Multiplication Explained: How to Multiply 3 Digit Numbers

It starts early. Third and fourth graders begin learning simple multiplication. They learn to multiply single digit numbers and ear expected to learn them well enough that they are memorized. Simple multiplication is when you multiply any of the numbers 0-9 by any other number 0-9. Flash cards are an excellent way to teach children multiplication. To make some yourself use index cards and a marker. Start with 0x0= and then move to the next card. 0x1=, 0x2=, 0x3=, and so on. When you are done with zero move on to one and work your way through the numbers up to nine. Make cards until you reach 9x9=. It is a good idea to make card for the number ten as well.

Fifth and sixth grade students need strong single digit multiplication skills to do well with the more complicated multiplication problems. In these grades single digits will need to be multiplied by double and triple digits. Double digit numbers will need to be multiplied by other double or triple digit numbers. For some of the problems you see on homework the answer will be a number in the millions. Knowing place value has never been so important. Your child benefits from your help, and also from you reading those numbers out loud. For example, if your child gets an answer of 2,345,678 then you would recite that number as two million three hundred forty five thousand six hundred seventy eight.

To multiply a single digit number is easy, even if you are multiplying it by a double or triple digit number. The large number is always on the top and the single digit always on the bottom. Draw the line and mark the problem with a multiplication sign. Starting at the right multiply the top number by the bottom number. If you are multiplying 45 by 3 then the three would be directly below the five. The first thing you'd do is to multiply five by three. 5x3=15. Write the five and carry the one. The one gets put above the four. Now, multiply 4x3 which equals 12. Add on that one. Write 13. Your answer is 135. Any time you multiply the top number by the bottom number and that number is over ten you must carry. To carry you write the right number where the answer goes but the left number carries over and gets set up above the top number that is to the left of the top number you just multiplied with. When you multiply that number by the bottom digit you add what gets carried over to the answer you get. If that answer is single digit there is no need to carry over again but if it is double digit you will need to carry over again.

To multiply a double digit number by another double digit number is a little more tricky. Lets use the example Start at the right, always. Multiply 3x1. 3x1=3 so write the three at the bottom and move on. Multiply 4x1. 4x1=4 so write the four at the bottom. Under the forty-three you need to place a zero in the ones place. It would go directly under the three. That zero is a space holder. Now you are ready to multiply the top two numbers by the second digit of the bottom number. 3x2=6. Write the six next to that zero. 4x2=8. The eight goes to the left of the six. Draw another line under the 860 because it's time to add it all up and get the answer. Don't forget to mark it with a plus sign once you draw the line. 3+0=3, 4+6= 10...wait! Double digit answers must be carried. Write the 0 and carry that 1. 0+8=8, plus the one that was carried =9.

When you encounter a triple digit number you proceed in the same way. The only change is that when you get ready to multiply the third number you drop another line down and add two zeros as place holders instead on one. For every extra number that is to be multiplied by another line gets dropped and an extra zero gets added. A four digit number would take you three lines down and the last line would require three zeros as place holders. Once all numbers are multiplied add up all of the lines. Carry over where needed. The sum is the answer of the multiplication problem.