Learn about Multiplication of Whole Numbers

TenMarks teaches you how to multiply whole numbers

Let’s learn about multiplication of whole numbers and we’re given three problems. Let’s do them one by one. The first problem says, “Joey had four bags containing marbles and each bag had 15 marbles in it. How many marbles did Joey have in all?” What do we know? What we know is there are 4 bags each with 15 marbles. If I need to find out how many marbles did Joey have, I have an easy way of doing it. I can just say 1 bag has 15 marbles. If I have 4 bags, I have 15+15+15+15 marbles which is 60 marbles in all. Because there were only 4 bags, I could simply add the 4 together to give me the answer. Whenever we have to add the same number different times or many times, it is easier to simply multiple. In order to multiply, I would basically say that I have 15 marbles in a bag and I have 4 bags. Instead of adding 15 to itself 4 times, I can simply multiply 15 by 4 to give me the same answer which would be 60. Let’s learn about more ways of doing multiplication, some of the tricks. The key is to multiply 15×4 is 60. Here’s what we need to remember. These numbers that are being multiplied, these are called factors. The final product which is the answer after multiplication, this is called the product and I always say the way to represent this is 15×4 or 4×15 and I can represent this as 15×4. I can also represent this as 15.4; a small period between the two. I can also represent this as just putting two braces around both these numbers; they all mean the same thing. Let’s go back. Let’s try and do the second question or the second problem which asks us to evaluate 28×24. Let’s look at the second problem which is 28×24. I have to multiply 28 with the number 24. The trick here is in order to multiply 28 by 24 or28 with 24, first, I multiply 28 with 4 then I multiply the same number 28 with 20 because that’s what’s left. Let’s do that first. First, what I do is I multiply 28 times 24. In order for me to do this, I first multiply 28×4 which is called a partial product. The partial product of 28×4 is 112. 28×20 is 560 which is again a partial product. This is 28×4, this is 28×20. In order to get 28×24, I simply add them, 560+112 gives me the answer 672 which is the final answer. 28×24 is 672. Let’s look at the third problem which is 200×92. Let’s write down 200×92 which is the same as 92×200. Because this is a number with many zeros at the end of it, I can simply say 92 multiplied by 200. First, I multiply 92 by 2 which gives me 184 and then I can just copy the zeros down. That’s a little trick we learn which is if we’re multiplying with a number which got zeros at the end of it, I can just multiply with the main number which is two and then copy the zeros down. The multiplication of 92×200 gives me 18400. Now, this is because the product of a number with zero is always zero. This is called zero property of multiplication. I used that because 92×0 will be 0, 92×0 will be zero; an easier way of doing it was just to copy with that. Let’s quickly recap what we’ve learned. What we’ve learned is when it comes to multiplying, if I have four numbers or a number being added to itself, a multiple number of times, I can simply use multiplication to get the same result. Let’s learn about how do we represent multiplication? There are many different ways. I can put a cross, 15×4. I can put 15.4 or 15 and 4 in braces next to each other, these all give you the same value which is 15×4. It’s all read the same now. Let’s learn about, if we multiply two digits, 28 and 24 together, the first thing I do is multiply 28 with the number 4 then I multiply 28 with the number 20 which is the balance and I add the two. In order to do this, I can show it here, 28×24. First, I do the partial product which is 28×4 which is 112 then 28×20 which is 560 and we add the two together to get the result. Third example was 200×92 or 92×200, one of the same. Because this number has two zeros at the end of it, I can simply this by saying 92×200 is the same as 92×2 which is 184 and then I copy the zero down. The final product becomes 18400 and this property is because anything that is multiplied with zero results in a zero which is called a zero property.