Reducing Equations to Simpler Form | Class 8 Maths Last Updated : 15 Apr, 2025 Summarize Comments Improve Suggest changes Share Like Article Like Report Reducing equations is a method used to simplify complex equations into a more manageable form. This technique is particularly useful when dealing with non-linear equations, which cannot always be solved directly. By applying specific mathematical operations, such as cross-multiplication, these equations can often be transformed into linear equations, making it easier to find the value of the variable.Reducing equations is a method of solving a complex equation and writing the equation into a simpler form. Not all the equations are in the form of linear equationsTable of ContentLinear equationSteps for Reducing Equations to Simpler FormLet us now take some examples to understand the method of reducing equations in simpler form.Example 1. x - 1 / x + 2 = 1 / 6Example 2. 2x - 3 / 2x + 2 = 1 / 6Example 3. x/2 - 1/5 = x/3 + 1/4Example 4. x - 1 = x/3 + 3/4Linear equationLinear equation is an equation of the first order, but they can be solved by putting them into the form of linear equations by performing some mathematical operations on them like cross-multiplication. After reducing these non-linear equations in linear form, they can be solved, and the value of the variable can be calculated easily. Steps for Reducing Equations to Simpler Form1. If the given equation is in non-linear form, so it cannot be directly solved. Therefore, first, we will need to simplify the given equation by using the Cross Multiplication technique.2. Cross-multiply both sides of the equation i.e. the denominator on one side is multiplied by the numerator on the other side.3. Use the distributive law to open the brackets.4. Bring all the variables on one side (LHS) and constants on the other side of the equation (RHS)5. Solve the rest of the equation as a linear equation in one variable. x - y / y = y - x / xStep 1 : Doing cross multiplication we get: x (x - y) = y (y - x) x2 - xy = y2 - xyStep 2 : Bring all the x variables on one side i.e. LHS and all the y variable on the other side i.e. RHS x2 - xy + xy = y2 x2 = y2Step 3 : Taking square root on both the side we get, x = yLet us now take some examples to understand the method of reducing equations in simpler form.Example 1. x - 1 / x + 2 = 1 / 6Solution :Step 1 : As the equation is in non-linear form, so this cannot be directly solved. Therefore, first we will need to simplify the given equation by using the Cross Multiplication technique. x - 1 / x + 2 = 1 / 6Cross Multiplication technique : The denominator on both sides are multiplied to the numerator on the other side.Step 2 : After cross multiplication, the equation can be written as: 6 (x - 1) = 1 (x + 2) Step 3 : Now open the parentheses by using distributive law 6x - 6 = x + 2Step 4 : Bring all the variables on one side i.e. LHS and all the constants on the other side i.e. RHS 6x - x = 2 + 6 5x = 8Step 5: Dividing both the sides by 5 x = 8/5Example 2. 2x - 3 / 2x + 2 = 1 / 6Solution : = 2x - 3 / 2x + 2 = 1 / 6 [simplifying the given equation by using the Cross Multiplication technique]= 6 (2x - 3) = 1 (2x + 2) =12x - 18 = 2x + 2 [using distributive law]=12x - 2x = 2 + 18=10x = 20= x = 2 [Dividing both the sides by 10]Example 3. x/2 - 1/5 = x/3 + 1/4Solution :As the given equation is in the complex form, we have to reduce it into a simpler form.= Take the L.C.M. of the denominators 2, 5, 3 and 4 which is 60.= x * 60 / 2 - 1 60 / 5 = x * 60 /3 + 1 * 60 /4 [Multiply both the sides by 60]= 30x −12 = 20x + 15= 30x − 20x = 15 + 12=10x = 27= x = 2.7 [Dividing both the sides by 10]Example 4. x - 1 = x/3 + 3/4Solution:= Take the L.C.M. of the denominators 3 and 4 which is 12.= x * 12 - 1 * 12 = x * 12 /3 + 3 * 12 /4 [Multiply both the sides by 12]= 12x −12 = 4x + 9= 12x − 4x = 9 + 12 = 8x = 21= x = 21/8 [Dividing both the sides by 8]Related Articles:Difference Between Linear and Non-Linear EquationsEquations Reducible to Linear FormReduction FormulaAlgebra in MathSummaryReducing equations to a simpler form is an essential technique in algebra, especially when dealing with non-linear equations. By transforming these equations into linear ones, we can apply straightforward algebraic methods to solve them. The process typically involves cross-multiplication, distribution, and rearranging terms to isolate the variable. Comment More infoAdvertise with us Next Article Equations Reducible to Linear Form M Mandeep_Sheoran Follow Improve Article Tags : Mathematics Maths Linear Equations Maths-Class-8 Similar Reads CBSE Class 8th Maths Notes CBSE Class 8th Maths Notes cover all chapters from the updated NCERT textbooks, including topics such as Rational Numbers, Algebraic Expressions, Practical Geometry, and more. Class 8 is an essential time for students as subjects become harder to cope with. At GeeksforGeeks, we provide easy-to-under 15+ min read Chapter 1: Rational Numbers Rational NumbersA rational number is a type of real number expressed as p/q, where q ≠0. Any fraction with a non-zero denominator qualifies as a rational number. Examples include 1/2, 1/5, 3/4, and so forth. Additionally, the number 0 is considered a rational number as it can be represented in various forms such a 9 min read Natural Numbers | Definition, Examples & PropertiesNatural numbers are the numbers that start from 1 and end at infinity. In other words, natural numbers are counting numbers and they do not include 0 or any negative or fractional numbers.Here, we will discuss the definition of natural numbers, the types and properties of natural numbers, as well as 11 min read Whole Numbers - Definition, Properties and ExamplesWhole numbers are the