Verify Math Calculations: Are These Equations Correct?

Hey guys! Let's dive into some math problems and see if we can verify if these calculations are correct. We've got a bunch of equations here, and it's our job to put on our math hats and figure out if they add up. We will go through each of these equations step by step, double-checking the arithmetic to make sure everything is in order. So, grab your calculators (or your mental math skills!) and let's get started!

a) 29 * 36 = 1044

Let's start by verifying the multiplication of 29 and 36. When we look at this equation, 29 multiplied by 36 equals 1044, our first step is to actually perform the multiplication ourselves. You can do this manually using long multiplication, or you can use a calculator to quickly find the result. Either way, we need to make sure we are accurate. When we do the math, we see that 29 multiplied by 36 indeed equals 1044. The process involves multiplying 29 by 6, which gives us 174, and then multiplying 29 by 30, which gives us 870. Adding these two results (174 + 870) gives us the grand total. This is a fundamental multiplication problem, and accuracy is key. Now, think about why it's important to verify calculations like this. In everyday life, we use multiplication for a variety of tasks, from calculating expenses to figuring out measurements for a project. Getting it right is crucial! So, in this case, the calculation is correct. We've verified that 29 times 36 does indeed equal 1044. Good job on this one!

b) 3486 : 7 = 498

Next up, we're going to verify the division of 3486 by 7. The equation states that 3486 divided by 7 equals 498. So, how do we check if this is correct? The most straightforward way is to perform the division ourselves. You can use long division, which is a classic method for solving these kinds of problems, or you can use a calculator. If we divide 3486 by 7, we get exactly 498. No remainders, no decimals – a clean division. Think about the steps involved in long division. First, you figure out how many times 7 goes into 34 (which is 4 times), then you multiply 4 by 7 and subtract that from 34. You bring down the next digit (8) and repeat the process. It’s a bit like reverse multiplication, and it's an essential skill in arithmetic. Now, why is it important to verify division problems like this? Well, division is used in all sorts of situations, from splitting a bill with friends to calculating rates and ratios. Accuracy matters, especially when money is involved! In this instance, the calculation is accurate, and 3486 divided by 7 is indeed 498.

c) 38 - 6 = 228

Alright, let's tackle the subtraction: 38 - 6 = 228. Hold on a second… does that look right to you guys? Subtraction is one of the basic arithmetic operations, and this one seems a bit off. The equation suggests that 38 minus 6 equals 228, but our intuition might already be telling us that something is wrong. Let's verify it to be sure. When we subtract 6 from 38, we get 32, not 228. It seems like there's a big mistake in the original equation. Subtraction is all about taking away one quantity from another. In this case, we're taking away 6 from 38. Think of it like having 38 apples and eating 6 of them – you'd have 32 apples left. The idea here is quite simple, but it's essential to get it right. Why is it so important to verify subtractions? Subtraction is used in countless everyday situations, from figuring out how much change you'll get at the store to calculating time differences. Getting the subtraction wrong can lead to significant errors. So, in this case, the calculation is incorrect. 38 minus 6 is not 228; it's 32. This is a clear example of why verification is crucial in math!

d) 128 : 4 = 32

Now, let's move on to another division problem: 128 divided by 4. This equation claims that 128 divided by 4 equals 32. Does that sound right? Division involves splitting a number into equal parts, and in this case, we are splitting 128 into 4 equal parts. To verify this, we can perform the division ourselves. You can use long division, which we talked about earlier, or a calculator. When we divide 128 by 4, we do indeed get 32. This means that if you have 128 items and you want to divide them equally among 4 groups, each group would have 32 items. Division is fundamental in many areas of life. Think about sharing a pizza with friends – you're essentially dividing the pizza into slices. Or, if you're figuring out how many buses you need for a school trip, you're dividing the total number of students by the capacity of each bus. Accuracy in division is essential for fair and efficient distribution. So, in this instance, the calculation is correct. 128 divided by 4 does indeed equal 32. We’ve got another one right!

e) 29 * 124 = 3596

Finally, let's verify the multiplication of 29 and 124. The equation states that 29 multiplied by 124 equals 3596. This is a larger multiplication, so it might be a little more challenging to do mentally, but we can still check it to be sure. Just like before, we can perform the multiplication manually using long multiplication, or we can use a calculator to quickly find the result. Either way, our goal is to confirm the accuracy of the equation. When we multiply 29 by 124, we indeed get 3596. This process involves multiplying 29 by each digit in 124 (4, 20, and 100) and then adding the results together. It's a multi-step process, and accuracy is vital at each step. Multiplication is one of the core arithmetic operations, and it's used in a wide variety of applications. From calculating the area of a room to figuring out the total cost of multiple items, multiplication is a daily necessity. That's why it's so important to verify these kinds of calculations. In this final case, the calculation is correct. 29 multiplied by 124 does equal 3596. Great job everyone, we've verified all the equations!

So, there you have it! We've gone through each calculation, verifying whether they are correct or not. It's always a good idea to double-check our work, especially in math, to make sure we're on the right track. Remember, accuracy is key, whether you're doing simple arithmetic or more complex calculations. Keep practicing and stay sharp!