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Breaking Down the Division Process

When dividing large numbers, breaking them down into multiples of 10 can simplify the process. For instance, consider 240 divided by 3. Instead of directly dividing the large three-digit number, we can utilize our understanding of tens.

1. Convert to Tens:240 can be rewritten as 24 tens, or 24 × 10.
   Thus, 240 ÷ 3 becomes (24 × 10) ÷ 3.
   

2. Rearrange for Simplicity:By the associative property of multiplication, (24 × 10) ÷ 3 can be rearranged to 24 ÷ 3 × 10.
   This simplifies the division problem to 24 ÷ 3, which equals 8.
   

3. Multiply by 10:Finally, multiplying the quotient by 10 gives us 8 × 10, resulting in 80.
   Therefore, 240 ÷ 3 equals 80.
   

This method can be extended to larger numbers and different divisors, making division more manageable.

Another Example with Thousands

Let's tackle a more complex problem: 4,200 divided by 7.

1. Convert to Hundreds:4,200 is the same as 42 hundreds, or 42 × 100.
   Rewriting, we get 4,200 ÷ 7 as (42 × 100) ÷ 7.
   

2. Simplify:Using the same property, (42 × 100) ÷ 7 simplifies to 42 ÷ 7 × 100.
   Solving 42 ÷ 7 gives us 6.
   

3. Multiply by 100:Multiplying the quotient by 100 results in 6 × 100, equaling 600.
   Therefore, 4,200 ÷ 7 equals 600.
   

Using place value and multiples of 10 not only simplifies division but also builds a stronger foundation for understanding more complex mathematical concepts.

Conclusion

Mastering division using multiples of 10 can transform seemingly difficult problems into manageable tasks. By breaking down numbers into tens or hundreds and simplifying the division, students can achieve accurate results with ease.

To reinforce this learning, utilize our flashcards and practice video, and be sure to check out the detailed explanations and examples provided by Khan Academy.