Operatii Matematice: Calculeaza Si Verifica In 3 Moduri

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Hey there, math enthusiasts! Ready to dive into some calculations and, most importantly, check our work in multiple ways? Today, we'll tackle a series of arithmetic operations, covering subtraction and addition. But it's not just about getting the answers; we're going to make sure those answers are rock solid! We'll perform each operation and then verify our results using three different methods. This approach helps us build confidence in our calculations and reinforces our understanding of these fundamental mathematical concepts. So, let's get started and make sure our math skills are sharp!

1. 8345 - 5267 =

This is our first challenge: a subtraction problem. We are going to start by subtracting 5267 from 8345, let's get to it!

Method 1: Direct Subtraction

  • Write down the numbers one below the other, aligning the digits by their place value (ones, tens, hundreds, thousands).
  • Start subtracting from the rightmost column (ones place). If the top digit is smaller than the bottom one, borrow from the next column.
  • In our case, we start with 5 - 7. Since 5 is smaller, we borrow 1 from the 4 in the tens place, making the 5 a 15, and the 4 a 3. Now, 15 - 7 = 8.
  • Moving to the tens place, we have 3 - 6. Again, we need to borrow. Borrow 1 from the 3 in the hundreds place, making the 3 a 13, and the 3 a 2. So, 13 - 6 = 7.
  • In the hundreds place, we have 2 - 2 = 0.
  • Finally, in the thousands place, we have 8 - 5 = 3.

Therefore, 8345 - 5267 = 3078.

Method 2: Addition to Check

  • To check subtraction, we use addition. Add the result (3078) to the number you subtracted (5267).
  • If the sum equals the original number (8345), your subtraction is correct.
  • 3078 + 5267:
    • 8 + 7 = 15 (write down 5, carry-over 1).
    • 7 + 6 + 1 (carry-over) = 14 (write down 4, carry-over 1).
    • 0 + 2 + 1 (carry-over) = 3.
    • 3 + 5 = 8.

3078 + 5267 = 8345. Our answer is correct!

Method 3: Using a Number Line

  • Visualize a number line. Start at 8345.
  • Subtract 5267 by breaking it down: first subtract 5000, then 200, then 60, then 7.
  • Alternatively, you can add from 5267 until you reach 8345. This also ensures the accuracy of the result.

After going through those three ways of calculating, we can confirm that the result for the first math problem is 3078

2. 3456 + 998 =

Alright, let's switch gears and tackle an addition problem! This time, we'll add 3456 and 998, and we'll check our work the same way.

Method 1: Direct Addition

  • Write the numbers one below the other, aligning digits by their place value.
  • Start adding from the rightmost column (ones place).
  • 6 + 8 = 14 (write down 4, carry-over 1).
  • 5 + 9 + 1 (carry-over) = 15 (write down 5, carry-over 1).
  • 4 + 9 + 1 (carry-over) = 14 (write down 4, carry-over 1).
  • 3 + 0 + 1 (carry-over) = 4.

So, 3456 + 998 = 4454.

Method 2: Subtraction to Check

  • To check addition, use subtraction. Subtract one of the addends (e.g., 998) from the sum (4454).
  • If the difference equals the other addend (3456), your addition is correct.
  • 4454 - 998:
    • We need to borrow from the tens place: 14 - 8 = 6.
    • We need to borrow from the hundreds place: 14 - 9 = 5.
    • 13 - 9 = 4.
    • 3 - 0 = 3.

4454 - 998 = 3456. Correct!

Method 3: Breaking Down and Adding

  • Break down the numbers to make addition easier. For example: 998 can be seen as 1000 - 2.
  • Add 3456 + 1000 = 4456, and then subtract 2, which equals 4454. So, 3456 + 998 = 4454.

We are able to ensure the correctness of the second math problem! The answer is 4454.

3. 6004 - 1897 =

Let's move on to another subtraction problem. This one involves some borrowing, so pay close attention!

Method 1: Direct Subtraction

  • Write the numbers one below the other.
  • Start from the right: 4 - 7. We need to borrow.
  • Since the tens and hundreds places are 0, we borrow from the thousands place (6), making it 5. The hundreds place becomes 9, the tens place becomes 9, and the ones place becomes 14.
  • 14 - 7 = 7.
  • 9 - 9 = 0.
  • 9 - 8 = 1.
  • 5 - 1 = 4.

So, 6004 - 1897 = 4107.

Method 2: Addition to Check

  • Add the result (4107) to the number subtracted (1897).
  • 4107 + 1897:
    • 7 + 7 = 14 (carry-over 1).
    • 0 + 9 + 1 = 10 (carry-over 1).
    • 1 + 8 + 1 = 10 (carry-over 1).
    • 4 + 1 + 1 = 6.

4107 + 1897 = 6004. Perfect!

Method 3: Using a Number Line

  • Start at 6004 on the number line.
  • Subtract 1897 in stages, or add up from 1897 until you reach 6004.

Again, using the three methods, we can guarantee the correctness of the third calculation. The result is 4107.

4. 2453 + 3678 =

Time for more addition! Let's see how this one goes.

