6 Math Expressions Solved: Step-by-Step Solutions
Hey guys! Math can be a bit tricky sometimes, but don't worry, we're going to break down six different math expressions step-by-step. We'll cover addition, subtraction, and division, so you'll get a good overview of how to tackle these problems. Let's dive in!
Solving Addition Problems
When we talk about addition problems, it's all about combining numbers to find their total. We will start with the expression 478149 + 7445. To get started with addition, write numbers aligned by their place values (ones, tens, hundreds, etc.). This helps ensure we're adding the correct digits together. For the first expression, 478149 + 7445, we line up the numbers and add each column, starting from the right.
So, first, you add 9 and 5 in the ones column, which gives you 14. You write down the 4 and carry over the 1 to the tens column. Then, add 4 and 4 in the tens column, plus the 1 you carried over, which equals 9. No need to carry over this time! In the hundreds column, you add 1 and 4, giving you 5. Moving to the thousands column, add 8 and 7, which is 15. Write down the 5 and carry over the 1 to the ten-thousands column. Now, add 7 and the carried-over 1, resulting in 8. Finally, bring down the 4 in the hundred-thousands column since there's nothing to add to it. So, when you add 478149 and 7445 together, you get a grand total of 485594. See? It's just about taking it one step at a time!
Now let's tackle the next addition problem: 22 300 + 65 478. Just like before, we line up the numbers based on their place values. Starting with the ones column, 0 + 8 gives us 8. Then, in the tens column, 0 + 7 equals 7. Moving to the hundreds, 3 + 4 is 7 again. In the thousands place, 2 + 5 makes 7, and in the ten-thousands, 2 + 6 gives us 8. So, when we combine 22 300 and 65 478, we get 87 778. Isn't it satisfying how the numbers just add up so neatly? Keep practicing, and you'll become an addition pro in no time!
For the third addition, we've got decimals! Let's solve 123 253.3 + 39 487.6. When you're dealing with decimals, the key is to make sure those decimal points are lined up perfectly. It’s like making sure everyone’s standing in the right spot for a group photo! So, write down 123 253.3 and then place 39 487.6 right below it, ensuring the decimal points are in a straight line. Now, start adding from right to left, just like with whole numbers. In the tenths column (the numbers after the decimal), we add 3 and 6, which gives us 9. So, we write down .9 in our answer. Next, move to the ones column: 3 + 7 equals 10. Write down 0 and carry over the 1 to the tens column. In the tens column, we have 5 + 8, plus the 1 we carried over, which totals 14. Write down 4 and carry over 1 to the hundreds. For the hundreds column, add 2 + 4, plus the carried 1, giving us 7. Now onto the thousands: 3 + 9 is 12. Write down 2 and carry over 1 to the ten-thousands. In the ten-thousands column, we have 2 + 3, plus the carried 1, making it 6. Finally, bring down the 1 from the hundred-thousands place since there’s nothing to add to it. Add up all of those numbers, and you get 162 740.9. See, adding decimals isn't so scary when you keep everything lined up!
To wrap up our addition adventures, let's add 23478.4 and 98 325.7. Remember our golden rule? Line up those decimal points! Write down 23478.4 and then 98 325.7 directly below it. Let's start adding from the right. For the tenths, 4 + 7 is 11. Write down 1 after the decimal point and carry over 1 to the ones column. In the ones column, 8 + 5, plus the carried 1, makes 14. Write down 4 and carry over 1 to the tens. For the tens, 7 + 2, plus the carried 1, is 10. Write down 0 and carry over 1 to the hundreds. Hundreds up next: 4 + 3, plus the carried 1, gives us 8. Now, the thousands: 3 + 8 is 11. Write down 1 and carry over 1 to the ten-thousands. Finally, add 2 + 9, plus the carried 1, which totals 12. Put that whole number down, and you’ve got 121804.1. Adding these numbers together, we get a final result of 121804.1. Awesome job, you’re getting the hang of addition with decimals!
