Problem 599 - Prealgebra

Question

Simplify. $$733-291$$

Step-by-Step Solution

Answer

442

Step 1: Identify the Operation

In this exercise, the operation required to simplify the expression is subtraction.

Step 2: Write Down the Expression

Write the given expression clearly: 733 - 291.

Step 3: Perform the Subtraction

Subtract 291 from 733.Begin with the units column: 3 - 1 = 2.Move to the tens column: 3 - 9. Since you cannot subtract 9 from 3 directly, you need to borrow 1 from the hundreds column.With the borrowed 1, the tens column becomes 13: 13 - 9 = 4.Now the hundreds column: 7 (original) - 1 (borrowed) - 2 = 4.Therefore, 733 - 291 = 442.

Key Concepts

Borrowing

Borrowing is a technique used in subtraction when a digit in the minuend (the number from which another number is subtracted) is smaller than the corresponding digit in the subtrahend (the number being subtracted).
This involves moving a '1' from the next higher place value column in the minuend.
When you borrow 1, it is equal to 10 in the column from where it was borrowed, which makes the subtraction possible.
For example, in the problem 733 - 291:
When we need to subtract 9 from 3 in the tens column, we borrow 1 from the hundreds column.
This borrowed 1 changes the 3 in the tens column to 13, making the operation feasible.
The original 7 in the hundreds column then becomes 6 after borrowing.
Fully understanding borrowing aids in accurate and efficient subtraction.

Place Value

Place value is a fundamental concept in arithmetic that represents the value of the position of a digit in a number.
It determines how much a digit is worth based on its position within the number.
For instance, in the number 733:

• The 3 in the ones place has a value of 3.
• The 3 in the tens place has a value of 30.
• The 7 in the hundreds place has a value of 700.

When performing subtraction, understanding place value helps in arranging the numbers correctly and borrowing properly if necessary.
In the subtraction problem 733 - 291, place value informs us about how to handle each digit in its relevant column.
It ensures that we align the digits correctly: ones under ones, tens under tens, and hundreds under hundreds.
This alignment guarantees that the subtraction across each column is done accurately.

Arithmetic Operations

Arithmetic operations form the foundation of all calculations in mathematics.
There are four primary arithmetic operations: addition, subtraction, multiplication, and division.
Subtraction is one of these fundamental operations and is performed by removing a number from another number.
In the exercise 733 - 291:
Subtraction is applied column-wise starting from the rightmost digit (units place).

• We subtract 1 from 3 in the ones place to get 2.
• In the tens place, we need to borrow because 3 is smaller than 9. After borrowing, 13 - 9 equals 4.
• In the hundreds place, we now have 6 (after borrowing) minus 2, which equals 4.

Performing these steps methodically ensures the correct result, which is 442.
Mastery of these operations, especially subtraction, is essential for solving real-world problems and more complex mathematical equations.