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Chapter 1: Problem 2

Perform each addition. Show the expanded form in problems 1 and 2 . Add 4,026 and 1,501.

Short Answer

Expert verified
The sum of 4,026 and 1,501 is 5,527.

Step by step solution

01

Write the Numbers in Expanded Form

Convert each number into its expanded form. The number 4,026 can be written as 4,000 + 20 + 6, and the number 1,501 can be written as 1,000 + 500 + 1.
02

Add Each Corresponding Place Value

Add the thousands, hundreds, tens, and ones place separately. For the thousands place: 4,000 + 1,000 = 5,000 For the hundreds place: 0 + 500 = 500 For the tens place: 20 + 0 = 20 For the ones place: 6 + 1 = 7
03

Combine the Sums

Now add all the sums from each place value: 5,000 + 500 + 20 + 7 = 5,527.

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Key Concepts

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

Expanded Form
Expanded form is a way of expressing a number by breaking it down into the value of each of its digits based on their position. This method helps us understand how each digit contributes to the overall value of the number. It鈥檚 like taking apart a puzzle to see all its pieces and how they fit together. For example, the number 4,026 can be expanded into 4,000 + 20 + 6. This means:
  • '4' is in the thousands place, thus contributing 4,000.
  • '0' is in the hundreds place, making no contribution in this case.
  • '2' is in the tens place, contributing 20.
  • '6' is in the ones place, contributing 6.
Likewise, 1,501 expands to 1,000 + 500 + 1. By writing numbers in expanded form, it simplifies arithmetic processes like addition, especially for complex numbers, by handling each place value separately.
Place Value
Place value is the foundation of our numerical system, which is the decimal system. It describes the value of each digit in a number, depending on its position within the number. Each position is ten times the value of the position to its right. Consider the number 4,026:
  • The thousands place is occupied by '4', hence it contributes 4,000.
  • The hundreds place has a '0', that's why it remains 0.
  • The tens place houses '2', adding 20 to the number.
  • The ones place contains '6', contributing 6.

Knowing this allows you to add numbers more effectively by focusing on each individual place value, just as we did when adding 4,026 and 1,501 in the exercise.
Basic Arithmetic Operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. Addition is one of the simplest and most fundamental operations. It involves combining numbers to find a total. In the exercise, when adding 4,026 and 1,501, we use addition to combine values of the same place:
  • Thousand's place: 4,000 + 1,000 = 5,000
  • Hundred鈥檚 place: 0 + 500 = 500
  • Ten鈥檚 place: 20 + 0 = 20
  • One鈥檚 place: 6 + 1 = 7

Afterward, we sum these results: 5,000 + 500 + 20 + 7 to get the final result, 5,527. This process highlights how breaking numbers down by place value simplifies addition, making it easier to deal with each part of the number separately before coming to a complete answer.

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