Problem 199 - Prealgebra

Question

In the following exercises, translate and simplify. $$ 76-47 $$

Step-by-Step Solution

Answer

29

Step 1: Identify the operation

The problem is asking to subtract 47 from 76. This is a simple arithmetic operation.

Step 2: Perform the subtraction

Subtract 47 from 76: \[ 76 - 47 \].

Step 3: Calculate the result

Calculate the difference: \[ 76 - 47 = 29 \]. This is the simplified answer.

Key Concepts

Arithmetic Operation

An arithmetic operation is the process of using basic math operations to solve problems. These fundamental operations include addition, subtraction, multiplication, and division. Understanding these operations is essential because they form the foundation of all mathematical concepts.

In our exercise, we focus on subtraction, which is one of these core arithmetic operations. When we see an expression like \(76 - 47\), we identify it as a subtraction problem. Always start by identifying what each number represents and the operation required for solving the problem.

Subtracting Numbers

Subtracting numbers involves taking one number away from another. This can be visualized by imagining that we're removing objects from a group. For example, if you have 76 apples and you give away 47 apples, you want to find out how many apples you have left.

In the exercise, we have the numbers 76 and 47. To subtract them, align 76 above 47 so that corresponding digits are in the same columns. Then subtract each digit starting from the rightmost digit (units place) towards the left.

Here’s the step-by-step solution:
1. Write 76 above 47.
2. Subtract the units digit: 6 - 7. Since 6 is smaller than 7, we need to borrow 1 from the tens digit of 76.
3. Now, 16 - 7 = 9 in the units place.
4. Next, subtract the tens digit with the borrowed value: (7-1) - 4 = 2.
5. The final answer is written as 29.

Calculating Difference

Calculating the difference between two numbers is one of the simplest yet most crucial skills in math. The 'difference' is another term for the result we get from subtracting one number from another.

In our exercise, 76 is the minuend and 47 is the subtrahend. The formula to calculate the difference is straightforward: \[ \text{Difference} = \text{Minuend} - \text{Subtrahend} \].

By following the arithmetic steps mentioned, we subtract 47 from 76. Here, 76 is the larger number, making it the minuend, and 47 is the number we subtract, the subtrahend. Performing the subtraction: \[ 76 - 47 = 29 \], the difference is 29.

Understanding this concept is critical because subtraction is used in various real-life situations, such as calculating remaining money after spending, finding out how much time is left, and much more. Always practice these kinds of problems to strengthen your understanding.