Arranging Fractions and Decimals: A Step-by-Step Guide

On the TEAS 7 Math section, you will frequently encounter questions that require you to compare and order different types of numbers, including fractions, decimals, and percentages. The most efficient way to solve these problems is to convert all numbers into a common format. Decimals are usually the easiest format to use for quick comparison.

Step 1: Convert Everything to Decimals

Let's convert each number in the set to a decimal value:

• 0.22: This is already a decimal.
• $1/4$: To convert a fraction to a decimal, divide the numerator by the denominator ($1 \div 4$). This equals 0.25.
• $2/5$: Divide 2 by 5 ($2 \div 5$). This equals 0.4. To make it easier to compare with other numbers that have two decimal places, we can write it as 0.40.
• 0.45: This is already a decimal.
• $1/2$: Divide 1 by 2 ($1 \div 2$). This equals 0.5. We can write this as 0.50 for consistency.

Step 2: Compare the Values

Now that we have a consistent list, we can easily compare their magnitudes:

1. 0.22 (The smallest)
2. 0.25 ($1/4$)
3. 0.40 ($2/5$)
4. 0.45
5. 0.50 ($1/2$)

Step 3: Identify the Correct Order

Based on our comparison, the order from least to greatest is: 0.22, 1/4, 2/5, 0.45, 1/2.

Why Other Answers are Incorrect

• Choice B is incorrect because it places $1/4$ (0.25) before 0.22. In numerical order, 0.22 is smaller than 0.25.
• Choice C is incorrect because it places 0.45 before $2/5$ (0.40). Since 0.45 is larger than 0.40, it should appear later in the sequence.
• Choice D is incorrect because it lists the numbers from greatest to least ($1/2$ is the largest value in the set). Always read the question carefully to see if it asks for "least to greatest" or "greatest to least."

Memory Tip for the TEAS

Think of decimals like money.

• $0.22$ is 22 cents.
• $1/4$ (a quarter) is 25 cents.
• $2/5$ is 40 cents.
• $0.45$ is 45 cents.
• $1/2$ (half a dollar) is 50 cents. Visualizing money makes it much harder to make a simple ordering error!