Problem 24 - Prealgebra

Question

Change to percent. $$\frac{150}{250}$$

Step-by-Step Solution

Answer

The fraction \( \frac{150}{250} \) is equal to 60\%.

Step 1: Understand the Problem

To convert a fraction to a percentage, we need to determine how much the fraction represents in terms of 100. This involves multiplying the fraction by 100 to get the percent value.

Step 2: Calculate the Fraction as a Decimal

First, divide the numerator by the denominator to convert the fraction into a decimal. For the fraction \( \frac{150}{250} \), perform the division: \( 150 \div 250 = 0.6 \).

Step 3: Convert the Decimal to a Percent

Multiply the decimal result by 100 to change it into a percentage. Thus, \( 0.6 \times 100 = 60 \).

Step 4: Write the Final Answer

The fraction \( \frac{150}{250} \) as a percentage is \( 60\% \).

Key Concepts

Fractions to Decimals

Converting fractions to decimals is a foundational math skill, useful for percentage conversion and many other applications. A fraction consists of a numerator (top number) and a denominator (bottom number). To convert a fraction into a decimal, you simply divide the numerator by the denominator. This operation transforms the fraction into an easily understandable decimal form.
For example, with the fraction \( \frac{150}{250} \):

• 150 is the numerator.
• 250 is the denominator.

Performing the division \( 150 \div 250 \) gives us the decimal 0.6.

Division

Division is a basic arithmetic operation with wide applications. In the context of converting fractions to decimals, division helps in understanding parts of a whole. By dividing the numerator by the denominator, we determine how many parts out of a unitary whole the fraction represents.
Using our example, divide 150 by 250:- Set up the division: 150 \( \div \) 250.- The result is 0.6.This operation reveals that \( \frac{150}{250} \) equates to 0.6 in decimal form. Division is crucial because it simplifies fractions and enables precise percentages once further calculations, like multiplication, are applied.

Multiplication by 100

Multiplication by 100 is a straightforward yet essential process in converting a decimal to a percentage. Percentages express a fraction as parts per hundred, so multiplying by 100 scales the decimal to a more relatable value.
In our example of converting a decimal to a percent:- We have the decimal 0.6.- Multiply 0.6 by 100 to convert it to a percentage.The calculation \( 0.6 \times 100 = 60 \) results in the percentage of 60%. This operation anchors the concept of a percentage, demonstrating how decimals are rescaled to fit the "per hundred" framework.

Numerator and Denominator

Understanding numerators and denominators is vital for any fraction-related operations. The numerator, placed above the line, represents the number of parts we have. The denominator, placed below the line, indicates how many parts make up a whole unit.
Take \( \frac{150}{250} \) as an example:

• 150 (numerator) signifies the number of parts being considered.
• 250 (denominator) shows the total number of equal parts making up the whole.

Grasping these terms enables better comprehension of how fractions convert to other numerical forms, such as decimals or percentages. In our specific case, recognizing \( 150 \) as 150 parts out of a total of 250 allows for an accurate and complete transformation into decimals and percentages.