Question

635 = 600 + 30 + 5
519 = 500 + 10 + 9
subtract the hundreds, the tens, and th
635 - 519 = \square + \square + \square
now find the answer.
635 - 519 = \square

Explanation:

Step1: Subtract hundreds place

Subtract the hundreds digits: \(600 - 500 = 100\)

Step2: Subtract tens place

Subtract the tens digits: \(30 - 10 = 20\)

Step3: Subtract ones place

Subtract the ones digits: \(5 - 9\) (but we can't do that directly, wait, actually, we should consider the place values correctly. Wait, no, the problem says to subtract hundreds, tens, and then combine? Wait, no, the original numbers are decomposed as \(635 = 600 + 30 + 5\) and \(519 = 500 + 10 + 9\). So when subtracting, we do \(600 - 500 = 100\), \(30 - 10 = 20\), and \(5 - 9\) is not possible, but wait, maybe there's a mistake in my initial thought. Wait, no, the problem is structured as subtracting each place: hundreds, tens, and then the ones? Wait, no, maybe it's a decomposition subtraction where we do \(635 - 519=(600 - 500)+(30 - 10)+(5 - 9)\), but \(5 - 9\) is negative, which doesn't make sense. Wait, maybe the problem is actually a different approach. Wait, no, maybe I misread. Wait, the problem says "Subtract the hundreds, the tens, and the..." (maybe the ones, but with borrowing). Wait, no, the first part is \(635 - 519=\square+\square+\square\), so let's do each place:

Hundreds: \(600 - 500 = 100\)

Tens: \(30 - 10 = 20\)

Ones: \(5 - 9\) is not possible, but wait, maybe the problem is designed to have positive differences? Wait, no, \(635 - 519 = 116\). Let's check: \(600 - 500 = 100\), \(30 - 10 = 20\), \(5 - 9 = -4\), but that would be \(100 + 20 - 4 = 116\). Wait, but the problem's first box is for the hundreds subtraction, second for tens, third for ones. So:

Hundreds: \(600 - 500 = 100\)

Tens: \(30 - 10 = 20\)

Ones: \(5 - 9 = -4\)? But that's negative. Wait, maybe the problem has a typo, or maybe I misinterpret. Wait, no, maybe the decomposition is different. Wait, \(635 = 600 + 30 + 5\), \(519 = 500 + 10 + 9\). So \(635 - 519 = (600 - 500) + (30 - 10) + (5 - 9) = 100 + 20 - 4\). But the problem's boxes are for three terms, so maybe the ones term is \(5 - 9\) but we have to write it as is? Wait, no, that can't be. Wait, maybe the problem is actually a subtraction with borrowing, but decomposed. Wait, \(635 - 519\):

First, subtract hundreds: \(600 - 500 = 100\)

Subtract tens: \(30 - 10 = 20\)

Subtract ones: \(5 - 9\) is not possible, so we need to borrow from the tens place. Wait, but the problem's decomposition is \(635 = 600 + 30 + 5\), so maybe we can adjust the tens place: \(30 = 20 + 10\), and then the ones place becomes \(10 + 5 = 15\). Then \(15 - 9 = 6\), and the tens place becomes \(20\) (since we borrowed 10 from 30, making it 20). Then:

Hundreds: \(600 - 500 = 100\)

Tens: \(20 - 10 = 10\) (wait, no, original tens was 30, we borrowed 10, so 30 - 10 = 20, then used 10 for ones, so tens is 20? No, maybe I'm overcomplicating. Wait, the problem's first part is to fill in the boxes as the subtraction of each place: hundreds, tens, ones. So:

\(635 - 519 = (600 - 500) + (30 - 10) + (5 - 9) = 100 + 20 + (-4)\), but that's not positive. Wait, maybe the problem has a mistake, or maybe I misread the numbers. Wait, \(635 - 519 = 116\). Let's calculate \(100 + 20 + (5 - 9)\) is \(116\) because \(100 + 20 = 120\), \(120 - 4 = 116\). So the three boxes are \(100\), \(20\), and \(-4\)? But that seems odd. Wait, maybe the problem is intended to have positive differences, so maybe the decomposition is wrong. Wait, no, the original numbers are \(635 = 600 + 30 + 5\) and \(519 = 500 + 10 + 9\). So when subtracting, we do \(600 - 500 = 100\), \(30 - 10 = 20\), and \(5 - 9\) is \(-4\), so \(100 + 20 - 4 = 116\). Then the first box is \(100\), second \(20\), third \(-4\), but that's unusual. Alternatively, maybe the problem is a typo and the ones digit of 635 is 15? No, 635 is 635. Wait, maybe I made a mistake in the subtraction. Let's do \(635 - 519\):

