Math Exercises Solved: Step-by-Step Solutions
Hey guys! Let's dive into solving some math problems together. We're going to break down three different exercises step-by-step, making sure everything is super clear. Whether you're brushing up on your math skills or tackling homework, this guide will help you conquer these types of problems with confidence. We'll cover the order of operations and how to handle different types of calculations. So, grab your pencils and let’s get started!
Exercise 1: (12 ÷ 3) + (4 • 2)
Okay, let's kick things off with our first mathematical challenge: (12 ÷ 3) + (4 • 2). To solve this, we need to remember the golden rule of math operations – the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This helps us to tackle the problem in the right sequence. Let's break it down step by step.
Step 1: Division
First up, we have 12 ÷ 3. This is a straightforward division problem. Think: how many times does 3 fit into 12? The answer is 4. So, we can simplify our expression to:
(4) + (4 • 2)
Step 2: Multiplication
Next on our list is the multiplication part: 4 • 2. This means 4 multiplied by 2. Super simple, right? 4 times 2 equals 8. Now our expression looks like this:
(4) + (8)
Step 3: Addition
Now, we're in the home stretch! We just need to add the two numbers together: 4 + 8. This is a basic addition problem. What do we get when we add 4 and 8? You guessed it – 12!
Final Answer
So, the final answer for the first exercise, (12 ÷ 3) + (4 • 2), is 12. See? Not so scary when we break it down into smaller steps. Remember, the key is to follow the order of operations and take your time. You’ve got this!
Exercise 2: (15 - 5) : (2 + 3)
Alright, let's move on to our second math problem: (15 - 5) : (2 + 3). This one looks a bit different, but don’t worry, we’ll tackle it using the same trusty order of operations (PEMDAS) we talked about earlier. The parentheses are our best friends here, so let's start there. Remember, taking it one step at a time makes even the trickiest problems manageable. Let’s get to it!
Step 1: Parentheses (Subtraction)
First, we'll handle the first set of parentheses: (15 - 5). This is a simple subtraction. What do we get when we subtract 5 from 15? The answer is 10. So, now our expression looks like this:
10 : (2 + 3)
Step 2: Parentheses (Addition)
Next up, we have another set of parentheses: (2 + 3). This is addition within parentheses. Adding 2 and 3 gives us 5. Our expression now becomes:
10 : 5
Step 3: Division
Now, we're left with just one operation: 10 : 5. This is division. How many times does 5 fit into 10? It fits in exactly 2 times. So, the result of this division is 2.
Final Answer
Therefore, the final answer for the second exercise, (15 - 5) : (2 + 3), is 2. Awesome job! You're doing great. Remember, practicing these steps will make you a math whiz in no time.
Exercise 3: (-8 - 4) (6 - 2) ÷ 2
Now, let’s tackle our third and final math problem: (-8 - 4) (6 - 2) ÷ 2. This one has a mix of negative numbers, parentheses, and division, but don’t sweat it! We’ll break it down just like the others, following the order of operations (PEMDAS). Remember, negative numbers just need a little extra attention, but the process is the same. Let's dive in and conquer this one!
Step 1: Parentheses (Subtraction - First Set)
First, let’s handle the first set of parentheses: (-8 - 4). We’re subtracting 4 from -8. Think of it as moving further into the negatives on a number line. So, -8 minus 4 gives us -12. Our expression now looks like this:
(-12) (6 - 2) ÷ 2
Step 2: Parentheses (Subtraction - Second Set)
Next, let's deal with the second set of parentheses: (6 - 2). This is a simple subtraction. 6 minus 2 equals 4. Now our expression looks like this:
(-12) (4) ÷ 2
Step 3: Multiplication
Now, we have a multiplication: (-12) (4). A negative number multiplied by a positive number results in a negative number. So, -12 multiplied by 4 gives us -48. Our expression now is:
-48 ÷ 2
Step 4: Division
Finally, we have the division: -48 ÷ 2. We’re dividing a negative number by a positive number, which will give us a negative result. 48 divided by 2 is 24, so -48 divided by 2 is -24.
Final Answer
Therefore, the final answer for the third exercise, (-8 - 4) (6 - 2) ÷ 2, is -24. You nailed it! See how breaking it down step by step makes even the more complex problems doable?
Final Thoughts
Awesome work, guys! You’ve successfully solved three different math exercises by following the order of operations. Remember, the key to mastering these problems is to break them down into smaller, manageable steps and to always follow PEMDAS. Keep practicing, and you'll become a math pro in no time. You've got this! And if you ever feel stuck, just revisit these steps. Happy calculating!