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Practice the worksheet on word problem on multiplication. 1. One complete set of class IV costs $264. How much money did a class of 42 children pay to the bookshop owner, if all of them bought their books from him? 2. One pair of football shoes costs $ 628. Find the cost of
Solved examples on word problems on multiplication.For a school trip 6 buses were hired. Each bus carried 42 children. How many children went on the trip? Solution: 2. The product of two numbers is 96. If one number is 8, find the other. Multiplicand × Multiplier = Product`
Practice the worksheet on word problem on addition and subtraction. 1. In a village, there are 4,318 men, 3,624 women and 5,176 children. What is the total population of the village? 2. In a school, there are 860 children in the pre-primary section, 1,200 children in th
We can make numbers from the given digits. Let us see the rules. Rule I. To get the smallest number, arrange the digits in ascending order from left to right. Rule II. To get the greatest number, arrange the digits in descending order from left to right. Example: Write the
Solved examples on Word problems on addition and subtraction . 1. In a school there are 2,392 boys and 2,184 girls. Find the total number of students in the school. Solution: Number of boys in the school = 2392 Number of girls in the school = + 2184 Total students in the
Practice the worksheet on facts about division. We know, dividend is always equal to the product of the divisor and the quotient added to the remainder. This will help us to solve the given questions. 1. Fill in the blanks: (i) Division is __ subtraction.
Practice the worksheet on facts about multiplication. We know in multiplication, the number being multiplied is called the multiplicand and the number by which it is being multiplied is called the multiplier. This will help us to solve the given questions.
Practice the worksheet on facts about subtraction. Subtraction with small numbers can be worked out horizontally and subtraction with large numbers is worked out vertically. 1. Fill in the missing numbers. (i) Take away 14 from 80 is ______ (ii) 150 decreased by 80 is ____
Practice the worksheet on facts about addition. Addition of small numbers can be done horizontally and large numbers are added in vertical columns. 1. Fill in the missing number/word. (i) 4315 + 101 = 101 + ______ = ______ (ii) 1795 + 241 = 241 + ______
We have learnt multiplication of numbers with 2digit multiplier. Now, we will learn more. Let us know some facts about multiplication. 1. In multiplication, the number being multiplied is called the multiplicand and the number by which it is being multiplied is called the
The operation to finding the difference between two numbers is called subtraction. Let us know some facts about subtraction which will help us to learn subtraction of large numbers. 1. Subtraction with small numbers can be worked out horizontally. Example: 8 – 5 = 3 24 – 4 =
The operation to find the total of different values is called addition. Let us know some facts about addition which will help us to learn to add 4-digit and 5-digit numbers. 1. Addition of small numbers can be done horizontally. Example: 6 + 2 + 3 = 11
We have already learned division by repeated subtraction, equal sharing/distribution and by short division method. Now, we will read some facts about division to learn long division. 1. If the dividend is ‘zero’ then any number as a divisor will give the quotient as ‘zero’.
When we write a number as a sum of place value of its digits, the number is said to be in expended form and when we write a number using digits, the number is said to be in short form. There are 3 ways to write the expanded form. There are 3 ways to write the expanded form
As we know that the division is to distribute a given value or quantity into groups having equal values. In long division, values at the individual place (Thousands, Hundreds, Tens, Ones) are dividend one at a time starting with the highest place.
Two matrices A and B are said to be conformable for the product AB if the number of columns of A be equal to the number of rows of B. If A be an m × n matrix and B an n × p matrix then their product AB is defined to be the m × p matrix whose (ij)th element is obtained by
Practice the problems given in the worksheet on addition of matrices. If M and N are the two matrices of the same order, then the matrices are said conformable for addition, and their sum is obtained by adding the corresponding elements of M and N. 1. Find the sum of A and B
We will discuss about the properties of scalar multiplication of a matrix. If X and Y are two m × n matrices (matrices of the same order) and k, c and 1 are the numbers (scalars). Then the following results are obvious. I. k(A + B) = kA + kB II. (k + c)A = kA + cA III. k(cA)
The operation of multiplying variables by a constant scalar factor may properly be called scalar multiplication and the rule of multiplication of matrix by a scalar is that the product of an m × n matrix A = [aij] by a scalar quantity c is the m × n matrix [bij] where bij
We proceed to develop the algebra of subtraction of matrices. Two matrices A and B are said to be conformable for subtraction if they have the same order (i.e. same number of rows and columns) and their difference A - B is defined to be the addition of A and (-B).
We will discuss about the properties of addition of matrices. 1. Commutative law of addition of matrix: Matrix multiplication is commutative. This says that, if A and B are matrices of the same order such that A + B is defined then A + B = B + A. Proof: Let A = [aij]m × n
We proceed to develop the algebra of matrices. Two matrices A and B are said to be conformable for addition if they have the same order (same number of rows and columns). If A = (aij)m, n and B = (bij)m,n then their sum A + B is the matrix C = (cij)m,n where cij = aij + bij
There are two types of triangular matrices. 1. Upper Triangular Matrix: A square matrix (aij) is said to be an upper triangular matrix if all the elements below the principal diagonal are zero (0). That is, [aij]m × n is an upper triangular matrix if (i) m = n and (ii) aij
We will solve different types of problems on height and distance with two angles of elevation. Another type of case arises for two angles of elevations. In the given figure, let PQ be the height of pole of ‘y’ units. QR be the one of the distance between the foot of the pole
We have already learnt about trigonometry in previous units in detail. Trigonometry has its own applications in mathematics and in physics. One such application of trigonometry in mathematics is “height and distances”. To know about height and distances, we have to start
A scalar matrix whose diagonal elements are all equal to 1, the identity element of the ground field F, is said to be an identity (or unit) matrix. The identity matrix of order n is denoted by In. A scalar matrix is said to be a unit matrix, if diagonal elements are unity.
