Have you ever tried to multiply two two-digit numbers?
Multiplying helps us to determine how many total objects are represented when we have multiple groups of the same size. For instance, we know that when we multiply three times eight, our answer will be twenty-four. We can think of this as having three groups of eight objects or eight groups of three objects. Either way, the result will be twenty-four total objects. Being able to switch the factors and still get the same product or answer in a multiplication equation is known as the Commutative Property of Multiplication. Multiplying a two-digit number by a two-digit number is the same idea as multiplying one-digit factors, except with larger numbers.
Imagine that you want to take some candy sticks to school to give to your class. You want each one of your classmates to have 16 candy sticks and there are 23 other students in your class. We could determine how many we need by adding 16, 23 times, but that would take a long time. Multiplication will help us achieve an accurate product in much less time.
In order to multiply these two numbers together, we can use the standard algorithm for multiplication. An algorithm is a step-by-step method for computing.
Using the standard algorithm for this multiplication, we first need to line up the numbers. Write the larger number first and then put the other number below it so that the ones digits and tens digits are in the same column. First, we will multiply the ones digits of the numbers. Six times 3 is 18. We will regroup 18 as 1 ten and 8 ones. Then multiply the tens digit of 23 by the ones digit of 16. Six times 2 is 12, plus the one we regrouped will give us 13. Since there is not a hundreds digit for 23, we will write 13 with no need to regroup. Next, we will multiply the tens digit of 13 with both digits of the 23. Because we are multiplying the tens digit of 13, we place a 0 under the 8 to show that we are multiplying the tens digit of 13. Now we can multiply 1 times 3 to get 3 and place it next to the 0. Multiply 1 times 2 to get 2. After all of the multiplication, we add the two numbers together to get the final answer. By adding 138 and 230, we will have a total of 368. This tells us that we have to buy 368 candy sticks in order for everyone in the class to get 16.
Remember, when multiplying two two-digit numbers, you will follow the standard algorithm. First, line up the numbers with the larger number on top to help make multiplication easier. Multiply the ones digit of the bottom number to both digits of the top number. Next, multiply the tens digit of the bottom number to both of the digits of the top number, but don’t forget to write a zero to show that we are using the tens digit of the bottom number.Last, add the two numbers we found together to get the total. Now that you see it is easy to multiply two two-digit numbers together, you can do it, too!