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Developing strategies for multiplying decimals

Sal uses place value and equivalent fractions to multiply decimals.

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  • duskpin sapling style avatar for user Jennifer
    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...
    (57 votes)
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  • winston default style avatar for user kko
    Why do you need multiple strategies can't ya just use one simple strategy?
    (18 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      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.
      (40 votes)
  • leaf green style avatar for user Asim Yigit Uludag
    what means conceptualize
    (15 votes)
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  • aqualine ultimate style avatar for user Soccer4Life
    so can we think of this with money if we want to make this easier?
    (19 votes)
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  • hopper cool style avatar for user Ava Medina
    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)
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  • marcimus pink style avatar for user Paige Bette
    Wouldn't you do 75 hundreths x 3?
    (6 votes)
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  • hopper happy style avatar for user arjunthakur302012
    I do not understand how the strategie works i tried it but i still couldn't figure it out
    (3 votes)
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  • blobby green style avatar for user jsantiago0425
    what is the easiest way to multiply decimals
    (0 votes)
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  • starky ultimate style avatar for user Mimi
    How I Discovered Khan Academy
    I looked, startled, up at A and C, my dearest friends, and wondered why we had to do this. It was just all conversions and hours to minutes to seconds to nanoseconds to milliseconds to my-head-hurts-seconds and please-just-stop-seconds.
    "Isn't there an easier way to do this than just sitting here?" I asked A, and that's when we saw an ad on an airplane, sailing through the sky like there were no troubles in the world (besides conversions). Are you having trouble doing conversions? Do you wish somebody would just save you from the endless amounts they can be? Then go to KHAN ACADEMY!
    M, which is me, A, and C all looked up in amazement as the ad flew past and... Opened our computers. We had to find out where this KHAN ACADEMY was located. Excitement building up in our throats, we typed in the enter key and...
    That was how it all began.
    And don't worry, it didn't actually happen that way. But Khan is a gift to all and all of us are gifts to Khan. Thank you for teaching us, KHAN!
    (5 votes)
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  • blobby green style avatar for user milania.j
    what is blank=0.01=0.01
    (4 votes)
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Video transcript

- [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.