If 40% is equal to the fraction x/30 .What is the value of x
The Correct Answer and Explanation is:
To solve the equation:
40% = x / 30
First, convert 40% into a decimal or a fraction.
We know that:
40% = 40 ÷ 100 = 0.4
So we now rewrite the equation:
0.4 = x / 30
To find the value of x, multiply both sides of the equation by 30:
0.4 × 30 = x
x = 12
Final Answer: x = 12
Explanation
In mathematics, percentages are a way to express numbers as parts of 100. The term “percent” comes from the Latin per centum, which means “by the hundred.” When you are given a percentage, like 40%, it can be converted to a fraction or decimal for calculation purposes. In this case, 40% is equal to 40 divided by 100, which is 0.4.
The problem asks us to find the value of x in the equation where 40% is equal to x divided by 30. This is a basic proportion problem. Proportions compare two ratios or fractions. In this example, 40% (or 0.4) is the same as x/30. The goal is to find the number that, when divided by 30, gives us 0.4.
To isolate x, we use the principle of cross multiplication or multiply both sides of the equation by 30. This is because multiplying both sides of an equation by the same number keeps the equation balanced. So:
0.4 × 30 = x
Multiplying 0.4 by 30 gives 12. That tells us x must be 12 for the equation to be true.
To check your work, substitute x = 12 back into the original equation:
12 / 30 = 0.4, which is 40%, so the solution is correct.
This type of question is common in problems involving percentages, ratios, or proportions. Understanding how to manipulate equations and convert percentages can help you solve them accurately and efficiently.