set of natural numbers (1, 2, 3, 4, 5, ...) plus zero. They do not include negative numbers, fractions, or decimals. Whole numbers range from zero to infinity. Natural numbers are a subset of whole numbers, and whole numbers are a subset of real numbers. Therefore, all natural 10 min read Integers | Definition, Examples & TypesThe word integer originated from the Latin word “Integer†which means whole or intact. Integers are a special set of numbers comprising zero, positive numbers, and negative numbers. So, an integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of intege 8 min read Rational NumbersRational numbers are a fundamental concept in mathematics, defined as numbers that can be expressed as the ratio of two integers, where the denominator is not zero. Represented in the form p/q​ (with p and q being integers), rational numbers include fractions, whole numbers, and terminating or repea 15+ min read Representation of Rational Numbers on the Number Line | Class 8 MathsRational numbers are the integers p and q expressed in the form of p/q where q>0. Rational numbers can be positive, negative or even zero. Rational numbers can be depicted on the number line. The centre of the number line is called Origin (O). Positive rational numbers are illustrated on the righ 5 min read Rational Numbers Between Two Rational Numbers | Class 8 MathsReal numbers are categorized into rational and irrational numbers respectively. Given two integers p and q, a rational number is of the form p/q, where q > 0. A special case arises when q=1 and the rational number simply becomes an integer. Hence, all integers are rational numbers, equal to p. Th 6 min read Chapter 2: Linear Equations in One VariableAlgebraic Expressions in Math: Definition, Example and EquationAlgebraic Expression is a mathematical expression that is made of numbers, and variables connected with any arithmetical operation between them. Algebraic forms are used to define unknown conditions in real life or situations that include unknown variables.An algebraic expression is made up of terms 8 min read Linear Equations in One VariableLinear equation in one variable is the equation that is used for representing the conditions that are dependent on one variable. It is a linear equation i.e. the equation in which the degree of the equation is one, and it only has one variable.A linear equation in one variable is a mathematical stat 7 min read Linear Equations in One Variable - Solving Equations which have Linear Expressions on one Side and Numbers on the other Side | Class 8 MathsLinear equation is an algebraic equation that is a representation of the straight line. Linear equations are composed of variables and constants. These equations are of first-order, that is, the highest power of any of the involved variables i.e. 1. 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The diagonals of a square are equal in length and bisect each other at right angles.Squares are used in various f 5 min read Chapter 4: Practical Geometry Construction of a QuadrilateralIt is famously said that Geometry is the knowledge that appears to be produced by human beings, yet whose meaning is totally independent of them. Practical geometry is an important branch of geometry that helps us to study the size, positions, shapes as well as dimensions of objects and draw them wi 7 min read Chapter 5: Data HandlingData HandlingData handling is the process of systematically collecting, organizing, analyzing, and presenting data to extract useful information and support decision-making. 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This circular graph divides data into slices, each representing a proportion of the whole, allowing for a clear comparison of different categories making it ea 11 min read Chance and ProbabilityChance is defined as the natural occurrence of any event without any interference, we can also say that the possibility of any event is the chance of the event, and mathematically we define the chance as the probability of an event.Probability refers to the likelihood of the occurrence of an event. 9 min read Random Experiment - ProbabilityIn a cricket match, before the game begins. Two captains go for a toss. Tossing is an activity of flipping a coin and checking the result as either “Head†or “Tailâ€. Similarly, tossing a die gives us a number from 1 to 6. All these activities are examples of experiments. An activity that gives us a 11 min read Probability in MathsProbability is the branch of mathematics where we determine how likely an event is to occur. It is represented as a numeric value ranging from 0 to 1. Probability can be calculated as:\text{Probability} = \dfrac{Favourable \ Outcome}{Total \ Number \ of \ Outcomes}Favourable outcomes refer to the ou 4 min read Chapter 6: Squares and Square RootsSquares and Square RootsSquares and Square roots are highly used mathematical concepts which are used for various purposes. Squares are numbers produced by multiplying a number by itself. Conversely, the square root of a number is the value that, when multiplied by itself, results in the original number. Thus, squaring and 13 min read How to Find Square Root of a Number?In everyday situations, the challenge of calculating the square root of a number is faced. What if one doesn't have access to a calculator or any other gadget? It can be done with old-fashioned paper and pencil in a long-division style. Yes, there are a variety of ways to do so. Let's start with dis 12 min read Pythagorean TriplesPythagorean triples are sets of three positive integers that satisfy the Pythagorean Theorem. This ancient theorem, attributed to the Greek mathematician Pythagoras, is fundamental in geometry and