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Chapter 1: Problem 28

$$ \begin{array}{r} 674 \\ -299 \\ \hline \end{array} $$

Short Answer

Expert verified
The answer is 375.

Step by step solution

01

Set Up the Problem

First, write down the numbers, aligning them vertically by their places: hundreds, tens, and ones.\[\begin{array}{c} 674 \- 299 \\hline\end{array}\]Ensure each digit is in the correct column.
02

Subtract the Ones Place

Look at the rightmost column first, which is the ones place. We have 4 (top) and 9 (bottom). Since 4 is less than 9, we need to borrow from the tens place. Borrow 1 (or 10) from the 7 in the tens place, making it 6 and adding 10 to the 4, making it 14. Subtract: 14 - 9 = 5.
03

Subtract the Tens Place

After borrowing, the tens place has 6 (top) and 9 (bottom). Since 6 is less than 9, we need to borrow again from the hundreds place. Borrow 1 from the 6, turning it into 5, and add 10 to the 6, making it 16. Subtract: 16 - 9 = 7.
04

Subtract the Hundreds Place

Now the hundreds place has 5 (top) and 2 (bottom). Subtract: 5 - 2 = 3.
05

Write the Final Answer

Now that we have subtracted from each column, combine the results from each place to get the final answer:\[\begin{array}{c} 674 \- 299 \\hline 375 \\end{array}\]Therefore, 674 - 299 = 375.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Borrowing
Borrowing is a fundamental technique in subtraction, especially when dealing with numbers where the minuend digit is smaller than the subtrahend digit. In the problem, 674 - 299, borrowing helps us manage such situations. Imagine you have just 4 apples but need to give away 9; it's not possible without borrowing from a neighbor. In subtraction, the neighbor is the next higher place value.
  • Step into the ones place: to subtract 9 from 4, borrow 1 ten (or 10 units) from the tens place, changing 7 to 6 and 4 to 14.
  • Tens place adjustments continue from above, subtracting 9 from the adjusted 16.
  • This ensures all digits can be subtracted smoothly, producing correct results.
Borrowing is about readjusting the numbers so subtraction can always proceed smoothly.
Place Value
Place value is a system where the position of a digit in a number determines its value, such as ones, tens, hundreds, etc. In our subtraction problem, this concept is crucial for correctly setting up and executing the arithmetic.
  • Ones are the rightmost digits; in this case, we started with 4 - 9.
  • Tens are the next set of digits; originally, we had 7 - 9 here after borrowing, which later became 16 - 9.
  • Hundreds, the third column from the right, shows 6 - 2, reduced to 5 - 2 after borrowing.
Understanding place value allows the smooth execution of subtraction by keeping like terms aligned.
Arithmetic Operations
Arithmetic operations are the basic math processes, including addition, subtraction, multiplication, and division. In this exercise, subtraction is the focus. Each operation has unique rules; subtraction often involves concept highlights like aligning place values and borrowing as seen.
  • The main operation was to find the difference between 674 and 299.
  • Using subtraction, we systematically handled each column, borrowing when needed.
  • The goal is to compute these operations accurately, giving us the correct difference of 375 in this case.
Mastery of arithmetic operations ensures numbers add up correctly, critical for more advanced math concepts.

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