Practice with Flashcards and Video

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.