\(635 - 500 = 135\), \(135 - 19 = 116\). Yes, that's correct. So decomposing the subtraction as \(635 - 519 = (600 - 500) + (30 - 10) + (5 - 9) = 100 + 20 - 4 = 116\). So the three boxes are \(100\), \(20\), and \(-4\), but that's not positive. Wait, maybe the problem is designed to have the ones place as \(15 - 9\) by borrowing, so we adjust the decomposition: \(635 = 600 + 20 + 15\) (borrowing 10 from tens to ones), then \(519 = 500 + 10 + 9\). Then subtracting: \(600 - 500 = 100\), \(20 - 10 = 10\), \(15 - 9 = 6\). Then \(100 + 10 + 6 = 116\). Ah, that makes sense! So the correct decomposition after borrowing is \(635 = 600 + 20 + 15\) (since we can't do \(5 - 9\), we borrow 10 from the tens place: 30 becomes 20, and 5 becomes 15). Then:

Hundreds: \(600 - 500 = 100\)

Tens: \(20 - 10 = 10\)

Ones: \(15 - 9 = 6\)

Then \(100 + 10 + 6 = 116\). So that's the correct way. So the first box is \(100\) (hundreds subtraction), second \(10\) (tens subtraction after borrowing), third \(6\) (ones subtraction after borrowing). Wait, but the original decomposition was \(635 = 600 + 30 + 5\), so maybe the problem expects us to do the subtraction as \(600 - 500 = 100\), \(30 - 10 = 20\), and then \(5 - 9\) is not possible, but the problem might have a different approach. Wait, the problem says "Subtract the hundreds, the tens, and the..." (maybe the ones, and then combine). But according to the correct subtraction, \(635 - 519 = 116\), which is \(100 + 10 + 6\) (after borrowing). So maybe the problem expects us to do the subtraction by place:

Hundreds: \(600 - 500 = 100\)

Tens: \(30 - 10 = 20\) (but then we have to borrow from tens to ones, so actually, \(30\) becomes \(20\) and \(5\) becomes \(15\), so tens subtraction is \(20 - 10 = 10\), ones subtraction is \(15 - 9 = 6\)). So the three boxes are \(100\), \(10\), \(6\), and then the sum is \(116\).

Step1: Subtract hundreds

\(600 - 500 = 100\)

Step2: Subtract tens (after borrowing)

\(30 - 10 = 20\) but we borrow 10 from tens to ones, so tens becomes \(20\), so \(20 - 10 = 10\)

Step3: Subtract ones (after borrowing)

\(5 + 10 - 9 = 6\) (since we borrowed 10 from tens, ones becomes \(15\))

Step4: Sum the results

\(100 + 10 + 6 = 116\)

Wait, maybe the problem's first part is to fill in the three boxes as \(100\), \(20\), and \(-4\), but that's not right. Alternatively, maybe the problem has a typo, but the correct answer for \(635 - 519\) is \(116\). Let's verify: \(519 + 116 = 635\). Yes, \(519 + 100 = 619\), \(619 + 10 = 629\), \(629 + 6 = 635\). Correct.

So going back, the first part: \(635 - 519 = (600 - 500) + (30 - 10) + (5 - 9)\) but that gives \(100 + 20 - 4 = 116\). So the three boxes are \(100\), \(20\), and \(-4\), but that's negative. Alternatively, the problem expects us to do the subtraction by place without considering borrowing, but that's incorrect. However, the second part is to find the answer, which is \(116\).

So for the first part, the boxes are \(100\), \(20\), and \(-4\), but that's odd. Alternatively, maybe the problem is designed to have positive differences, so the decomposition is wrong. Wait, maybe the original numbers are \(635 = 600 + 30 + 5\) and \(519 = 500 + 10 + 9\), so subtracting each place:

Hundreds: \(600 - 500 = 100\)

Tens: \(30 - 10 = 20\)

Ones: \(5 - 9\) is not possible, so we have to adjust. But the problem says "Subtract the hundreds, the tens, and the...", so maybe it's a mistake, but the answer for the subtraction is \(116\).

So to summarize:

First, \(635 - 519 = (600 - 500) + (30 - 10) + (5 - 9) = 100 + 20 - 4 = 116\). So the three boxes are \(100\), \(20\), and \(-4\), but that's not positive. Alternatively, using borrowing, we get \(100 + 10 + 6 = 116\).

But the problem's first part is to fill in the boxes, so let's do it as per the decomposition:

\(600 - 500 = 100\)

\(30 - 10 = 20\)

\(5 - 9 = -4\)

Then \(100 + 20 + (-4) = 116\).

Then the answer is \(116\).

Answer:

First, \(635 - 519 = \boldsymbol{100} + \boldsymbol{20} + \boldsymbol{(-4)}\) (but usually, we use borrowing, so it's \(100 + 10 + 6\)), and the final answer is \(\boldsymbol{116}\).

Wait, but the problem might expect the positive differences, so maybe the correct way is:

After borrowing, \(635 = 600 + 20 + 15\) (borrow 10 from tens to ones), \(519 = 500 + 10 + 9\)

Then \(600 - 500 = 100\), \(20 - 10 = 10\), \(15 - 9 = 6\)

So \(635 - 519 = 100 + 10 + 6 = 116\)

So the three boxes are \(100\), \(10\), \(6\), and the answer is \(116\).

So the final answer for \(635 - 519\) is \(\boldsymbol{116}\).