Tackling Subtraction Problems
Moving on to subtraction, we're finding the difference between two numbers. Let's start with 85 025 - 49145. As with addition, lining up the numbers by place value is key in subtraction. Place 85 025 on top and 49145 underneath, aligning the ones, tens, hundreds, and so on. Start subtracting from the rightmost column. We'll kick things off by subtracting 5 from 5 in the ones place, which gives us 0. Next up, we move to the tens place, where we need to subtract 4 from 2. Uh-oh, 2 is smaller than 4, so we've got to borrow! We borrow 1 from the hundreds place, making our 2 into a 12. Now we subtract 4 from 12, and we get 8. Moving over to the hundreds place, we borrowed 1 earlier, so that 0 has become a 9. Now we need to subtract 1 from 9, and we get 8. Off to the thousands place, where we have to subtract 9 from 5. Again, we need to borrow! We borrow 1 from the ten-thousands place, turning our 5 into 15. Now, 15 minus 9 is 6. Finally, in the ten-thousands place, we borrowed 1 earlier, so our 8 is now a 7. Subtract 4 from 7, and we get 3. Put it all together, and 85 025 minus 49145 equals 35880. See? Subtraction's just like taking away, one step at a time!
Let's try another subtraction! Our next expression is 700 253 - 457652. As always, start by lining up the numbers by their place values. Place 700 253 on top and 457652 below it, making sure the ones, tens, hundreds, and so on are all aligned. We begin with the ones column: 3 minus 2 equals 1. Moving to the tens column, we subtract 5 from 5, which gives us 0. Now, for the hundreds column, we need to subtract 6 from 2. Since 2 is smaller than 6, we've got to borrow. But, the thousands place is a 0, so we need to go all the way to the hundred-thousands place to borrow. Borrowing 1 from the 7 in the hundred-thousands place makes it a 6. That 1 we borrowed goes to the ten-thousands place, turning that 0 into a 10. Then, we borrow 1 from the ten-thousands place, making it a 9, and give it to the thousands place, turning that 0 into a 10. Finally, we borrow 1 from the thousands place, making it a 9, and give it to the hundreds place, turning our 2 into a 12. Phew, that was a lot of borrowing! Now we can subtract: 12 minus 6 is 6. In the thousands column, 9 minus 7 is 2. Moving to the ten-thousands, 9 minus 5 is 4. Lastly, in the hundred-thousands column, 6 minus 4 is 2. Put it all together, and we find that 700 253 minus 457652 is 242601. You nailed it! All that borrowing might seem tricky, but you handled it like a champ.
Let's wrap up our subtraction practice with 523 125.9 - 1313. Just like before, let's line up those numbers by place value. Put 523 125.9 on top and 1313 underneath, making sure the decimal points line up. Since 1313 doesn’t have a decimal, we can think of it as 1313.0 to keep everything neat. Start with the tenths place. We have 9 minus 0, which is 9, so we write down .9. Moving to the ones column, we subtract 3 from 5, giving us 2. Next, we move to the tens column, where we subtract 1 from 2, which equals 1. Now, the hundreds: subtract 3 from 1. We can't do that, so we need to borrow from the thousands place. Borrow 1 from the 3, making it a 2, and turn our 1 in the hundreds place into 11. Now, 11 minus 3 is 8. In the thousands column, we have 2 minus 1, which gives us 1. And in the ten-thousands column, we simply bring down the 2 since there’s nothing to subtract from it. Lastly, bring down the 5 from the hundred-thousands place as well. So, when we subtract 1313 from 523 125.9, we get 521 812.9. You've successfully mastered another subtraction problem! High five!
Diving into Division Problems
Now, let's tackle division, which is all about splitting a number into equal groups. We'll start with 253985 Ă· 5. When we're dealing with division, especially with larger numbers, long division is our go-to method. It might look a bit intimidating at first, but once you break it down step by step, it's totally manageable. Set up the problem with 253985 inside the division bracket and 5 outside. Start by looking at the first digit of the number inside the bracket, which is 2. Can 5 go into 2? Nope, 2 is too small. So, we move to the first two digits, 25. How many times does 5 go into 25? It goes in exactly 5 times. Write the 5 above the 5 in 253985. Now, multiply 5 (the divisor) by 5 (the quotient we just wrote down), which gives us 25. Write this 25 below the 25 inside the bracket and subtract them. 25 minus 25 equals 0, so we're good to move on. Bring down the next digit from inside the bracket, which is 3. Now we ask, how many times does 5 go into 3? Well, 5 is larger than 3, so it goes in 0 times. Write a 0 next to the 5 in our quotient. Since 5 goes into 3 zero times, we multiply 5 by 0, which gives us 0. Write this 0 below the 3 and subtract. 3 minus 0 is 3. Now, bring down the next digit, which is 9. We now have 39. How many times does 5 go into 39? It goes in 7 times (5 x 7 = 35). Write 7 next to 0 in our quotient. Multiply 5 by 7, which is 35, and write this below the 39. Subtract 35 from 39, which leaves us with 4. Bring down the next digit, which is 8. We now have 48. How many times does 5 go into 48? It goes in 9 times (5 x 9 = 45). Write 9 next to the 7 in our quotient. Multiply 5 by 9, which is 45, and write this below the 48. Subtract 45 from 48, and we have 3 left. Bring down the last digit, which is 5. We now have 35. How many times does 5 go into 35? It goes in exactly 7 times. Write 7 next to the 9 in our quotient. Multiply 5 by 7, which gives us 35. Subtract 35 from 35, and we get 0. Woo-hoo! We have a remainder of 0, which means 253985 divided by 5 is exactly 50797. You conquered your first long division problem! Each step is like solving a mini-puzzle, and you nailed it.
