Question

Fill in the blanks. Round each answer to the nearest whole percent _________ \(\%\) of \(41=20\)

Short answer

49%

Step-by-step solution

Identify what is being asked

The problem is asking to find what percentage of 41 equals 20. This can be expressed mathematically as \(\text{percentage} \times 41 = 20\).

Set up the equation

Let \(x\) be the percentage we need to find. The equation becomes \(x \times 41 = 20\).

Solve for x

To isolate \(x\), divide both sides of the equation by 41: \[x = \frac{20}{41}\].

Convert to a percentage

Multiply the result by 100 to convert it to a percentage: \[x = \frac{20}{41} \times 100\]. Calculate this value.

Round to the nearest whole percent

Perform the calculation and round the result. \[x \times 100 = \frac{20}{41} \times 100 \approx 48.78 \approx 49\text{\textpercent}\]

Key concepts

Algebra

Algebra is the branch of mathematics that deals with symbols and the rules for manipulating these symbols. In simple terms, it involves finding the unknowns in mathematical expressions and equations. When dealing with percentage calculations, we often use variables to represent these unknowns.
For example, in the given problem, we let the unknown percentage be represented by the variable \( x \). We then set up an algebraic equation based on the information provided in the problem. Here, \( x \times 41 = 20 \). Solving this reveals the value of the unknown variable. This process highlights the core of algebraic manipulation—breaking down a problem into solvable steps using variables and equations.

Equations

An equation is a mathematical statement that asserts the equality of two expressions. In our problem, the equation \( x \times 41 = 20 \) is set up to find the percentage value. Here's how:

• The left side of the equation ( \( x \times 41 \) ) represents the unknown percentage of 41.
• The right side of the equation (20) represents the given value.

To isolate the variable \( x \), we divide both sides of the equation by 41:
\[ x = \frac{20}{41} \].
This step is crucial as it turns the equation into a form where \( x \) is by itself, making it easier to solve. Solving equations, particularly linear equations, is a fundamental skill in algebra. It's all about keeping the balance—whatever you do to one side, you must do to the other.

Rounding

Rounding is a process of reducing the digits in a number while trying to keep its value similar. Often, we round numbers to make them easier to work with, especially in real-world situations where exact precision isn't always necessary.
In the exercise, after calculating the percentage value, we got \( \frac{20}{41} \times 100 \), which approximately equals to 48.78. Since we need to round to the nearest whole percent, we look at the digit right after the decimal point.
Here, the digit after the decimal point is 7 (in 48.78). Since 7 is greater than or equal to 5, we round up to the next whole number, making it 49\text{\textpercent}. Understanding rounding rules like this helps ensure accuracy and appropriateness of the final result.