Solve -5/7/3 + 28: A Step-by-Step Guide

Hey everyone! Today, we're diving into a mathematical expression that might seem a bit tricky at first glance: -5/7/3 + 28. Don't worry, we'll break it down step-by-step to make it super clear. Math can be fun, especially when you understand the process. So, grab your pencils and paper, and let's get started!

Understanding the Order of Operations

Before we jump into solving, it's crucial to remember the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This is our roadmap for solving any mathematical expression correctly. It tells us what to tackle first, ensuring we get the right answer.

In our expression, -5/7/3 + 28, we don't have any parentheses or exponents, so we move straight to multiplication and division. Now, here's where it gets a little interesting. We have two division operations right next to each other. The rule here is to perform these operations from left to right. So, we'll divide -5 by 7 first, and then we'll divide the result by 3. Once we've handled the division, we'll move on to the addition. Following this order is key to unraveling the expression accurately. Think of PEMDAS as the golden rule of math – stick to it, and you'll be just fine!

Step 1: Dividing -5 by 7

Alright, let's get into the nitty-gritty of our first division: -5 divided by 7. When we divide -5 by 7, we get a fraction, which can be represented as -5/7. This fraction simply means that we are taking a negative five and splitting it into seven equal parts. Now, if you prefer to see this as a decimal, you'd get approximately -0.714. It's helpful to keep at least three decimal places for accuracy as we move forward in the calculation. Understanding this basic division is crucial because it sets the stage for the next operation.

Visualizing this fraction can be super helpful. Imagine a pie cut into seven slices, and you're taking away five of those slices – that's essentially what -5/7 represents. Whether you stick with the fraction or the decimal form, remember this value as we head into the next step, where we'll divide this result by 3. So, we've successfully completed our first operation – onward and upward, guys!

Step 2: Dividing the Result by 3

Okay, now that we've got -5/7, which is approximately -0.714, we're going to divide this result by 3. This means we're taking that fraction or decimal and splitting it into three equal parts. When we divide -5/7 by 3, we're essentially performing the operation (-5/7) / 3. To make this division easier, we can rewrite 3 as a fraction, which is 3/1. Now, dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/1 is 1/3. So, our expression becomes (-5/7) * (1/3).

When we multiply fractions, we multiply the numerators (the top numbers) and the denominators (the bottom numbers). So, -5 multiplied by 1 is -5, and 7 multiplied by 3 is 21. This gives us the fraction -5/21. If we convert this fraction to a decimal, we get approximately -0.238. Remember, we're keeping three decimal places for accuracy. This step is all about breaking down the division into manageable parts, and now we've successfully divided -5/7 by 3. Let's keep this result handy as we move to the final step!

Step 3: Adding 28 to the Result

We're almost there, guys! Now that we've worked through the division, we've landed at -5/21, which is about -0.238. The final step is to add 28 to this result. This is a straightforward addition, but let's make sure we get it right. We're adding a positive number (28) to a negative number (-0.238).

So, we have -0.238 + 28. To visualize this, think of it as starting at -0.238 on a number line and then moving 28 units to the right. This will bring us into the positive territory. When we perform the addition, we get approximately 27.762. This is our final answer! We've taken a complex-looking expression and broken it down step-by-step, using the order of operations to guide us. Isn't it satisfying when the pieces all come together?

Final Answer

So, after carefully working through each step, we've arrived at our final answer: -5/7/3 + 28 = approximately 27.762. We started with a seemingly complicated expression and, by following the order of operations and breaking it down into smaller parts, we solved it! Remember, math is all about taking things one step at a time and understanding the underlying principles. Great job, everyone, for sticking with it! You've successfully decoded this mathematical expression. Keep practicing, and you'll become a math whiz in no time! Remember, every complex problem is just a series of simple steps put together. You've got this!