Solving 875 × 86 ÷ 9 A Step-by-Step Mathematical Guide

by Scholario Team 55 views

Hey guys! Ever stumbled upon a math problem that looks like a beast at first glance? Well, today we're going to tame one such beast: 875 × 86 ÷ 9. Don't let the numbers intimidate you; we'll break it down step by step, making it as clear as crystal. So, buckle up and let's dive into the fascinating world of calculations!

The Initial Setup Breaking Down the Components

Before we jump into the nitty-gritty, let's appreciate the problem itself. We have three numbers – 875, 86, and 9 – and two operations: multiplication and division. Remember the order of operations? PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction). This tells us we perform multiplication and division from left to right. So, we'll first multiply 875 by 86, and then divide the result by 9. Easy peasy, right?

The key here is to approach the problem systematically. Instead of trying to do everything in your head (unless you're a math wizard, of course!), break it down into manageable chunks. This not only makes the calculation easier but also reduces the chances of making silly mistakes. We'll start with the multiplication part, which is where the real action begins. Trust me, by the end of this, you'll be a pro at handling such calculations!

Multiplying 875 by 86 The Step-by-Step Guide:

Okay, let's get our hands dirty with the multiplication. We're tackling 875 multiplied by 86. This might seem daunting, but we'll break it down into smaller, friendlier steps. Think of it as climbing a staircase – each step gets you closer to the top, and each part of the multiplication brings us closer to the final answer.

First, we'll multiply 875 by the 'ones' digit of 86, which is 6. Then, we'll multiply 875 by the 'tens' digit, which is 8 (but remember, it's actually 80 because it's in the tens place). Finally, we'll add these two results together to get our answer. This method, known as long multiplication, is a classic for a reason – it works! So, grab your pen and paper, and let's get started on this mathematical journey.

Here’s how it unfolds:

  1. Multiply 875 by 6: 875 × 6 = 5250. This is our first partial product. Keep this number handy, we'll need it later.
  2. Multiply 875 by 80: Now, we multiply 875 by 80 (which is the same as multiplying by 8 and then adding a zero at the end). 875 × 8 = 7000. So, 875 × 80 = 70000. This is our second partial product. See, we're making progress!
  3. Add the partial products: Now for the grand finale of the multiplication step! We add our two partial products together: 5250 + 70000 = 75250. Voila! We've successfully multiplied 875 by 86. But hold on, we're not done yet. We still need to divide by 9. But hey, we've conquered the multiplication mountain; the division hill will be a breeze!

Division Time Dividing 75250 by 9

Alright, multiplication mission accomplished! Now, let’s tackle the final leg of our journey: dividing 75250 by 9. Division can sometimes seem like the trickiest of the four basic operations, but don't worry, we'll take it one step at a time. Think of it like sharing a huge pile of candies among 9 friends – how many does each friend get?

Long division is our trusty tool here. It helps us break down a large division problem into smaller, more manageable steps. We'll look at each digit (or group of digits) of 75250 and see how many times 9 fits into it. It’s a bit like a puzzle, where we figure out the best fit at each stage. So, let’s roll up our sleeves and dive into the division process!

Step-by-Step Division:

Here’s how we divide 75250 by 9 using long division:

  1. Divide 75 by 9: How many times does 9 go into 75? It goes 8 times (8 × 9 = 72). So, we write 8 above the 5 in 75250.
  2. Subtract 72 from 75: 75 - 72 = 3. This is our remainder from this step.
  3. Bring down the next digit: We bring down the next digit, which is 2, and place it next to the 3, making it 32.
  4. Divide 32 by 9: How many times does 9 go into 32? It goes 3 times (3 × 9 = 27). So, we write 3 next to the 8 above 75250.
  5. Subtract 27 from 32: 32 - 27 = 5. Another remainder!
  6. Bring down the next digit: We bring down the next digit, which is 5, and place it next to the 5, making it 55.
  7. Divide 55 by 9: How many times does 9 go into 55? It goes 6 times (6 × 9 = 54). We write 6 next to the 3 above 75250.
  8. Subtract 54 from 55: 55 - 54 = 1. Yet another remainder!
  9. Bring down the last digit: We bring down the last digit, which is 0, and place it next to the 1, making it 10.
  10. Divide 10 by 9: How many times does 9 go into 10? It goes 1 time (1 × 9 = 9). We write 1 next to the 6 above 75250.
  11. Subtract 9 from 10: 10 - 9 = 1. This is our final remainder.

So, when we divide 75250 by 9, we get 8361 with a remainder of 1. Woo-hoo! We've cracked the division code. But what does this remainder mean in the context of our problem? Let's delve into that next.

The Final Verdict Interpreting the Remainder and Final Answer

Okay, guys, we've done the heavy lifting! We multiplied 875 by 86 and then divided the result by 9. We arrived at 8361 with a remainder of 1. But what does this all mean? In the world of mathematics, especially in practical scenarios, the remainder is a crucial piece of the puzzle.

The answer to 875 × 86 ÷ 9 is 8361 with a remainder of 1. This means that 9 goes into 75250 a total of 8361 full times, with 1 left over. If this were a real-world problem, like dividing 75250 cookies among 9 friends, each friend would get 8361 cookies, and there would be 1 cookie left over (maybe for the baker!).

In some cases, we might express the remainder as a fraction. In this scenario, the remainder 1 becomes the numerator, and the divisor 9 becomes the denominator, giving us the fraction 1/9. So, the answer could also be expressed as 8361 1/9. But for most practical purposes, understanding the whole number and the remainder separately is perfectly sufficient. We did it! We've successfully navigated this mathematical maze and emerged victorious. Give yourselves a pat on the back!

Real-World Applications Why This Matters

Now, you might be thinking,