Solving (0.25 × 1/5) × 2²: A Step-by-Step Guide

by Elias Adebayo 48 views

Hey guys! Today, we're going to break down a numerical expression step-by-step so that everyone can follow along easily. We'll be tackling the expression (0.25 × 1/5) × 2². Don't worry if it looks a bit intimidating at first; we'll take it one piece at a time, just like solving a puzzle. Let's dive in and make math a little less scary and a lot more fun!

Understanding the Order of Operations

Before we jump into solving our expression, it’s super important to understand the order of operations. Think of it as the golden rule of math – it tells us in what order we should perform calculations to get the correct answer. The most common mnemonic for remembering this order is PEMDAS, which stands for:

  • Parentheses (or Brackets)
  • Exponents (or Orders)
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

So, following PEMDAS, we first look for any parentheses or brackets and solve what’s inside them. Then, we deal with exponents. After that, we perform multiplication and division from left to right, and finally, addition and subtraction, also from left to right. Sticking to this order is key to cracking any numerical expression correctly. It's like following a recipe – if you mix up the steps, the final result might not be what you expected! Trust me, mastering PEMDAS is a game-changer in math.

Step 1: Solving Inside the Parentheses (0.25 × 1/5)

Okay, so our numerical expression is (0.25 × 1/5) × 2². According to PEMDAS, the first thing we need to tackle is what's inside the parentheses. We have 0.25 × 1/5. Now, to make things a bit easier, let's convert 0.25 into a fraction. We know that 0.25 is the same as 1/4. So, our expression inside the parentheses becomes 1/4 × 1/5.

When we multiply fractions, it's pretty straightforward – we just multiply the numerators (the top numbers) and the denominators (the bottom numbers). So, 1/4 × 1/5 becomes (1 × 1) / (4 × 5), which simplifies to 1/20. Awesome! We've knocked out the parentheses part. Remember, taking things one step at a time like this makes even complex-looking problems much more manageable. Now we can move on to the next part of our expression.

Step 2: Dealing with the Exponent (2²)

Alright, we've successfully handled the parentheses in our expression, and now we're moving on to the next part: the exponent. Our expression now looks like (1/20) × 2². Remember PEMDAS? Exponents come before multiplication, so let's tackle that 2².

When we see an exponent, it means we're multiplying the base number by itself a certain number of times. In this case, 2² means 2 multiplied by itself, which is 2 × 2. And what does that equal? You guessed it – 4! So, 2² = 4. Now we've simplified the exponent part of our expression. See how breaking it down like this makes it much less intimidating? We're making great progress, guys! Now we just have one more step to go.

Step 3: Performing the Multiplication (1/20 × 4)

Okay, we're in the home stretch now! We've taken care of the parentheses and the exponent, and our expression has been simplified to (1/20) × 4. All that's left is a simple multiplication. Now, remember that we can think of the number 4 as a fraction by putting it over 1, so we can rewrite the expression as 1/20 × 4/1.

To multiply fractions, we multiply the numerators (top numbers) and the denominators (bottom numbers). So, 1/20 × 4/1 becomes (1 × 4) / (20 × 1). This simplifies to 4/20. But we're not quite done yet! We can simplify this fraction further.

Both 4 and 20 are divisible by 4. If we divide both the numerator and the denominator by 4, we get 4 ÷ 4 = 1 and 20 ÷ 4 = 5. So, the simplified fraction is 1/5. And there you have it! We've solved the entire numerical expression. (0.25 × 1/5) × 2² equals 1/5. High five! You guys nailed it.

Final Answer and Conclusion

So, we've reached the end of our numerical expression journey! We started with (0.25 × 1/5) × 2², and by following the order of operations (PEMDAS) step-by-step, we've arrived at our final answer: 1/5. Isn't it satisfying to see how a seemingly complex problem can be broken down into manageable chunks?

Let's recap what we did: First, we tackled the parentheses by converting 0.25 to a fraction (1/4) and then multiplying it by 1/5. That gave us 1/20. Next, we dealt with the exponent, 2², which equals 4. Finally, we multiplied 1/20 by 4, simplified the fraction 4/20, and arrived at our final answer of 1/5. Remember, guys, math isn't about magic; it's about method. By understanding the rules and taking things one step at a time, you can conquer any numerical expression that comes your way. Keep practicing, and you'll become math superstars in no time!

I hope this step-by-step explanation has been helpful. Keep practicing, and you'll become a pro at solving numerical expressions! And remember, math can be fun when you break it down. Until next time, happy calculating!