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Current time:0:00Total duration:4:33

Multiplying decimals and whole numbers with visuals

CCSS.Math:

Video transcript

so what we have here on this number line that we've now marked off with the tenths and you can see that this is 3 tenths here we can think about this as a multiplication of a decimal and so what is this representing and I'll give you a hint it's representing something times 3/10 so pause the video and try to think about that well let's see we are going 1 times 3/10 2 times 3/10 three times 3/10 and then 4 times 3 tenths so what's represented here is 4 times 3 tenths and so what is this going to be equal to well you can see you go from 3 tenths to 6 tenths to 9 tenths and then you could view this as 12 tenths but twelve tenths is the same thing as 1 1 & 2 tenths so you could view this as one point 2 1 & 2 tenths let's do another example not like she'll do it on the same number line if we wanted to represent 3 times 3 times 0.2 what would that look like on this number line and what would this be equal to so I'll put it a little equal sign here pause this video and see if you can figure that out all right so let's think about where to tense is this is 1/10 2/10 is right over there this is 0.2 and we're going to multiply at times 3 so we're going to multiply it times 1 then we're going to multiply it times 2 that takes us to 4 tens and then we're going to multiply it times 3 to get us to six tenths zero point six so it's six tenths just like that now you can also visualize two tenths as parts of a whole so for example this represents two tenths I have this whole the squares a whole it's it's split into ten equal columns here and we have two of them filled in so this represents two tenths so if you have three times two tenths well this is one times two tenths this is two times two tenths and this is three times two tenths and so how many tenths do we now have well we have one two three four five five six tenths which is exactly what we have here six tenths let's do one more example that gets a little bit more involved so here we're told to multiply it says you may use the model shown to help find the product and this is a screenshot from the exercise on Khan Academy so pause this video and see if you can figure out what this is all right so they're saying 52 hundredths times 3 and they have 52 hundredths depicted right over here and then they have it depicted three times so the total number of hundredths depicted here that is 5200 times 3 because we have 52 hundredths here another 52 hundredths and then another 52 hundredths so how many hundredths is that going to be well you could view this as 52 times 3 and that I will give you the number of hundredths we have so let's think about this so if we were to just say 52 times 3 well this is going to be 2 times 3 is equal to 6 and then 5 tens times 3 is 15 tens which is the same thing we could either just write it as 15 tens or that's 105 tens but either way if I have 52 of something and I multiply that by 3 and I have 156 of that something and here the something is hundreds so if I say 52 hundredths hundredths times 3 that's going to be 156 hundredths and how do we represent 156 hundredths well there's a couple of ways to think about it if this is the ones place this is the tenths place this is the hundredths place well we would write the six there the five there and the one there so you could recognize this as hey look a hundred hundredths let me color code it a hundred hundredths is the same thing as a whole and I'll circle that in red and 50 hundredths is the same thing as five tenths and of course six hundredths is the same thing as six hundredths so this is going to be equal to we could say one point five six or you could view this as one hundred fifty six hundredths so you could view this as a whole which is a hundred hundredths and 5/10 which is 50 hundredths and 6 hundredths