From Digits to Decimals: Multiplying with Precision and Accuracy

Multiplication is when you add a number to itself multiple times. For example, 5 times 4 means you add 5 four times. So, 5 + 5 + 5 + 5 = 20. You can also switch the order and do 4 times 5, which means you add 4 five times. So, 4 + 4 + 4 + 4 + 4 = 20. Multiplication is just a faster way of adding the same number over and over again. You can use a calculator to help you, but it's important to understand why the answer is what it is.

What is 6 times 5? Well, we can add 6 five times. So, 6 + 6 is 12, and then we add another 6 four more times. That gives us 30!

Now, what about 4 times 8? We can add 8 four times, or we can add 4 eight times. Let's add 8 four times. So, 8 + 8 is 16, and then we add another 8 two more times. That gives us 32!

See, multiplication isn't so hard after all. It's just a different way of adding.

Let's talk about multiplying big numbers. For example, what is 20 times 13? Well, imagine you have 13 twenty-dollar bills. How much money is that? We know that 5 twenty-dollar bills make $100, so 10 twenty-dollar bills make $200. And 3 twenty-dollar bills make $60. So, in total, you have $260. That means 20 times 13 is 260.

It's easier to understand multiplication when you can relate it to something you can visualize, like money. Let's try another example. What is 25 times 15? Imagine you have 15 quarters. Four quarters make $1, so 8 quarters make $2, and 12 quarters make $3. We need 15 quarters, so the other 3 quarters make 75 cents. That means 15 quarters is $3.75. So, 25 times 15 is 375.

If you don't have a calculator, you can also do multiplication by hand. First, multiply 5 times 5, which is 25. Carry over the 2, and then multiply 5 times 2, which is 10. Add the carried over 2, and you get 12. Then, add a zero and multiply 1 times 5, which is 5, and 1 times 2, which is 2. Finally, add 5 plus 0, which is 5, 2 plus 5, which is 7, and 1 plus 2, which is 3. That gives you 375.

Let's do another example to get some practice. We're going to multiply 36 by 42. You can pause the video if you need to.

First, we're going to multiply 2 times 6, which equals 12. We need to carry over the one to the next step. Then, we'll multiply 3 times 2, which equals 6, and add the carried over one, which gives us 7.

Next, we need to add a zero and multiply 4 times 6, which equals 24. We'll write down the 4 and carry over the 2. Then, we'll multiply 4 times 3, which equals 12, and add the carried over 2, which gives us 14.

Now, we can add up the numbers. We'll start with 0 plus 2, which equals 2. Then, we'll add 4 plus 7, which equals 11. We'll carry over the one and add 4 plus 1, which equals 5. Finally, we'll bring down the one.

So, the answer to 36 times 42 is 1512. You can check this answer by typing it into a calculator. That's how you can multiply two big numbers!

So, you know how multiplying big numbers can be tricky because there are so many steps? Well, when it comes to multiplying decimals, it's not much harder than multiplying whole numbers. The trick is to pretend that the decimal point isn't even there! I know, it sounds weird, but trust me. We'll do the multiplication just like we would with whole numbers, and then at the end, we'll make sure the decimal point is in the right spot. Don't worry, if we forget to move the decimal point, we'll still get the right answer, it just won't be in the right place. But we can fix that easily!

I know this might be a little confusing, but I'm here to help you out. Let's say you need to multiply 3.65 by 2.4, but that seems tricky. So, let's pretend that the decimal points aren't there for now. We can think of 3.65 as 365 and 2.4 as 24. We already know how to multiply those two numbers, right? We just follow the steps we learned in multi-digit multiplication. The answer we get is 8,760, but that's the answer for 365 times 24, not 3.65 times 2.4. So, we need to understand what's going on with those decimal points. When we pretended the decimal points weren't there, we were really shifting them to the right. We shifted the top decimal point two places to the right and the bottom decimal point one place to the right. But doing that changed the numbers. It made the top number 100 times bigger and the bottom number 10 times bigger. That means the answer we got is way too big.

Okay, so basically we have a big number because the decimal points got moved three places to the right. To fix it, we need to move the decimal point in our answer three places to the left. That will make it smaller by three factors of ten. So, we start with the answer 8760 and move the decimal point three places to the left to get 8.76. That's the answer to 3.65 times 2.4.

Here's a cool trick: when you're doing decimal multiplication, you can set up the problem just like regular multiplication. But don't erase the decimal points! You'll need them later to figure out how many places to shift the decimal point in your answer. After you do the multiplication, count up how many places the decimal points are shifted in the problem. That's the total shift of both the top and bottom decimal points. Then, shift the decimal point in your answer to the left that same number of places.