how to do 3 digits to 3 digits multiplecation for a year 4
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Welcome to 3-digit by 3-digit multiplication! This is an advanced skill for Year 4 students. Today we'll learn the long multiplication method step by step. Let's start with the example 123 times 456. First, we set up the problem by writing the numbers one above the other, making sure to align the digits by place value - ones under ones, tens under tens, and hundreds under hundreds.
Now let's multiply by the ones digit. We multiply 123 by 6, which is the ones digit of 456. Starting from the right: 3 times 6 equals 18. We write down 8 and carry the 1. Next, 2 times 6 equals 12, plus the carried 1 makes 13. We write down 3 and carry the 1. Finally, 1 times 6 equals 6, plus the carried 1 makes 7. Our first partial product is 738.
Now we multiply by the tens digit. We multiply 123 by 5, but since 5 is in the tens place, we're actually multiplying by 50. First, we write a zero as a placeholder in the ones column. Then we calculate: 3 times 5 equals 15, write 5 and carry 1. Next, 2 times 5 equals 10, plus the carried 1 makes 11, write 1 and carry 1. Finally, 1 times 5 equals 5, plus the carried 1 makes 6. Our second partial product is 6150.
Now we multiply by the hundreds digit. We multiply 123 by 4, but since 4 is in the hundreds place, we're actually multiplying by 400. First, we write two zeros as placeholders in the ones and tens columns. Then we calculate: 3 times 4 equals 12, write 2 and carry 1. Next, 2 times 4 equals 8, plus the carried 1 makes 9. Finally, 1 times 4 equals 4. Our third partial product is 49200.
Finally, we add all the partial products together. We have 738, 6150, and 49200. Starting from the rightmost column: 8 plus 0 plus 0 equals 8. Next column: 3 plus 5 plus 0 equals 8. Hundreds column: 7 plus 1 plus 2 equals 10, so we write 0 and carry 1. Thousands column: 0 plus 6 plus 9 plus the carried 1 equals 16, so we write 6 and carry 1. Ten thousands: 0 plus 0 plus 4 plus the carried 1 equals 5. Therefore, 123 times 456 equals 56,088!