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Chapter 1: Problem 171

In the following exercises, subtract and then check by adding. $$ 75-47 $$

Short Answer

Expert verified
The answer is 28. Verification: 28 + 47 = 75.

Step by step solution

01

Perform Subtraction

Subtract 47 from 75. \(75 - 47 = 28\)
02

Check by Adding

To verify the answer, add the result of the subtraction (28) to the number that was subtracted (47). \(28 + 47 = 75\)
03

Verify

Since the sum is equal to the original number, the subtraction is correct.

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Key Concepts

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

arithmetic operations
Arithmetic operations are basic calculations that involve numbers. They include operations like addition, subtraction, multiplication, and division. Starting with simpler processes, like addition and subtraction, helps build a strong foundation for more complex mathematics.
In arithmetic, the order in which you perform calculations can matter. For simple operations, performing them step by step ensures accuracy and understanding.
Let's dive deeper into subtraction and addition through an exercise to see how these operations work together to verify each other.
subtraction
Subtraction is one of the key arithmetic operations. It involves taking one number away from another. In our exercise, we start with subtracting 47 from 75.
\(75 - 47 = 28\)
Subtraction can be seen as removing or reducing a quantity. For instance, if you have 75 apples and you give away 47, you're left with 28 apples. When performing subtraction, align numbers correctly to ensure that you subtract corresponding digits, starting from the rightmost digit.
addition
Addition is another fundamental arithmetic operation that combines two numbers into a larger value. To check your subtraction work, you can use addition.
In our exercise, we confirm if the subtraction was done correctly by adding the result (28) back to the number we subtracted (47): \(28 + 47 = 75\)
This step is crucial because it shows whether our initial subtraction was correct. In this case, the sum equals back to the original number (75), proving the subtraction was accurate.
checking work
Checking your work is an essential practice in math. It ensures that you didn't make any errors in your calculations. After performing subtraction, you can quickly verify it by adding the result to the subtracted number.
For example, from our subtraction step: \(75 - 47 = 28\), we add the difference (28) back to the subtracted number (47). If we get the original number (75), our subtraction is correct.
Engaging in the habit of checking your work through the opposite operation builds confidence and bolsters your mathematical skills, ensuring greater accuracy.

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