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Understanding the Basics

The first step in adding multi-digit numbers is to understand the place value of each digit. Consider the numbers 40,762 and 30,473. We start by identifying the place values: ten thousands, thousands, hundreds, tens, and ones.

Place Value Chart Representation:

• 40,762: Four ten thousands, zero thousands, seven hundreds, six tens, two ones.

• 30,473: Three ten thousands, zero thousands, four hundreds, seven tens, three ones.

Using the Standard Algorithm:

• Begin with the ones place: 2 + 3 = 5.

• Move to the tens place: 6 + 7 = 13 (write down 3, carry over 1).

• Proceed to the hundreds place: 7 + 4 + 1 (carried over) = 12 (write down 2, carry over 1).

• Next, the thousands place: 0 + 0 + 1 (carried over) = 1.

• Finally, the ten thousands place: 4 + 3 = 7.

The sum is 71,235.

Breaking Down the Process:

• Adding ones: 2 (from 40,762) + 3 (from 30,473) = 5.

• Adding tens: 6 + 7 = 13. Write down 3 in the tens place and carry over 1 to the hundreds place.

• Adding hundreds: 7 + 4 + 1 (carried over) = 12. Write down 2 in the hundreds place and carry over 1 to the thousands place.

• Adding thousands: 0 + 0 + 1 (carried over) = 1.

• Adding ten thousands: 4 + 3 = 7.

The final result, 71,235, shows that both the place value method and the standard algorithm yield the same result, demonstrating how these two approaches are interconnected.

By practicing with our flashcards and videos, you can reinforce your understanding of this essential math skill, ensuring you can add multi-digit numbers with ease and confidence.