trigonometry. The theorem states that in any right-angled triangle, the square of the length of the hyp 13 min read Chapter 7: Cubes and Cube Roots Cube RootsA cube root of a number a is a value b such that when multiplied by itself three times (i.e., b \times b \times b), it equals a. Mathematically, this is expressed as:b3 = a, where a is the cube of b.Cube is a number that we get after multiplying a number 3 times by itself. For example, 125 will be t 7 min read Check if given number is perfect cubeGiven a number N, the task is to check whether the given number N is a perfect cube or not. Examples: Input: N = 216 Output: Yes Explanation: As 216 = 6*6*6. Therefore the cube root of 216 is 6.Input: N = 100 Output: No Table of ContentNaive Approach:Using Build-in Functions: Using Prime Factors :Us 15+ min read Chapter 8: Comparing QuantitiesRatios and PercentagesRatios and Percentages: Comparing quantities is easy, each of the quantities is defined to a specific standard and then the comparison between them takes place after that. Comparing quantities can be effectively done by bringing them to a certain standard and then comparing them related to that spec 6 min read Fractions - Definition, Types and ExamplesFractions are numerical expressions used to represent parts of a whole or ratios between quantities. They consist of a numerator (the top number), indicating how many parts are considered, and a denominator (the bottom number), showing the total number of equal parts the whole is divided into. For E 7 min read PercentageIn mathematics, a percentage is a figure or ratio that signifies a fraction out of 100, i.e., A fraction whose denominator is 100 is called a Percent. In all the fractions where the denominator is 100, we can remove the denominator and put the % sign.For example, the fraction 23/100 can be written a 5 min read Discount FormulaDiscount in Mathematics is defined as the reduction in price of any service and product. Discount is offered by the business owner to easily and quickly sell their product or services. Giving discounts increases the sales of the business and helps the business retain its customer. Discount is always 9 min read Sales Tax, Value Added Tax, and Goods and Services Tax - Comparing Quantities | Class 8 MathsTax is a mandatory fee levied by the government to collect revenue for public works providing the best facilities and infrastructure.The first known Tax system was in Ancient Egypt around 3000–2800 BC, in First Dynasty of Egypt. The first form of taxation was corvée and tithe. In India, The Tax was 5 min read Simple InterestSimple Interest (SI) is a method of calculating the interest charged or earned on a principal amount over a fixed period. It is calculated based solely on the principal amount, which remains unchanged throughout the calculation.Simple Interest is widely used across industries such as banking, financ 9 min read Compound Interest | Class 8 MathsCompound Interest: Compounding is a process of re-investing the earnings in your principal to get an exponential return as the next growth is on a bigger principal, following this process of adding earnings to the principal. In this passage of time, the principal will grow exponentially and produce 9 min read Compound InterestCompound Interest is the interest that is calculated against a loan or deposit amount in which interest is calculated for the principal as well as the previous interest earned. Compound interest is used in the banking and finance sectors and is also useful in other sectors. A few of its uses are:Gro 9 min read Chapter 9: Algebraic Expressions and Identities Algebraic Expressions and IdentitiesAn algebraic expression is a mathematical phrase that can contain numbers, variables, and operations, representing a value without an equality sign. Whereas, algebraic identities are equations that hold true for all values of the variables involved. Learning different algebraic identities is crucial 10 min read Types of Polynomials (Based on Terms and Degrees)Types of Polynomials: In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations. There are mainly four types of polynomials based on degree-constant polynomial (zero degree), linear polynomial ( 1st degree), quadratic polynomial (2n 9 min read Like and Unlike Algebraic Terms: Definition and ExamplesLike terms are terms in algebraic expressions that have the same variables raised to the same powers. Like and Unlike Terms are the types of terms in algebra, and we can differentiate between like and unlike terms by simply checking the variables and their powers. We define algebraic terms as the in 7 min read Mathematical Operations on Algebraic Expressions - Algebraic Expressions and Identities | Class 8 MathsThe basic operations that are being used in mathematics (especially in real number systems) are addition, subtraction, multiplication and so on. These operations can also be done on the algebraic expressions. Let us see them in detail. Algebraic expressions (also known as algebraic equations) are de 5 min read Multiplying PolynomialsPolynomial multiplication is the process of multiplying two or more polynomials to find their product. It involves multiplying coefficients and applying exponent rules for variables.When multiplying polynomials:Multiply the coefficients (numerical values).Multiply variables with the same base by add 8 min read Standard Algebraic IdentitiesAlgebraic Identities are algebraic equations that are always true for every value of the variable in them. The algebraic equations that are valid for all values of variables in them are called algebraic identities. It is used for the factorization of polynomials. In this way, algebraic identities ar 7 min read Like