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Binary subtraction is also similar to that of decimal subtraction with the difference that when 1 is subtracted from 0, it is necessary to borrow 1 from the next higher order

Continue reading "Binary Subtraction |Rules of Subtract of Binary Numbers| Binary Decimal Subtract"

We will learn how to divide a number into two parts in a given ratio (i.e., dividing into a given ratio). Let the number be M. It is to be divided into two parts in the ratio a : b. The two parts

Continue reading "Dividing into a Given Ratio | Dividing a Quantity in a given Ratio"

In comparing ratios we will learn how to arrange the ratios. How to Compare Ratios? To compare two ratios, follow these steps: Step I: Make the second term of both the ratios equal.

Continue reading "Comparing Ratios | Comparison of Ratios|Which of the following ratios is grater?"

We will discuss here about the different types of ratios. 1. Compounded ratio: For two or more ratios, if we take antecedent as product of antecedents of the ratios and consequent as product

Continue reading "Types of Ratios |Compounded Ratio|Duplicate Ratio|Inverse Ratio|Triplicate Ratio"

Some of the important properties of ratios are discussed here. 1. Ratio a/b has no unit and can be written as a : b (read as a is to b). 2. The quantities a and b are called terms of the ratio.

Continue reading "Important Properties of Ratios |Ratio in its Lowest Terms|Ratio is a Pure Number"

We will discuss here about the basic concept of ratios. Definition: The ratio of two like quantities a and b is the fraction a/b, which indicates how many times b is the quantity a. In other words

Continue reading "Basic Concept of Ratios | Definition of Ratio | Antecedent : Consequent "

Practice the questions given in the worksheet on solution of a linear inequation in one variable 1. If x ∈ N, find the solution set of the linear inequations. (i) 5x + 3 ≤ 2x + 18

Continue reading "Worksheet on Solution of a Linear Inequation in One Variable | Inequalities"

Practice the questions given in the worksheet on laws of inequality. 1. State true or false (i) x < - y ⟹ -x > y (ii) -5x ≥ 15 ⟹ x ≥ -3 (iii) 2x ≤ -7 ⟹ 2x/-4 ≥ -7/-4

Continue reading "Worksheet on Laws of Inequality | Properties of Inequalitie | Inequations"

Here we will solve various types of problems on linear inequation. By applying the law of inequality, we can easily solve simple inequations. This can be seen in the following examples

Continue reading "Problems on Linear Inequation | Practice with Solving Inequalities"

What are the basic differences between equation and inequation? We have seen that equations are expressed by sign of equality and inequations are expressed by sign of inequality.

Continue reading "Difference Between Equation and Inequation | Inequation vs Equation"

We will discuss here about the replacement set and solution set in set notation. Replacement Set: The set, from which the values of the variable which involved in the inequation, are chosen, is known

Continue reading "Replacement Set and Solution Set in Set Notation | Set of Whole Numbers "

Here we will solve various types of problems on law of inequality. Mark the statement true or false. Justify your answer. (i) If m + 6 > 15 then m - 6 > 3 (ii) If 4k > - 24 then - k > 6. Solution:

Continue reading "Problems on Law of Inequality | Solving Inequalities | Inequality Problem"

Method of Solving a linear inequation algebraically ax + b >, <, ≥, ≤ cx + d To solve a given linear inequation means to find the value or values of the variable used in it.

Continue reading "Solving a Linear Inequation Algebraically | Solving Inequalities | Inequalities"

We will discuss here about the laws of inequality. I. 1. If m > n then (i) m + k > n + k (ii) m – k > n – k, where k is any positive or negative number.

Continue reading "Laws of Inequality | Properties of Inequalities |Law and Inequality |Inequations"

We will discuss here about the linear inequation in one variable. The mathematical statement which says that one quantity is not equal to another quantity is called an inequation.

