Tag: Maths

Introduction

The most fundamental application of percentages is to compare two amounts while setting the second amount to 100. The use of percentages is widespread and varied aside from this. For instance, a lot of statistics in the media are expressed as percentages, including bank interest rates, retail discounts, and inflation rates. Percentages are essential for understanding the financial aspects of daily life.

The Latin word “per centum,” which means “per hundred,” is where the word “percent” originates. The task of comparing unlike fractions is very challenging. Because percentages are the numerators of fractions with a denominator of 100. Percentages have a wide range of applications in daily life, including making simple comparisons, allocating discounts in marketing, and calculating profits and losses for businesses.

Percentages

Per means “out of” in percentage, and cent means a century. In essence, the whole is always set to 100, and the relationship is between a part and the entire. The ratio known as a percentage has a denominator of 100 and the percentage symbol %.

The percentage formula is as follows:

How to find percentage from data?

To find percentage from a given data, we first need to find the fraction of the quantity from the given data. By dividing the number by a whole and multiplying the result by 100, any fraction can be expressed in percentages. Consider a society with 1000 members, 650 of whom are voters. Then the percentage of voters out of all the residents is,

% Of voters = × 100

= × 100

= 65%

Percentage of a Number

When a number is divided into 100 equal parts, the percentage of that number is the sum of those 100 parts. Calculating percentages involves multiplying the total number by the percent expressed as a fraction. For instance, let’s say we need to find 30% of 600. We can figure it out as:

30% of 600 = 600 ×  = 180

Here, 600 is total, so 30% of 600 is 180.

Applications of Percentages

One of the most useful mathematical ideas is the percentage, which has applications in practically every branch of science as well as in everyday life.

To compare fractions

Fractions can be converted to percentages to create a clear comparison representation. This is very useful when the denominators of two fractions have different values. For instance, suppose you need to compare the fractions 2/5 and 1/4. We use percentages because making a direct comparison in this situation is very difficult. For 2/5, the percentage form is 40%, and for 1/4, the percentage form is 25%. We can categorically state that 2/5 is greater than 1/4.

To estimate increment or decrement

Any change in a quantity can be expressed in terms of a percentage. For instance, a 20% decrease would occur if a person’s salary was Rs. 5000 per month one year and Rs. 4000 the following.

The formula to calculate % change in a quantity is

Change% = × 100

To calculate ‘How much’ or ‘How many’

Sometimes numbers are expressed as percentages, for example the case of a city where 40% of the people are vegan. Therefore, the percentage will enable us to determine the precise number of vegans.

The formula to calculate the number from percentage is as follows,

Quantity =  × Total

To calculate profit or loss in percentage, to mark discounts etc.

If the selling price and cost price are known, the seller can use percentages to determine its loss or profit. For instance, a seller may charge Rs. 5000 for a fan while only paying Rs. 4000. The profit margin in this case is 25%.

Solved Examples

Example: What is the discount given on an article marked Rs. 6000 with a discount of 30%.

Solution: The discount on the article is given by

Discount% = × 100

Discount = × Marked Price

Substituting values

Discount = × 6000 = Rs. 1800

A discount of Rs. 1800 is given.

Example: By what percentage is Amit’s salary, Rs. 35000, is less than from Sagar’s salary, Rs. 40000?

Solution: The difference between Amit’s and Sagar’s Salaries is

Sagar’s Salary – Amit’s Salary = 40000 – 35000 = Rs. 5000

The percentage difference between their salaries

Thus, Amit’s salary is 12.5% less than Sagar’s salary.

Summary

When portions of a quantity are given, we have seen how to convert ratios into percentages. We discussed the formula for calculating the percentage of a number. An increase or decrease in a specified quantity can also be expressed as a percentage. The profit or loss in a specific transaction can be expressed in terms of percentages.

Frequently Asked Questions

1.What is the Importance of Percentage in Sciences other than Mathematics?

Ans. Percentage plays an important role in many aspects of business science, physical science, chemical science etc. In business science (statistics in particular) percentage is used to represent the parts of a data. In physical science percentage is used in various formulae, and derivations to represent efficiency, error and other such things. In chemical science percentage is used to calculate the concentration of different chemicals and composition of solutions etc.

2.How is Percentile Different from Percentage?

Ans. The value in the distribution or level at or below which a specific percentage of the score lies is represented by the percentile. For every hundred, which is the measurement unit, is referred to as the percentage.

3.What is the Relationship between Percentage and Probability?

Ans. Probability of an event can also be expressed as a percentage. For example, if the probability of an event is x, then the percentage probability is given by

% Probability = 𝑥 x 100%

Read More: Ratio and Percentage Formula and Examples

Introduction

The relationship between two expressions on either side of the equal to sign is represented by an equation in mathematics. One equal symbol and one variable are used in this kind of equation. Simple equations use arithmetic operations to balance the expressions.

A simple equation is an equation that shows the relationship between two expressions on both sides of the sign. Only one variable appears in these kinds of equations, either on the first side or the other side of the equal symbol. For instance, 83 = 5 – 4z. In the provided example, the variable is z. Simple equations use arithmetic operations to balance the expressions on both sides. Linear equations in one variable are also regarded as simple equations.

