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Chapter 1: Problem 36

Estimate each sum or difference by first rounding to the nearest hundred. Show your work. $$ \begin{array}{r} 9438 \\ -2787 \\ \hline \end{array} $$

Short Answer

Expert verified
6600

Step by step solution

01

- Round the numbers to the nearest hundred

First, round each number to the nearest hundred. 9438 rounds to 9400 and 2787 rounds to 2800.
02

- Set up the rounded subtraction problem

Write the subtraction problem with the rounded numbers: 9400 - 2800.
03

- Perform the subtraction

Now, subtract the rounded numbers: 9400 - 2800 = 6600

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Key Concepts

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

estimation
Estimation is a technique used to find an approximate answer that is close enough to the exact answer for practical purposes. This is especially useful when dealing with large numbers or when making quick calculations. It helps in getting a rough idea of what the answer might be without needing to spend too much time on precise arithmetic. For example, if you need to estimate the difference between 9438 and 2787, you can round both numbers to the nearest hundred before subtracting.

This way, you simplify the problem and make it easier to solve. In our exercise, 9438 is rounded to 9400 and 2787 is rounded to 2800. Once rounded, the subtraction becomes much simpler.
subtraction
Subtraction is one of the basic arithmetic operations that involves taking one number away from another. In our example, we are subtracting 2787 from 9438. By breaking down the process and rounding the numbers first, we simplify the subtraction.

One can follow these steps to subtract:
  • Align the numbers by their place values.
  • Subtract each digit starting from the rightmost place value, borrowing if necessary.
After rounding to the nearest hundred, our problem simplifies to 9400 - 2800, making it easier to compute.
nearest hundred
Rounding to the nearest hundred means adjusting a number up or down to the closest multiple of 100. This makes numbers simpler to work with, especially when estimating. The general rule is:

  • If the tens digit is 5 or more, round up.
  • If the tens digit is 4 or less, round down.
For instance, to round 9438 to the nearest hundred, look at the tens digit (3). Since 3 is less than 5, you round down to 9400. For 2787, the tens digit is 8. Since 8 is greater than or equal to 5, you round up to 2800.
arithmetic operations
Arithmetic operations are basic mathematical processes like addition, subtraction, multiplication, and division. In our exercise, subtraction is used to find the difference between two numbers. Understanding these operations is fundamental to solving various math problems.

Here is a quick summary of the four primary arithmetic operations:

  • Addition: Combining two or more numbers into a single sum.
  • Subtraction: Determining the difference between two numbers by removing one from another.
  • Multiplication: Finding the total when one number is taken a certain number of times.
  • Division: Splitting a number into equal parts.
Focusing on the rounded numbers (9400 and 2800) and using subtraction, we get 9400 - 2800 = 6600.

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