Problem 60 - Prealgebra

Question

Find each difference. $$53-17$$

Step-by-Step Solution

Answer

The difference is 36.

Step 1: Understand the Problem

The problem requires us to find the difference between the two numbers 53 and 17. Finding the difference involves subtracting the smaller number (17) from the larger number (53).

Step 2: Set Up the Subtraction

Write the subtraction problem vertically to ensure clarity and ease of calculation. Arrange the numbers with the larger number (53) on top and the smaller number (17) below it: 53 - 17 ----

Step 3: Perform Subtraction

Start subtracting from the rightmost digit (units place). Subtract 7 from 3, which cannot be done directly because 3 is smaller than 7. We need to borrow 1 from the tens place of the top number.

Step 4: Borrowing

Decrease the tens digit of 53 from 5 to 4 (borrowed 1 to make the units digit 13). Now, perform 13 - 7, which equals 6. Write 6 under the units column.

Step 5: Subtract Tens Place

Now, subtract in the tens place: 4 - 1 = 3. Write 3 under the tens column. So, after performing the subtraction we have: 53 - 17 ---- 36

Step 6: Verify the Result

Add the difference we found (36) and the number we subtracted (17), and we should get the starting number (53): 36 + 17 = 53. This confirms that our subtraction is correct.

Key Concepts

Borrowing in Subtraction

Borrowing, also known as regrouping, is a crucial technique in subtraction that comes into play when you subtract a larger digit from a smaller one. This concept can sometimes be a little tricky, but understanding it is key to mastering subtraction.

When you have a subtraction problem like 53 - 17, and you need to subtract a larger number (7) from a smaller one (3), you use borrowing:

• Look at the digit immediately to the left (10s place in this case).
• Decrease the tens digit by one, turning the 5 in 53 into a 4.
• Add 10 to the digit in the units place making it 13.

Now, you can subtract 7 from 13.

By borrowing, we're essentially regrouping parts of the number to make subtraction possible. It's important to remember this method for future problems involving subtraction.

Basic Arithmetic Operations

Subtraction is one of the four fundamental arithmetic operations, along with addition, multiplication, and division. It is used to find the difference between two numbers.

In our example of 53 - 17, subtraction helps define how far 17 is from 53 in numerical terms. Here are the steps broken down:

• Identify the larger number (53) and the smaller number (17).
• Arrange the numbers in a vertical column with the larger number on top.
• Subtract each digit, starting from the rightmost digit.

Subtraction requires understanding the principle of finding what remains after a certain amount is taken away. Practicing subtraction will make these steps familiar and strengthen your problem-solving skills.

Place Value System

The place value system is foundational to understanding subtraction because it helps us determine the value of digits in numbers. Each place in a number has a different value: units, tens, hundreds, etc.

In the problem 53 - 17, understanding place value clarifies why borrowing is necessary:

• The 3 is in the units place, representing 3 ones.
• The 5 is in the tens place, representing 50 (5 sets of ten).

When borrowing, you are actually shifting value between these places:

• Turning the 50 into 40 and increasing the 3 ones to 13 ones.

Recognizing the role of place value in subtraction allows you to apply borrowing accurately and efficiently, ensuring that your calculations are correct. This system is how numbers maintain their order and structure, aiding in clear numerical calculations.