Equality of two matrix: Two matrices [aij] and [bij] are said to be equal when they have the same number of rows and columns and aij = bij for all admissible values of i and j. Definition of Equal Matrices: Two matrices A and B are said to be equal if A and B have the same
If each element of an m × n matrix be 0, the null element of F, the matrix is said to be the null matrix or the zero matrix of order m × n and it is denoted by Om,n. It is also denoted by O, when no confusion regarding its order arises. Null or zero Matrix: Whether A is a
Here we will discuss about the column matrix with examples. In an m × n matrix, if n = 1, the matrix is said to be a column matrix. Definition of Column Matrix: If a matrix have only one column then it is called column matrix. Examples of column matrix:
In an m × n matrix, if m = 1, the matrix is said to be a row matrix. Definition of Row Matrix: If a matrix have only one row then it is called row matrix. Here we will discuss about the row matrix with examples. Examples of row matrix:
If square matrixes have n rows or columns then the matrix is called the square matrix of order n or an n-square matrix. Definition of Square Matrix: An n × n matrix is said to be a square matrix of order n. In other words when the number of rows and the number of columns in
A rectangular array of mn elements aij into m rows and n columns, where the elements aij belongs to field F, is said to be a matrix of order m × n (or an m × n matrix) over the field F. Definition of a Matrix: A matrix is a rectangular arrangement or array of numbers
One variable quantity is said to vary jointly as a number of other variable quantities, when it varies directly as their product. If the variable A varies directly as the product of the variables B, C and D, i.e., if.A ∝ BCD or A = kBCD (k = constant ), then A varies jointly
When two variables change in inverse proportion it is called as indirect variation. In indirect variation one variable is constant times inverse of other. If one variable increases other will decrease, if one decrease other will also increase. This means that the variables
When two variables change in proportion it is called as direct variation. In direct variation one variable is constant times of other. If one variable increases other will increase, if one decrease other will also decease. This means that the variables change in a same ratio
There are different methods for solving simultaneous linear Equations: 1. Elimination of a variable 2. Substitution 3. Cross-multiplication 4. Evaluation of proportional value of variables This topic is purely based upon numerical examples. So, let us solve some examples
The next method of solving linear equations in two variables that we are going to learn about is method of cross multiplication. Let us see the steps followed while soling the linear equation by method of cross multiplication: Assume two linear equation be A1 x + B1y + C1=
We will discuss about some of the properties of angles of a triangle. 1. The three angles of a triangle are together equal to two right angles. ABC is a triangle. Then ∠ZXY + ∠XYZ + ∠YZX = 180° Using this property, let us solve some of the examples. Solved examples
The three altitudes of triangle are concurrent. The point at which they intersect is known as the orthocentre of the triangle. In the adjoining figure, the three altitudes XP, YQ and ZR intersect at the orthocentre O.
Here we will discuss about Medians and Altitudes of a Triangle. Median: The straight line joining a vertex of a triangle to the midpoint of the opposite side is called a median. A triangle has three medians. Here XL, YM and ZN are medians. A geometrical property of medians
Here we will discuss about classification of triangles on the basis of their sides and angles Equilateral triangle: An equilateral triangle is a triangle whose all three sides are equal. Here, XYZ is an equilateral triangle as XY = YZ = ZX. Isosceles triangle: An isosceles
A triangle is a plane figure bounded by three straight lines. A triangle has three sides and three angles, and each one of them is called an element of the triangle. Here, PQR is a triangle, its three sides are line segments PQ, QR and RP; ; ∠PQR, ∠QRP and ∠RPQ are its
We will solve different types of problems on change the subject of a formula. The subject of a formula is a variable whose relation with other variables of the context is sought and the formula is written in such a way that subject is expressed in terms of the other
Practice the questions given in the worksheet on change of subject When a formula involving certain variables is known, we can change the subject of the formula. What is the subject in each of the following questions? Change the subject as indicated.
Practice the questions given in the worksheet on framing a formula. I. Frame a formula for each of the following statements: 1. The side ‛s’ of a square is equal to the square root of its area A.
We will discuss here about establishing an equation. In a given context, the relation between variables expressed by equality (or inequality) is called a formula. When a formula is expressed by an equality, the algebraic expression is called an equation.
What is Rectangular Cartesian Co-ordinates? Let O be a fixed point on the plane of this page; draw mutually perpendicular straight line XOX’ and YOY’ through O. Clearly, these lines divide the plane
What is co-ordinate geometry? The subject co-ordinate geometry is that particular branch of mathematics in which geometry is studied with the help of algebra. This branch of mathematics was fir
We will discuss here the method of using the table of tangents and cotangents. This table shown below is also known as the table of natural tangents and natural cotangents. Using the table we can