Multiplying by one or two digits

Find the product of six hundred and thirty eight and 47. Try it first. Pause if you like. 47 has 7 ones and 4 tens. We will multiply by 7, then by 40, and add. 8 ones times 7 is 56 ones. Rename 56 ones as 5 tens and 6 ones. Write 6, and carry 5 above the tens digit. 3 tens times 7 is 21 tens. Add the 5 renamed tens to get 26 tens. Rename 26 tens as 2 hundreds and 6 tens. Write 6, and carry 2 above the hundreds digit. 6 hundreds times 7 is 42 hundreds. Add the 2 renamed hundreds to get 44 hundreds. Write 4 thousands and 4 hundreds. The first partial product is four thousand, four hundred and sixty six. The 4 in 47 means 4 tens. This row multiplies by 40, so put a zero in the ones column. 8 ones times 4 tens is 32 tens. Rename 32 tens as 3 hundreds and 2 tens. Write 2 in the tens column, and carry 3 to the next multiplication. 3 tens times 4 tens is 12 hundreds. Add the 3 renamed hundreds to get 15 hundreds. Rename 15 hundreds as 1 thousand and 5 hundreds. Write 5 in the hundreds column, and carry 1. 6 hundreds times 4 tens is 24 thousands. Add the renamed thousand to get 25 thousands. Write 2 ten thousands and 5 thousands. The second partial product is twenty five thousand, five hundred and twenty. Now add the two rows, starting with ones. 6 ones and zero ones make 6 ones. 6 tens and 2 tens make 8 tens. 4 hundreds and 5 hundreds make 9 hundreds. 4 thousands and 5 thousands make 9 thousands. Write the 2 ten thousands. The product is twenty nine thousand, nine hundred and eighty six. The tens partial product starts one place left. Add the two rows to finish the product.

Find the product of three thousand, two hundred and eight and 6. Try it first. Pause if you like. Start with the ones. Keep each renamed digit above the next place. 8 ones times 6 is 48 ones. Rename 48 ones as 4 tens and 8 ones. Write 8, and carry 4 above the zero in the tens place. Zero tens times 6 is zero tens. Add the 4 renamed tens, and write 4 in the tens column. 2 hundreds times 6 is 12 hundreds. Rename 12 hundreds as 1 thousand and 2 hundreds. Write 2, and carry 1 above the thousands digit. 3 thousands times 6 is 18 thousands. Add the renamed thousand to get 19 thousands. Write 1 ten thousand and 9 thousands. The product is nineteen thousand, two hundred and forty eight. Multiply one place at a time, and keep each renamed digit in the next place.