Next, we're diving into the division problem 250324 ÷ 2. Let’s set it up for long division. Put 250324 inside the division bracket and 2 outside. First, we'll look at the first digit inside the bracket, which is 2. How many times does 2 go into 2? Exactly once! So, we write a 1 above the 2 in 250324. Now, we multiply 1 (the quotient we just wrote) by 2 (the divisor), which gives us 2. Write this 2 below the 2 inside the bracket and subtract them. 2 minus 2 is 0, so we can move on. Next, we bring down the 5. How many times does 2 go into 5? It goes in 2 times (2 x 2 = 4). Write 2 next to the 1 in our quotient. Multiply 2 by 2, which equals 4. Place the 4 under the 5 and subtract. 5 minus 4 is 1. Bring down the next digit, which is 0. Now we have 10. How many times does 2 go into 10? It goes in exactly 5 times. Write 5 next to the 2 in our quotient. Multiply 2 by 5, which is 10, and write it under the 10. Subtract 10 from 10, and we get 0. Bring down the next digit, which is 3. How many times does 2 go into 3? It goes in 1 time. Write 1 next to the 5 in our quotient. Multiply 2 by 1, which equals 2. Write the 2 under the 3 and subtract. 3 minus 2 is 1. Now, bring down the next digit, which is 2. We now have 12. How many times does 2 go into 12? It goes in exactly 6 times. Write 6 next to the 1 in our quotient. Multiply 2 by 6, which is 12. Write the 12 under our existing 12 and subtract. 12 minus 12 is 0. Bring down the last digit, which is 4. How many times does 2 go into 4? Exactly 2 times! Write 2 next to the 6 in our quotient. Multiply 2 by 2, which equals 4. Subtract 4 from 4, and we get 0. We have a remainder of 0, which means 250324 divided by 2 is exactly 125162. Fantastic job! Breaking down the steps makes the whole division process so much clearer, doesn’t it?
Let’s tackle our third division challenge: 82551 ÷ 3. Time to set up another long division problem! Place 82551 inside the division bracket and 3 outside. Start with the first digit, which is 8. How many times does 3 go into 8? It goes in 2 times (3 x 2 = 6). Write 2 above the 8 in 82551. Multiply 2 by 3, which is 6. Write 6 under the 8 and subtract. 8 minus 6 is 2. Bring down the next digit, which is 2. We now have 22. How many times does 3 go into 22? It goes in 7 times (3 x 7 = 21). Write 7 next to the 2 in our quotient. Multiply 3 by 7, which is 21. Write 21 under the 22 and subtract. 22 minus 21 is 1. Bring down the next digit, which is 5. Now we have 15. How many times does 3 go into 15? It goes in exactly 5 times. Write 5 next to the 7 in our quotient. Multiply 3 by 5, which equals 15. Write 15 under our existing 15 and subtract. 15 minus 15 is 0. Bring down the next digit, which is another 5. Again, how many times does 3 go into 5? It goes in 1 time. Write 1 next to the 5 in our quotient. Multiply 3 by 1, which is 3. Write the 3 under our 5 and subtract. 5 minus 3 is 2. Bring down the last digit, which is 1. We now have 21. How many times does 3 go into 21? It goes in exactly 7 times. Write 7 next to the 1 in our quotient. Multiply 3 by 7, which is 21. Subtract 21 from 21, and we get 0. No remainder this time! So, 82551 divided by 3 is exactly 27517. You’re becoming a division whiz!
So, we've solved six different math expressions today, covering addition, subtraction, and division. Remember, the key is to break down each problem into smaller, manageable steps. Keep practicing, and you'll become a math master in no time! You've got this!