Problem 62 - Algebra 1: Concepts and Skills

Question

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 225 \% $$

Step-by-Step Solution

Answer

225% in simplest form as a fraction or mixed number is 2 1/4

Step 1: Express the Given Percentage as a Fraction

The first step of this exercise is expressing the given 225% as a fraction. Percentage means 'out of 100', so 225% can be written as the fraction 225/100.

Step 2: Simplify the fraction

Our current fraction is 225/100. At first glance, it's clear that both numbers are divisible by 25. Dividing both numerator and denominator by 25, we get a simplified fraction of 9/4.

Step 3: Convert the Fraction into a Mixed Number

The fraction we have now, 9/4, is improper (the numerator is larger than the denominator). We convert it into a mixed number by dividing 9 by 4. This gives us 2 remainder 1. Therefore, the mixed number is 2 1/4.

Key Concepts

Simplifying Fractions

Simplifying fractions is an essential skill for math students, and it involves reducing a fraction to its simplest form. When we say simplest form, it means the numerator (the top number) and the denominator (the bottom number) have no common factors other than 1. To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator.
For example, let's look at the fraction \( \frac{225}{100} \).

• First, determine the GCD. For 225 and 100, both numbers share a common factor of 25.
• Next, divide both the numerator and the denominator by 25.
• This calculation gives us \( \frac{9}{4} \), which is the simplified form of \( \frac{225}{100} \).

Simplifying fractions makes them easier to work with, and it's a critical step in fraction conversion.

Improper Fractions

An improper fraction is a fraction where the numerator is larger than the denominator.
In simpler terms, it's when the top number is bigger than the bottom number. Improper fractions can represent values greater than a whole number, and they are often converted into mixed numbers to make them easier to understand.
In our exercise, we ended up with the improper fraction \( \frac{9}{4} \) after simplifying \( \frac{225}{100} \). This fraction indicates that the value is more than one whole part.
To convert an improperly fraction to a mixed number:

• Divide the numerator by the denominator. Here, divide 9 by 4.
• The whole number result of the division is part of your mixed number. 9 divided by 4 is 2.
• The remainder becomes the new numerator in the fractional part of the mixed number. The remainder here is 1.
• So, \( \frac{9}{4} \) converts to the mixed number \( 2 \frac{1}{4} \).

Understanding improper fractions and how to convert them is useful in various math problems and real-life situations.

Mixed Numbers

Mixed numbers combine a whole number and a fraction, representing values greater than one.
For example, \( 2 \frac{1}{4} \) is a mixed number, combining the whole number 2 with the fraction \( \frac{1}{4} \). Converting improper fractions to mixed numbers helps us interpret and use large values more practically, especially in measurement and everyday math tasks.
To work with mixed numbers:

• Add the fractional part to the whole number to compute its total value.
• If working with another mixed number or fraction, ensure the fractions have a common denominator to perform addition or subtraction.
• In multiplication, convert the mixed number back into an improper fraction first.

Mixed numbers allow us a clearer representation of numbers, smoothing the journey from theoretical math to practical application.