54 is 150 of what number? This is a common question that many people come across when dealing with mathematical calculations or solving equations. In this article, we will explore the concept of finding a number when given a certain percentage. We will also provide a step-by-step guide on how to solve such problems and answer some frequently asked questions related to this topic.
Before we dive into the specifics of finding a number when given a percentage, let’s start by understanding the concept of percentages. A percentage is a way of representing a fraction or a portion of a whole, usually out of 100. It is denoted by the symbol “%”.
For example, if we say that 50% of a pizza has been eaten, it means that half of the pizza has been consumed. Similarly, if we say that a store is offering a 20% discount on a product, it implies that the price of the product has been reduced by one-fifth.
Finding a Number Given a Percentage:
When we are given a percentage and need to find the number it represents, we can use a simple formula. Let’s take the example of finding the number when 54 is 150% of it.
Step 1: Set up the equation:
Let’s assume the unknown number is “x”. We can write the equation as follows:
54 = 150% of x
Step 2: Convert the percentage to a decimal:
To convert a percentage to a decimal, divide it by 100. In this case, 150 divided by 100 equals 1.5.
54 = 1.5x
Step 3: Solve for x:
To find the value of x, divide both sides of the equation by 1.5:
54 ÷ 1.5 = x
x = 36
Therefore, 54 is 150% of 36.
Q: How do I find a percentage of a number?
A: To find a percentage of a number, multiply the number by the percentage expressed as a decimal. For example, to find 30% of 50, multiply 50 by 0.30.
Q: What is the formula for finding a number when given a percentage?
A: The formula is: Number = (Percentage ÷ 100) × Total. For example, to find a number that is 25% of 80, you would calculate (25 ÷ 100) × 80 = 20.
Q: Can a percentage be greater than 100%?
A: Yes, a percentage can be greater than 100%. It indicates that the value being referred to is more than the whole. For example, if you scored 120% on a test, it means you scored higher than the maximum possible score.
Q: What does it mean when a percentage is negative?
A: A negative percentage indicates a decrease or reduction in value. For example, if a stock’s value decreased by 10%, it would be expressed as -10%.
Q: How do percentages relate to fractions and decimals?
A: Percentages can be converted to fractions by dividing the percentage by 100 and simplifying the fraction if needed. They can also be converted to decimals by dividing the percentage by 100. For example, 35% is equivalent to the fraction 7/20 or the decimal 0.35.
In conclusion, finding a number when given a percentage is a simple mathematical calculation that involves converting the percentage to a decimal and using basic algebraic equations. By following the step-by-step guide provided in this article, you can easily determine the number when given a certain percentage. Understanding percentages and their applications is essential in various fields, from finance to everyday life.