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Chapter 1: Problem 175

In the following exercises, subtract and then check by adding. $$ 525-179 $$

Short Answer

Expert verified
346

Step by step solution

01

- Perform the Subtraction

Start by subtracting the smaller number from the larger one. In this case, subtract 179 from 525.\[525 - 179 = 346\]
02

- Check by Adding

To check the result of the subtraction, add the difference just found (346) to 179. If the sum is equal to 525, the subtraction is correct.\[346 + 179 = 525\]

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Key Concepts

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

Subtraction
Subtraction is one of the basic arithmetic operations, symbolized by the minus sign (-). It involves taking away one number from another. For instance, in the exercise, we subtract 179 from 525. Here鈥檚 how it works:
  • Line up the numbers by their place values (units, tens, hundreds, etc.).
  • Starting from the right, subtract each digit of the smaller number from the corresponding digit of the larger number. If necessary, borrow from the next higher place value.
This is how we perform: \[ 525 - 179 = 346. \] We started by subtracting 9 from 5 in the units place, but since 5 is smaller, we borrowed 1 from the tens place making it 15 - 9 = 6. We continued with the tens place: 1 (which is now 4) minus 7, borrowing from the hundreds. Finally, 4 minus 1 from the hundreds place gives us, 3. Subtraction simplified the problem and is the reverse of addition.
Addition
Addition is another fundamental arithmetic operation, symbolized by the plus sign (+). It involves combining two or more numbers to get a total sum. Addition can also be used to verify the correctness of subtraction.
  • Add the numbers back to check if the original number can be obtained.
  • Place the numbers one below the other and line up by place values.
  • Start adding from the right-most digits in the units place.
In our example, we check: \[ 346 + 179 \] We add 6 and 9 in the units place, which sums to 15. Write down 5 and carry 1 to the tens place. Next, add 4, 7, and the carried-over 1, resulting in 12. Write down 2 and carry 1 over to the hundreds place. Lastly, add 3, 1, and the carried over 1 making it 5, arriving at: \[ 346 + 179 = 525. \] Hence, the addition confirms our subtraction is correct, reinforcing our understanding of both operations.
Arithmetic Operations
Arithmetic operations are basic mathematical procedures that include addition, subtraction, multiplication, and division. These operations form the foundation for most mathematics. Each has a definitive role:
  • Addition: Combining numbers.
  • Subtraction: Finding the difference between numbers.
  • Both can be used for verifying results, as demonstrated in checking subtraction results through addition.
Knowing these operations well aids in solving basic to complex mathematical problems. Understanding, practicing, and verifying calculations ensure accuracy and strengthen fundamental math skills.

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