Equations

Equations are relationships between two or more expressions connected by the equals sign, or “=.” Variables, coefficients, and constants are the three components of an equation.

Variables: Variables are the names given to the symbols (typically English alphabets) that are assigned to an arbitrary, unknowable value.

Coefficients: The coefficients of a term are the numbers that are multiplied by a variable or the product of two variables in that term.

Constants: Constants are the numbers that are independent of variables.

Simple Equations

A type of equation known as a simple equation compares two linear expressions with just one variable in common. Several instances of basic/simple equations are

3x + 4 = 7

4x + 5 = 3x + 8

Since many of the situations, we encounter in real life can be formulated as simple equation problems, we can use simple equations to obtain the desired results in a variety of areas of life.

Simple Equations questions

Simple equation problems, which can be represented by a simple equation to find the value of something unknown based on some given conditions, are known as simple equation questions. One such example of applying simple equations to real-world situations is provided, 

Let’s say Amar and Bipin, two friends, are purchasing apples. Amar might have purchased 5 kg and Bipin 3 kg. If Amar paid Rs. 80 more than Bipin, we must determine the cost of a kg of apples. The following simple equation can be used to represent this situation:

5x = 3x + 80, where x is the price of 1 kg apples.

Solving Simple Equations

To answer questions involving simple equations, we change the equation so that the term with the variables is on one side of the equation and the term with constants is on the other. We then simplify both sides so that there is only one term on each side, one with variables and the other with constants.

The value of the variable is then obtained by simply multiplying the equation by the reciprocal of the coefficient.

Now, let’s look at some examples to help us better understand it.

Example: Solve the following simple equation, 5x – 20 = 3x + 60

Solution: Here we have 5x – 20 = 3x + 60

Adding 20 to both sides while subtracting 3x to move terms with variables to one side and constants to the other.

⇒ 5x – 20 + 20 – 3x = 3x + 60 + 20 – 3x

⇒ 5x – 3x = 60 + 20

⇒ 2x = 80

Dividing by 2 on both sides

⇒ x = 40

Simple Equation Problems

Simple equation problems are mathematical issues from the real world that are modelled by simple equations. We must first determine the number of arbitrary values present and their relationships to represent a given situation using a simple equation. If there is only one arbitrary value, it is easy to create a simple equation to describe it; however, if there are several arbitrary values, we must establish a direct relationship between them to do so.

Example: Determine whether the following scenario can be modelled as a simple equation or not. Amit is currently twice as older than his younger brother Sagar. The combined age of Amit and Sagar was 23, two years ago. Identify their current ages.

Solution: Since Amit’s age and Sagar’s age are arbitrary values, the only way we can depict this situation in a simple equation is if there is a direct correlation between their ages, which is implied by the first statement that Amit is currently twice as old as Sagar. As a result, we can express this as a simple equation problem.

Let Sagar’s present age be x years

And Amit’s present age be y years

Then, ATQ

In present, y = 2x

Also, two years ago, (x – 2) + (y – 2) = 23

Substituting y = 2x in the second equation,

⇒ x – 2 + 2x – 2 = 23

Equations in Everyday Life Examples

When a value for a quantity or identity is unknown in a real-world situation and cannot be determined by a simple mathematical operation, linear equations are used, such as when estimating future income, forecasting future profits, or figuring out mileage rates.

Here are a few real-world instances where applications of linear equations are used.

• Can be used to identify age-related problems.
• It is used to determine the distance, duration, and speed of a moving object.
• It is used to resolve problems involving money, percentages, etc.

Solved Examples

Example: Calculate the value of y from the equation:  – 5 = 6.

Solution: We will simplify the equation first by separating the variables and constants,

– 5 = 6

Add 5 on both sides,

⇒  – 5 + 5 = 6 + 5

⇒  = 11

Multiply by 3 on both sides,

⇒  x 3 = 11 x 3

⇒ 11y = 33

Divide by 11 on both sides,

⇒ y = 3

Summary

Simple equations are also known as linear equations when they contain multiple variables and can be resolved using a variety of techniques. To solve problems from daily life, such as how to measure an unknown length, etc., we use simple equations. The typical method of representing the relationship between variables is through simple equations. A simple equation is a linear equation that only has one variable. Simple equations were credited to Rene Descartes as their creator. One of the foundations of algebra is simple equations.

Frequently Asked Questions (FAQs)

1. What are Linear Equations?

Linear equations are the mathematical relations that relate two expressions of degree 1 with the equal to symbol.

2. What are Simple Equations?

Simple equations are linear equations that have only one variable. Simple equations can be solved easily and are very useful in many days to day life problems.

3. What are the different methods of Solving Simple Equations?

There are two ways that we can solve simple equations. The techniques are the systematic method and the trial-and-error method.

4. What is a Rational Expression?

A rational expression is expressed in terms of the fraction of two algebraic expressions, and it also belongs to the class of simple equations.