Numbers & Operations - The Real & Complex Number Systems 211-217
- Developing strategies for multiplying decimals
- Multiply decimals tenths
- Developing strategies for multiplying 2-digit decimals
- Multiply decimals (1&2-digit factors)
- Multiply decimals (up to 4-digit factors)
- Multiplying decimals (no standard algorithm)
This video is all about understanding how to multiply decimals, specifically focusing on the strategy of converting decimals to fractions to make the multiplication process easier. Multiplying decimals can be made easier by thinking of the decimals as fractions. This helps understand what we are multiplying, and it also lays the groundwork for the standard method of decimal multiplication.
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- Why do you need multiple strategies can't ya just use one simple strategy?(27 votes)
- There are some advantages of using multiple strategies in mathematics.
1. This is a great way to check your work. If you use two different strategies and get the same answer, you can be much more confident that your answer is correct. If you get different answers, then that will let you know that something's wrong with one of the answers, giving you an opportunity to correct a mistake and make your two answers agree.
2. Even in math problems of a similar type, some problems are easier to solve with one strategy and some are easier to solve with another strategy. There are some beautiful arithmetic strategies. For example:
i) Multiplying a number by 5 is the same as multiplying the number by 10 and taking half (in either order).
ii) Multiplying a number by 99 is the same as multiplying by 100 and then subtracting the original number.
iii) Zeros at the end of a whole number cancel out decimal places in another number in multiplication problems (for example, 0.324 times 1600 is the same as 32.4 times 16).
You will also see this later on in algebra: there are multiple strategies for solving systems of equations, and multiple strategies for solving quadratic equations. The easiest strategy to use depends on the equation(s).
3. If you decide to teach math some day, you will see that not all students learn the same way. By teaching multiple strategies, you might be able to accommodate more students' learning styles.
4. Overall, understanding multiple strategies develops your mathematical intuition. Having a strong, accurate intuition will make it easier for you to remember material and to solve more challenging problems. The strongest math students are not the ones who memorize the most facts, but instead are the ones who have the best intuition and conceptual understanding.
While this is slightly off topic, think of chess. If you know only one strategy or tactic, you're unlikely to beat a good player. However, if you know multiple strategies and/or tactics, you're much more likely to beat a good player. Having the attitude of thinking like a chess player can help you become stronger in math.(51 votes)
- I still am a little confused... I want to dig deeper into the meaning of doing this. I want to learn why do we multiply decimals and fractions across, like we do for multiplication. I wonder why we move the decimal like we do. I am in a pile of questions...(70 votes)
- what means conceptualize(17 votes)
- so can we think of this with money if we want to make this easier?(20 votes)
- Yes. Lots of people use decimals when talking about money because they think it's easier for them.
Other people like to use fractions. It's up to you.(9 votes)
- So if you do a problem like 5/10 x 6/10 would you after the whole problem turn it into a decimal or do you keep it as a fraction?(13 votes)
- Here in Khan Academy, when you click the place where you have to put your answer, they will tell you if they want a fraction or a decimal or any of those.
What you do in life, it's up to what's more comfortable to you.(3 votes)
- Wouldn't you do 75 hundreths x 3?(6 votes)
- No, because 75 hundredths is the answer. You're doing 0.25 x 3, so you're are basically doing 0.25 + 0.25 + 0.25.(5 votes)
- I do not understand how the strategie works i tried it but i still couldn't figure it out(3 votes)
- what is the easiest way to multiply decimals(0 votes)
- It is mainly a personal preference. I feel that converting the decimals to fractions (like at4:05) is the easiest way to do it. For more complex problems though, it's much easier to use the standard method . Here's a video that shows you how it's done.
Hope this helps! :)(11 votes)
- Is it correct to think of this strategy as multiplying by 10, or 100, to work with whole numbers for the purpose of making the calculations easier (but then you have to divide back to get the accurate answer). But for division, when you multiply the numerator and denominator by 10/10 or 100/100 (essentially 1), the answer must actually remain in the new form to be correct? 6 x 0.2 = 6 x 2 / 10, but 6 / 0.2 = 60 / 2 (no reverting back)(2 votes)
- The reason they are different is in the case of division, you are multiplying by values that = 1.
