Understanding Mixed Numbers: Simplifying 75 1/2 for Middle School Students

Understanding Mixed Numbers: What is 75 1/2?

A mixed number is a whole number combined with a fraction. In this case, 75 1/2 consists of the whole number 75 and the fraction 1/2. Let's break down how to handle this number step by step.

Step 1: Understanding the Components

The number 75 represents the whole part, while 1/2 represents the fractional part. To visualize it, think of 75 as 75 whole units, and 1/2 as an additional half unit.

Step 2: Converting to Improper Fraction

To express the mixed number 75 1/2 as an improper fraction, we need to combine it into one fraction:

1. Multiply the whole number by the denominator of the fraction: 75 x 2 = 150
2. Add the numerator of the fraction: 150 + 1 = 151
3. Place this result over the original denominator: 151/2

So, 75 1/2 as an improper fraction is 151/2.

Step 3: Visualizing the Value

To better grasp what 75 1/2 represents, think about a number line. If you mark 75 and then move halfway to 76, you land exactly at 75 1/2.

Step 4: Practical Application

Understanding mixed numbers is practical in everyday life—whether you’re measuring ingredients in a recipe or dealing with time. For instance, if a recipe calls for 75 1/2 cups of sugar, you know you need to measure 75 whole cups and then add half of one more cup.

Conclusion

In summary, 75 1/2 can easily be converted to the improper fraction 151/2. Mixed numbers are an essential part of mathematics, and knowing how to work with them will serve you well in various real-life scenarios.