Problem 514 - Prealgebra

Question

Subtract and then check by adding. $$110-87$$

Step-by-Step Solution

Answer

110 - 87 = 23

Step 1: Subtract the numbers

Start by subtracting 87 from 110. Let's set up the subtraction: \( 110 - 087 \)Perform the subtraction: \( 110 - 87 = 23 \)

Step 2: Check by adding

Next, check our subtraction by adding the result (23) back to the subtrahend (87). If the addition equals the original minuend (110), the subtraction is correct.Set up the addition: \( 87 + 23 \)Perform the addition: \( 87 + 23 = 110 \)

Step 3: Conclusion

Since adding the result of our subtraction (23) to the number we subtracted (87) gives us the original number (110), our subtraction is correct.

Key Concepts

checking subtraction with addition

Subtraction can sometimes be tricky, and it is easy to make small mistakes. A brilliant way to ensure that you've done it right is by checking your subtraction result with addition. This method leverages the relationship between addition and subtraction, basic arithmetic operations that are inverses of each other. Let's take the problem from the original exercise: subtracting 87 from 110.

• First, we perform the subtraction: \(110 - 87 = 23\)
• Next, to double-check our work, we add the result (23) back to the subtrahend (87): \(87 + 23\)
• If our subtraction was correct, the result should equal the initial minuend (110): \(87 + 23 = 110\)

This addition verification confirms that the subtraction was performed correctly.

math verification

Math verification is crucial in ensuring accuracy and correctness in solving problems. In the case of subtraction, verifying with addition is a useful technique. Verification helps to catch mistakes and reinforces understanding of the relationships between different math operations.
Consider the previous exercise:

• Start by doing the subtraction: \(110 - 87\) which equals \(23\)
• To verify, add the result back to the subtrahend: \(87 + 23\)
• If the sum equals the original minuend, then the subtraction is verified: \(87 + 23 = 110\)

By practicing verification, you develop better accuracy and confidence when performing arithmetic operations. Whether you're double-checking subtraction with addition or using another method, this practice is an essential habit for mastering math.

basic arithmetic operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. Mastering these operations is fundamental to advancing in mathematics. Each operation has its unique properties but also relates to the others in various ways.
Let's break down how subtraction and addition, specifically, are related:

• Addition involves combining numbers to get a total: \(a + b = c\)
• Subtraction is essentially the reverse of addition: \(c - b = a\)
• To check a subtraction result, you can use addition: if \(110 - 87 = 23\), then \(23 + 87\) should return \(110\)

Understanding these relationships helps in using one operation to verify the result of another. Mastery of these basic operations is a stepping stone to tackling more complex math problems.