Welcome to 5th grade multiplication. In 5th grade, students learn to multiply multi-digit numbers using the standard algorithm. Let's look at an example: 123 multiplied by 45. First, we set up the problem vertically, with the numbers aligned by place value.
Now, let's multiply by the ones digit. We multiply each digit in 123 by 5, starting from the right. First, 5 times 3 equals 15. We write down 5 and carry the 1. Next, 5 times 2 equals 10, plus the carried 1 equals 11. We write down 1 and carry the 1 again. Finally, 5 times 1 equals 5, plus the carried 1 equals 6. So our first partial product is 615, which represents 123 multiplied by 5.
Now, we multiply by the tens digit. Since 4 is in the tens place, it represents 40. First, we add a zero as a placeholder in the ones column. Then we multiply each digit in 123 by 4. First, 4 times 3 equals 12. We write down 2 and carry the 1. Next, 4 times 2 equals 8, plus the carried 1 equals 9. Finally, 4 times 1 equals 4. So our second partial product is 4920, which represents 123 multiplied by 40.
The final step is to add the partial products. We add 615, which is 123 multiplied by 5, and 4920, which is 123 multiplied by 40. Adding these numbers gives us 5535. So, 123 multiplied by 45 equals 5535. This is the standard algorithm for multi-digit multiplication that students learn in 5th grade.
To summarize what we've learned about 5th grade multiplication: The standard algorithm breaks multiplication into smaller, manageable steps. First, we multiply by the ones digit, which in our example was 5, giving us 615. Then we multiply by the tens digit, which was 4, giving us 4920. Finally, we add these partial products to get our answer: 5535. This method can be extended to multiply numbers of any size, making it a powerful tool for students to master.