Mastering the Basics: Squaring Fractions with ALEKS

If (7/2)^-2 can be rewritten as (2/7)^2, which of the following represents squaring the fraction?

• A. (2^2)/(7^2)
• B. 2+7
• C. (2-7)^2
• D. (2×7)^2

Answer: (A)

When you square a fraction, you square both the numerator and the denominator separately. In this case, when you have (2/7) and you want to square it, you would calculate (2/7)^2. This results in squaring the numerator (2) and squaring the denominator (7), which can be expressed as (2^2)/(7^2). So, the correct answer illustrates this process perfectly, showing that when the fraction 2/7 is squared, it becomes (2^2)/(7^2). This is the correct representation of squaring the fraction. The other choices, while potentially interesting, do not reflect the action of squaring both parts of the fraction as required.

When tackling fractions, especially within the quirky realm of the ALEKS Basic Math Placement Test, understanding how to manipulate them correctly is crucial. Here’s the thing: squaring a fraction is more than just a mathematical operation; it’s about clarity and precision in your calculations. So, let’s break it down.

Ever pop open your math book and seen something like (7/2)^-2? You might wonder, why the negative exponent? Well, it indicates that you’re dealing with its reciprocal. Essentially, (7/2)^-2 can be flipped to (2/7)^2. But how do you square this fraction? Here’s the magic: when squaring a fraction, each part—the numerator and the denominator—must take on the square.

Imagine you’ve got a fraction, say 2/7. Squaring this means you’re looking at (2/7)^2. You’ll square the numerator (2) and the denominator (7) separately. So, it’s like cheering on each number: “Go, 2! Time to shine, 7!” This results in what we’d write as (2^2)/(7^2). Voila! The correct representation of squaring the fraction is (2^2)/(7^2).

Now, let’s consider some other choices—like B, which offers you 2+7. Interesting, but not relevant here! When you square a fraction, you must square both parts, not just throw them together. The other options, C and D, while jazzy in their own way, miss the mark completely with the action of squaring.

Why does this matter in the big picture? Mastering these fundamentals prepares you for all sorts of math-related challenges ahead. Math isn’t just about crunching numbers; it’s about understanding relationships and operations, whether it’s in algebra, geometry, or real-world applications. This understanding not only comes handy during exams but applies wonderfully outside the classroom.

Now, if you think you’ve got a handle on squaring fractions, that’s awesome! But let’s not forget about practice and reinforcement in other areas. Consider exploring topics like ratios, proportions, or even basic algebra equations. They mesh nicely with fraction operations and help solidify your overall math prowess.

So next time you see a question asking about squaring fractions, take a deep breath. You’ve got the skills to tackle it head-on. Cheer for those numbers, square them up, and let your math journey blossom with confidence and clarity!