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Practice with Flashcards and Video

Exploring the Magic of Regrouping Whole Numbers

To reinforce your understanding, we've created a set of flashcards and a practice video. These resources will help you test your knowledge and ensure you can apply the concept of regrouping whole numbers with confidence. Download our flashcards or watch the practice video to start practicing!

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Understanding Regrouping with Our Guide

Breaking Down 675

To understand regrouping, let's start by breaking down the number 675 into its place values:

  • The 6 is in the hundreds place, representing 600.

  • The 7 is in the tens place, representing 70.

  • The 5 is in the ones place, representing 5.

So, 675 can be represented as: 600+70+5600 + 70 + 5600+70+5


Regrouping from Hundreds to Tens

Suppose we take 100 from the hundreds place and add it to the tens place. This changes the breakdown:

  • Hundreds: 600 - 100 = 500

  • Tens: 70 + 100 = 170

So now, 675 is represented as: 500+170+5500 + 170 + 5500+170+5

Since 170 can be broken down into 17 tens, we can write: 500+17×10+5500 + 17 \times 10 + 5500+17×10+5


Regrouping from Tens to Ones

Next, let's take 10 from the tens place and add it to the ones place:

  • Tens: 170 - 10 = 160

  • Ones: 5 + 10 = 15

Now, 675 can be represented as: 500+160+15500 + 160 + 15500+160+15


Regrouping Hundreds to Tens and Ones

For a more complex example, we can take 200 from the hundreds place and distribute it between the tens and ones places:

  • Hundreds: 600 - 200 = 400

  • Tens: 70 + 100 = 170

  • Ones: 5 + 100 = 105

So, 675 can be represented as: 400+170+105400 + 170 + 105400+170+105


Regrouping All Hundreds

Finally, let’s redistribute all 600 from the hundreds place to the tens and ones places:

  • Tens: 70 + 400 = 470 (or 47 tens)

  • Ones: 5 + 200 = 205

So, 675 can be represented as: 0+470+2050 + 470 + 2050+470+205


Summarizing the Concept

No matter how we regroup, the total value remains the same. The flexibility of regrouping helps us understand the value of each digit within a number and provides a powerful tool for performing arithmetic operations.

By breaking down and regrouping numbers, we gain deeper insight into how numbers work and develop stronger number sense.

When it comes to understanding whole numbers, regrouping offers a fascinating way to break them down and see their component parts. One of the best resources for mastering this concept is Khan Academy, which provides an excellent explanation and practical examples to help learners grasp the topic. Check out the Khan Academy video here to see how Sal Khan regroups the number 675 into various addition problems.

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