Continue reading "Linear Inequation in One Variable | Solving Linear Inequations | Inequalities"

Practice the questions given in the worksheet on share and dividend. Michael has a choice to invest in 10-dollar shares of two firms at $ 13 or at $ 16. If the first firm pays 5% dividend and the

Continue reading "Worksheet on Share and Dividend | Dividend on the Shares | Shares at a Premium "

We will discuss here some of the problems on shares and dividends. Michael buys shares of face value $ 50 of a company which pays 10 % dividend. At what price did he buy each share from the

Continue reading "Problems on Shares and Dividends | Dividend, Rate of Dividend | Value of Shares"

We will discuss here some of the problems on income and return from shares. Matthew invested $ 67200 in $ 100 shares which are quoted at $ 120. Calculate the income if 12% dividend is declared

Continue reading "Problems on Income and Return from Shares | Shares and Dividends"

We will discuss here about the calculation of income, return and number of shares. Computation of income and return If the number of shares held by a shareholder = n, rate of dividend = r% per annum

Continue reading "Calculation of Income, Return and Number of Shares | Share and Dividend"

We will discuss here about the dividend and rate of dividend. The part of the annual profit of a company distributed among its shareholders is called dividend.

Continue reading "Dividend and Rate of Dividend | What is the Dividend Rate? | Dividend Rate"

We will discuss here about the share and value of shares. To establish a big business organisations (company or industry), a large number of money is required. It is sometime not possible for

Continue reading "Share and Value of Shares | Face Value of Shares | Market Value of Shares"

Practice the questions given in the worksheet on income and return from shares. William bought $ 40 shares at a premium of 40%. Find the income, if William invests $ 14000 in these shares and receives

Continue reading "Worksheet on Income and Return from Shares | The Rate of Dividend"

Practice the questions given in the worksheet on basic concept on shares and dividends. 1. How much money will be required to buy 200, $ 25 shares at a premium of $ 2?

Continue reading "Worksheet on Basic Concept on Shares and Dividends | Market Price of One Share"

Problems on condition of perpendicularity Here we will solve various types of problems on condition of perpendicularity of two lines. 1. Prove that the lines 5x + 4y = 9 and 4x – 5y – 1 = 0

Continue reading "Problems on Condition of Perpendicularity | Solved Examples on Perpendicularity"

Practice the questions given in the worksheet on equation of a straight line. 1. Determine the equation of the straight line whose gradient is (-3/2) and which intersects the y-axis

Continue reading "Worksheet on Equation of a Straight Line | Equation of Line Worksheet"

Practice the questions given in the worksheet on collinearity of three points using the equation of a line.1. Find the equation of the straight line passing through the points (3, - 4) and (1, 2)

Continue reading "Worksheet on Collinearity of 3 Points | Collinearity of Points"

Practice the questions given in the worksheet on point-slope form of the straight line. If the slope = m and the line passes through the point (x1, y1), the equation of the lien is y - y1 = m(x - x1)

Continue reading "Worksheet on Point-slope Form | Point-slope Form (Practice Worksheet)"

Practice the questions given in the worksheet on two-point form of the straight line. If a straight line passes through the points (x1, y1) and (x2, y2) then its equation is y - y1 =

Continue reading "Worksheet on Two-point Form | Two Point Form Worksheet | Slope From Two Points"

Practice the questions given in the worksheet on slope and intercepts of the straight line. 1. Write the slope of the straight line whose inclination is (i) 30° (ii) 60° (iii) 45° (iv) 150° (v) 135°

Continue reading "Worksheet on Slope and Intercepts |Slopes & Inclinations of the Straight Lines "

Practice the questions given in the worksheet on slope intercept form of a straight line. 1. Find the equation of the line (i) whose slope is 2 and which cuts off an intercept 2 on the y-axis

Continue reading "Worksheet on Slope Intercept Form | Slope-intercept Form Worksheet"

We will discuss here about the condition of parallelism. If two lines are parallel then they are inclined at the same angle θ with the positive direction of the x-axis. So, their slopes are equal.

Continue reading "Condition of Parallelism | What Is The Condition Of Parallelism Of Two Lines? "

We will discuss here about the condition of perpendicularity of two straight lines. Let the lines AB and CD be perpendicular to each other. If the inclination of AB with the

Continue reading "Condition of Perpendicularity of Two Straight Lines | Perpendicularity Condition"

We will learn how to find the slope and y-intercept of a line. Consider the following steps to find the slope and y-intercept of a given line: Step I: Convert the given equation of the line in the

Continue reading "Slope and Y-intercept of a Line | Calculating Slope and Y Intercept | Examples"

Equally inclined lines mean: the lines which make equal angles with both the co-ordinate axes.

