Attention Getting Question:
Have you ever tried to multiply a four-digit number?
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 four times six, our answer will be twenty-four. We can think of this as having four groups of six objects or six groups of four 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 four-digit number by a one-digit number is the same idea, except with a larger number.
Suppose you are at dinner with yourfamilyand you are especially hungry. The best part ofit all is that youare havingyour favorite meal: spaghetti and meatballs! Each serving is 1,192 calories. By the end of the meal, you have eaten five servings and you want to know how many calories you just consumed. One way of determining the total calories is adding 1,192 five times. However, multiplication will allow us to determine the number much faster.
Since each serving was 1,192 calories and you ate 5 servings, we can multiply these two numbers together to find the total calories consumed using the standard algorithm for multiplication. Line up the numbers so that the 5, which represents 5 ones, is below the 2 in 1,192. The 2 represents 2ones. Start by multiplying the 5 to the ones digit of 1,192. Five times 2 equals 10. We regroup 10 as 1 ten and 0 ones. Write a 0 in the ones place and a 1 above the tens place. Next, multiply the 5 to the number in the tens place of 1,192. Since 1,192 has 9tens, multiply 5 and 9 to get 45. Add the 1 that was regrouped to get 46. Regroup 46 as 4tens and 6 ones. Write 6 in the tens place and 4above the hundreds place. Then multiply 5 by the number in the hundreds place. Five times 1 is 5. Add the 4 that was regrouped to get 9. Write the 9 in the hundreds place and there is no need to regroup. Last, multiply 5 by the thousands digit, which is 1, to get 5 and write it in the thousands place. This tells you that you have eaten 5,960 calories in one sitting. Now it is time to go play and burn off some of those calories!
You can multiply a four-digit number by a one-digit number by multiplying the one-digit number by the number in the ones place of the larger number. Repeat with the tens, hundreds, and thousands place. Regroup, as needed, and make sure to add regrouped numbers each time. Think about your product or answer. Does it make sense? Is it reasonable? Now that youcan see it is easy to multiply a four-digit number by a one-digit number, you can do it, too!