 
Whole Numbers The counting numbers including 0 are known as whole numbers. If counting numbers start from 0 then they include the set of whole numbers. Whole number is denoted by W. Prime Numbers The number which has only two factors, 1 and the number itself is called prime number. The number 2 does not have the factors other than 1 therefore, 2 is a prime number. 2 is only from the group of even numbers which has only two factors, so it is called even prime number. Look at the following table of prime numbers between 1 and 100:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 11 | 12 | more...
 Triangles
A plane figure bounded by three straight lines is called a triangle. The figure given below is a triangle ABC. The straight line AB, BC and CA are the line segments,
Therefore, the triangle ABC has: three sides, AB, BC and CA. Three angles B and  and three vertices A, B and C. 
Remember the following about a triangle:
A figure has three sides and three vertices if one of the angle of a figure is given then which one of the following is the name of the figure?
(a) An angle
(b) A point
(c) A triangle
(d) All of these
(e) None of these
Answer (c)
Explanation
A figure has three sides and three vertices. Hence, the name of the figure is triangle.
 Equilateral Triangle A triangle whose all sides are equal is called an equilateral triangle. In the given , AB = BC = CA =4 cm. Therefore, is an equilateral triangle. If the sides of a triangle are equal then its angles are also equal. Therefore, an equilateral triangle has equal sides and equal angles. In the given figure, the angles of the triangle are  Sum of the anglesof a triangle is always 
Therefore, 
Remember the following about the equilateral triangle:
Two angles of a triangle are equal. If third angle is half of the sum of two angles then which one of the following is the name of the triangle?
(a) A right angle
(b) An equilateral triangle
(c) Isosceles triangle
(d) All of these
(e) None of these
Answer (b)
Explanations: Let the angle of a triangle is 
Then third angle  more...  A Right Angle
When a straight line stands upright (perpendicular) on another straight line a right angle is formed. In the given figure, a straight line AB stands upright on the another straight line BC thus the ABC is formed is called a right angle. The line AB stands upright on BC called perpendicular line to BC and represented by AB -L BC. A right angle is represented by a box as shown in the figure. The measurement of a right angle is always  (90 degree). In the given figure 
Remember the following about a right angle:
Which one of the following options represents a right angle?
(a) 
(b) 
(c) 
(d) All of these
(e) None of these
Answer (c)
Explanation: A square box at the vertex represents the right angle.
Acute Angle
If the measurement of an angle is less than a right angle or 90° then it is called an acute angle. In the figure given below, is less inclined than the angle shown by a square box of right angle. Hence, is an acute angle.
Obtuse Angle
If the measurement of an angle is more than a right angle or  but less than two right angles or  then the angle is called an obtuse angle. In the given figure  is an obtuse angle.
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