Method 1: Direct Addition

  • Write the numbers, aligning the digits.
  • 3 + 8 = 11 (carry-over 1).
  • 5 + 7 + 1 = 13 (carry-over 1).
  • 4 + 6 + 1 = 11 (carry-over 1).
  • 2 + 3 + 1 = 6.

2453 + 3678 = 6131.

Method 2: Subtraction to Check

  • Subtract one addend from the sum.
  • 6131 - 3678:
    • 11 - 8 = 3.
    • 12 - 7 = 5.
    • 10 - 6 = 4.
    • 5 - 3 = 2.

6131 - 3678 = 2453. Correct!

Method 3: Breaking Down and Adding

  • Break down each number by place value (thousands, hundreds, tens, ones).
  • Add the corresponding place values separately and then combine them.

The fourth result, after calculating with the three methods, is 6131.

5. 3654 + 6346 =

Another addition problem. Let's keep the momentum going!

Method 1: Direct Addition

  • Write the numbers, aligning the digits.
  • 4 + 6 = 10 (carry-over 1).
  • 5 + 4 + 1 = 10 (carry-over 1).
  • 6 + 3 + 1 = 10 (carry-over 1).
  • 3 + 6 + 1 = 10.

3654 + 6346 = 10000.

Method 2: Subtraction to Check

  • Subtract one addend from the sum.
  • 10000 - 6346:
    • 10 - 6 = 4.
    • 9 - 4 = 5.
    • 9 - 3 = 6.
    • 9 - 0 = 3.

10000 - 6346 = 3654. The result is accurate!

Method 3: Rounding and Adjusting

  • Round each number to the nearest thousand. 3654 is approximately 4000 and 6346 is approximately 6000.
  • 4000 + 6000 = 10000. The initial estimate is 10000.

With all the different ways to check the accuracy of the operations, we can agree that the fifth result is 10000.

6. 8643 - 4748 =

Let's get back to subtraction. Another chance to put those borrowing skills to work!

Method 1: Direct Subtraction

  • Write the numbers, aligning the digits.
  • 3 - 8. Borrow from the tens place, making it 13 - 8 = 5.
  • 3 - 4. Borrow from the hundreds place, making it 13 - 4 = 9.
  • 5 - 7. Borrow from the thousands place, making it 15 - 7 = 8.
  • 7 - 4 = 3.

8643 - 4748 = 3895.

Method 2: Addition to Check

  • Add the result and the subtracted number.
  • 3895 + 4748:
    • 5 + 8 = 13 (carry-over 1).
    • 9 + 4 + 1 = 14 (carry-over 1).
    • 8 + 7 + 1 = 16 (carry-over 1).
    • 3 + 4 + 1 = 8.

3895 + 4748 = 8643. Awesome!

Method 3: Estimating and Adjusting

  • Round 8643 to 9000 and 4748 to 5000. 9000 - 5000 = 4000.
  • The actual result is slightly less than 4000, which matches the calculation.

After having tested all the methods, we can guarantee that the answer for this operation is 3895.

7. 4570 + 2987 =

Time for another addition! Let's see how we do!

Method 1: Direct Addition

  • Write the numbers, aligning the digits.
  • 0 + 7 = 7.
  • 7 + 8 = 15 (carry-over 1).
  • 5 + 9 + 1 = 15 (carry-over 1).
  • 4 + 2 + 1 = 7.

4570 + 2987 = 7557.

Method 2: Subtraction to Check

  • Subtract one addend from the sum.
  • 7557 - 2987:
    • 7 - 7 = 0.
    • 15 - 8 = 7.
    • 14 - 9 = 5.
    • 6 - 2 = 4.

7557 - 2987 = 4570. Correct!

Method 3: Adding in Parts

  • Break down 2987 into 3000 - 13.
  • 4570 + 3000 = 7570, and then subtract 13, which is 7557.

The seventh math problem is correctly calculated, and the result is 7557.

8. 10000 - 3765 =

Last one, guys! Let's make this one count!

Method 1: Direct Subtraction

  • Write the numbers, aligning the digits.
  • We need to borrow a lot. From the ten thousands, it becomes 9, then 9, then 9, and finally 10.
  • 10 - 5 = 5.
  • 9 - 6 = 3.
  • 9 - 7 = 2.
  • 9 - 3 = 6.

10000 - 3765 = 6235.

Method 2: Addition to Check

  • Add the result and the subtracted number.
  • 6235 + 3765:
    • 5 + 5 = 10 (carry-over 1).
    • 3 + 6 + 1 = 10 (carry-over 1).
    • 2 + 7 + 1 = 10 (carry-over 1).
    • 6 + 3 + 1 = 10.

6235 + 3765 = 10000. Nailed it!

Method 3: Using a Number Line

  • Start at 10000 and move backwards 3765 units.

We can confirm with confidence that the final result is 6235. Good job!

That’s a wrap, everyone! We’ve successfully performed and verified all the operations using three different methods. By using different methods, we can be sure that the calculations are on point. Keep practicing and happy calculating, guys!