Solutions For 63082 ÷ 62 And 390242 ÷ 45 Math Problems
Hey guys! Today, we're diving into the world of division to solve two interesting math problems: 63082 ÷ 62 and 390242 ÷ 45. Don't worry, we'll break it down step by step so everyone can follow along. Whether you're a math whiz or just trying to brush up on your skills, this guide will help you understand how to tackle these kinds of problems.
Understanding the Basics of Division
Before we jump into the calculations, let's quickly recap what division is all about. Division is one of the four basic arithmetic operations (the others being addition, subtraction, and multiplication). At its core, division is the process of splitting a whole into equal parts. Think of it like sharing a pizza equally among friends – you're dividing the pizza into slices.
The main components of a division problem are:
- Dividend: The number being divided (the total amount). In our problems, the dividends are 63082 and 390242.
- Divisor: The number by which the dividend is being divided (the number of parts to split the whole into). Our divisors are 62 and 45.
- Quotient: The result of the division (how many units are in each part).
- Remainder: If the dividend cannot be divided equally by the divisor, the remainder is the amount left over.
Knowing these terms will help us understand the process and the results we get. So, with the basics covered, let’s get into the first problem.
Solving 63082 ÷ 62
Okay, let's tackle our first problem: 63082 ÷ 62. This might seem like a big number, but we'll take it one step at a time using long division. Long division is a method that helps us divide large numbers by breaking the problem down into smaller, more manageable steps. It’s like solving a puzzle – you look at each piece individually to see how it fits into the bigger picture.
Step-by-Step Breakdown
-
Set up the problem: Write the dividend (63082) inside the division symbol and the divisor (62) outside.
______ 62 | 63082 -
Divide the first digit(s): Look at the first digit of the dividend (6). Can 62 go into 6? No, it can't. So, we look at the first two digits (63). How many times does 62 go into 63? It goes in 1 time. Write the 1 above the 3 in the quotient.
1_____ 62 | 63082 -
Multiply: Multiply the divisor (62) by the quotient digit we just wrote (1). 62 * 1 = 62. Write the 62 below the 63.
1_____ 62 | 63082 62 -
Subtract: Subtract the result (62) from the part of the dividend we're working with (63). 63 - 62 = 1. Write the 1 below the 62.
1_____ 62 | 63082 62 -- 1 -
Bring down: Bring down the next digit from the dividend (0) and write it next to the remainder (1). We now have 10.
1_____ 62 | 63082 62 -- 10 -
Repeat: How many times does 62 go into 10? It doesn't, so we write a 0 in the quotient.
10____ 62 | 63082 62 -- 10 -
Bring down again: Bring down the next digit (8) to make 108.
10____ 62 | 63082 62 -- 108 -
Divide: How many times does 62 go into 108? It goes in 1 time. Write 1 in the quotient.
101___ 62 | 63082 62 -- 108 -
Multiply: 62 * 1 = 62. Write 62 below 108.
101___ 62 | 63082 62 -- 108 62 -
Subtract: 108 - 62 = 46.
101___ 62 | 63082 62 -- 108 62 -- 46 -
Bring down: Bring down the last digit (2) to make 462.
101___ 62 | 63082 62 -- 108 62 -- 462 -
Divide: How many times does 62 go into 462? It goes in 7 times. Write 7 in the quotient.
1017__ 62 | 63082 62 -- 108 62 -- 462 -
Multiply: 62 * 7 = 434. Write 434 below 462.
1017__ 62 | 63082 62 -- 108 62 -- 462 434 -
Subtract: 462 - 434 = 28.
1017__ 62 | 63082 62 -- 108 62 -- 462 434 -- 28
So, 63082 ÷ 62 = 1017 with a remainder of 28. We can write this as:
63082 ÷ 62 = 1017 R 28
Verification
To make sure we did it right, we can check our answer: (1017 * 62) + 28 = 63054 + 28 = 63082. Great! It matches our original dividend.
Now that we've conquered the first problem, let's move on to the second one.
Solving 390242 ÷ 45
Next up, we have 390242 ÷ 45. This one looks like another fun challenge! We'll use the same method of long division to break it down and find the quotient and remainder.
Step-by-Step Breakdown
-
Set up the problem: Write the dividend (390242) inside the division symbol and the divisor (45) outside.
______ 45 | 390242 -
Divide the first digit(s): Can 45 go into 3? No. Can 45 go into 39? No. So, we look at the first three digits (390). How many times does 45 go into 390? Let's estimate – 45 is close to 50, and 390 is close to 400. 50 goes into 400 about 8 times, so let's try 8.
8_____ 45 | 390242 -
Multiply: Multiply the divisor (45) by the quotient digit we just wrote (8). 45 * 8 = 360. Write the 360 below the 390.
8_____ 45 | 390242 360 -
Subtract: Subtract the result (360) from the part of the dividend we're working with (390). 390 - 360 = 30. Write the 30 below the 360.
8_____ 45 | 390242 360 -- 30 -
Bring down: Bring down the next digit from the dividend (2) and write it next to the remainder (30). We now have 302.
8_____ 45 | 390242 360 -- 302 -
Divide: How many times does 45 go into 302? Again, let's estimate. 45 is close to 50, and 302 is close to 300. 50 goes into 300 about 6 times, so let's try 6.
86____ 45 | 390242 360 -- 302 -
Multiply: 45 * 6 = 270. Write 270 below 302.
86____ 45 | 390242 360 -- 302 270 -
Subtract: 302 - 270 = 32.
86____ 45 | 390242 360 -- 302 270 -- 32 -
Bring down: Bring down the next digit (4) to make 324.
86____ 45 | 390242 360 -- 302 270 -- 324 -
Divide: How many times does 45 go into 324? Let’s try 7 (since 45 * 7 is close to 324).
867___ 45 | 390242 360 -- 302 270 -- 324 -
Multiply: 45 * 7 = 315. Write 315 below 324.
867___ 45 | 390242 360 -- 302 270 -- 324 315 -
Subtract: 324 - 315 = 9.
867___ 45 | 390242 360 -- 302 270 -- 324 315 -- 9 -
Bring down: Bring down the last digit (2) to make 92.
867___ 45 | 390242 360 -- 302 270 -- 324 315 -- 92 -
Divide: How many times does 45 go into 92? It goes in 2 times.
8672_ 45 | 390242 360 -- 302 270 -- 324 315 -- 92 -
Multiply: 45 * 2 = 90. Write 90 below 92.
8672_ 45 | 390242 360 -- 302 270 -- 324 315 -- 92 90 -
Subtract: 92 - 90 = 2.
8672_ 45 | 390242 360 -- 302 270 -- 324 315 -- 92 90 -- 2
So, 390242 ÷ 45 = 8672 with a remainder of 2. We can write this as:
390242 ÷ 45 = 8672 R 2
Verification
To check our answer: (8672 * 45) + 2 = 390240 + 2 = 390242. Awesome, it checks out!
Conclusion: Mastering Division
And there you have it! We've successfully solved both division problems: 63082 ÷ 62 = 1017 R 28 and 390242 ÷ 45 = 8672 R 2. Division might seem tricky at first, but with a step-by-step approach and a little practice, you can conquer any division problem. Remember, it's all about breaking it down into manageable parts and taking your time.
I hope this guide has been helpful for you guys. Keep practicing, and you'll become a division master in no time! If you have any questions or want to try more problems, feel free to ask. Happy dividing!