Continue reading "Equally Inclined Lines | Equally Inclined Lines Mean | Solved Example"

We will discuss here about the method of finding the equation of a straight line in the two point form. To find the equation of a straight line in the two point form, Let AB be a line passing

Continue reading "Two-point Form of a Line |Two-point Form y - y1 = [(y1 - y2)/(x 1 - x2)](x - x1)"

We will discuss here about the method of finding the point-slope form of a line. To find the equation of a straight line passing through a fixed point and having a given slope, let AB be the line

Continue reading "Point-slope Form of a Line |Point-slope Form y - y1 = m(x - x1)|Point-slope Form"

We will discuss here about the method of finding the equation of a straight line in the slope-intercept form. Let the straight line AB intersect x-axis at C and y-intersect at D.

Continue reading "Slope-intercept Form |Slope-Intercept Form y=mx + b|Line in slope-intercept form"

We will discuss here about the meaning of equation of a straight line. Let the straight line be PQ which passes through the origin (0, 0) and inclined at 45° with the positive direction of the x-axis.

Continue reading "Equation of a Straight Line | Meaning of 'Equation of a Straight Line'"

We will discuss here about the slope of the line joining two points. To find the slope of a non-vertical straight line passing through two given fixed points: Let P(x1, y1) and Q (x2, y2) be the two

Continue reading "Slope of the Line Joining Two Points | Slope of a Line from Two Points"

We will discuss here about the intercepts made by a straight line on axes or intercepts of a line made on the axes of reference. Let a straight line ‘MN’ does not passes through the origin

Continue reading "Intercepts Made by a Straight Line on Axes | Convention for signs of intercepts"

We will discuss here about the slope of a line or gradient of a line. If θ (≠ 90°) is the inclination of a straight line, then tan θ is called its slope or gradient. The slope of any inclined

Continue reading "Slope of a Line | Slope of a Straight Line | Concept of Slope | Find the Slope"

The inclination of a line is the angle θ which the part of the line (above the x-axis) makes with x-axis. If measured in anti-clockwise direction then the inclination θ is positive and if measured

Continue reading "Inclination of a Line | Angle of Inclination | Inclination of a Straight Line"

Practice the questions given in the worksheet on section formula. To find the co-ordinates of a point which divides the line segment joining two given points in a given ratio.

Continue reading "Worksheet on Section Formula | Point of Trisection of the Line Segment "

Practice the questions given in the worksheet on finding the centroid of a triangle. We know the centroid of a triangle is the point of intersection of its medians and it divides each median in

Continue reading "Worksheet on Finding the Centroid of a Triangle | Centroid of a Triangle"

The Centroid of a triangle is the point of intersection of the medians of a triangle. To find the centroid of a triangle Let A (x1, y1), B (x2, y2) and C (x3, y3) are the three vertices of the ∆ABC.

Continue reading "Centroid of a Triangle | How to Find the Centroid of a Triangle? | Examples"

We will discuss here how to use the midpoint formula to find the middle point of a line segment joining the two co-ordinate points. The coordinates of the midpoint M of a line segment AB

Continue reading "Midpoint Formula | How Do You Find the Midpoint Between Two Coordinates?"

We will proof the definition of section formula. Section of a line segment Let AB be a line segment joining the points A and B. Let P be any point on the line segment such that AP : PB = λ : 1

Continue reading "Section Formula | Section of a Line Segment | Definition of Section Formula"

Practice the questions given in the worksheet on collinearity of three points. We know that in general, P, Q and R are collinear if the sum of the lengths of any two line segments among PQ, QR and RP

Continue reading "Worksheet on Collinearity of Three Points |Condition of Collinearity of 3 Points"

We will discuss here how to use the distance formula in geometry. 1. Show that the points A (8, 3), B (0, 9) and C (14, 11) are the vertices of an isosceles right-angled triangle. Solution:

Continue reading "Distance Formula in Geometry | Practice with Distance Formula | Distance Formula"

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