10/10 = 1
100/100 = 1
And, the identity property of multiplication tells us that we can multiply any number by 1 and we don't change the value of the original number. So, you are basically changing the way the numbers look in the fraction, but you haven't changed their value.
But, when you try to use the same technique with multiplying by 10 or 100 to have whole number, the value you are multiplying by does not equal 1. So, you need to divide by the 10 or 100 to return to the number's original value.
Hope this helps.(6 votes)
- [Instructor] So right over here we wanna compute what three times 0.25 or three times 25 hundredths is. And so I encourage you to pause the video and see if you can figure this out. Alright, now let's work through this together. And in this video, we're gonna explore multiple strategies. In the future, we're going to show you what's called the standard strategy, which you might use a lot, but the strategies we're gonna look at in this video are actually very helpful for understanding what multiplying decimals actually means, how it relates to multiplying fractions, as often the way that people, even people who have a lot of math behind them, how they actually multiply decimals. So here, three times 25 hundredths. There's a couple of ways to think about it. One way is to say, hey, this is the same thing as three times, and I'm just gonna write it a different way. 25 hundredths, hundredths. If I have three times 25 of something, what is it going to be? Well, what's three times 25? Let's see. Two times 25 is 50, three times 25 is 75. So it's going to be 75, and I'm multiplying, not just three times 25, I'm multiplying three times 25 hundredths. Instead of 25 hundredths, I'm gonna have 75, 75 hundredths. Written out in words, this would be 75 hundredths. How would we write that as a decimal? That is the same thing as this, 75 hundredths. Another way to conceptualize this, to think about what this is, is if we were to write three times, we could write it as a fraction. We could write 25/100. This is another way of writing 25 hundredths. These are all equivalent. What is three times 25/100? Same idea. This is going to be equal to, you could say this is 25/100 plus 25/100 plus 25/100. This is going to be 75 hundredths, which once again is 0.75. If you wanted to more formally view it as fraction multiplication, you could view it as 3/1 times 25/100, and you multiply the numerators, you get 75, you multiply the denominators, you get 100. Either way, in all of these situations, you're gonna get 75 hundredths. Or, another way to think about it, is hey look, this thing right over here, this 25/100, this is the same thing as 1/4. So you could view this as three times 1/4. In fact, this is a decimal that it's good to recognize that this is the same thing as 1/4. So you could view this as three times 1/4, or 3/4, this is a fourth right here, 1/4 could be viewed as a fourth, so this is going to be equal to 3/4, three over four, 3/4. All of these are equivalent. If someone wanted it written out as a decimal, you could, you might know that 3/4 can be expressed as 75 hundredths, which in general, is a good thing to know. Now let's tackle slightly more complicated examples. Let's say we wanted to figure out, we wanted to figure out what 0.4 times zero, let me just do this in a new color, times 0.3 is going to be equal to. Pause the video and see if you can compute this, and I'll give you a hint, see if you can express these as fractions. What we have here in white, we could read this as four tenths, and we could write it as a fraction, as 4/10, and we're gonna multiply that by what we have over here. This is three tenths, three tenths, which we could write as a fraction as 3/10, and so you could view this as 4/10 of 3/10 or 3/10 of 4/10, but we're multiplying these fractions, which we've seen before in other videos. What's going to happen? Well, if we multiply the numerator we get 12, or the numerators. We multiply the denominators, you get 100. So you get 12 hundredths. If you wanted to write that as a decimal, it would be 0.12, 12 hundredths. You might notice something interesting here, and you'll see this more and more as you learn the standard method. 12 is four times three is 12, but now I have two digits behind the decimal, but notice, I have one digit behind the decimal here, one digit behind the decimal here, for a total of two digits behind the decimal. I'm giving you a little bit of a hint about where we're going, but the important thing for this video is to recognize that you can re-express each of these as fractions, and then multiply the fractions to get something expressed in terms of hundredths, and then express that as a decimal.