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# Decomposing hundredths

CCSS.Math:

## Video transcript

so this this picture right over here we've taken this square and we've divided it into a hundred equal smaller squares and then we've colored in let's see how many we've colored in each of these rows has ten squares so this is 10 20 30 40 41 42 43 44 45 46 47 so over here we have colored in 47 out of the hundred equal smaller squares or you could say that this what's shaded in in blue in green right over here this represents 47 hundredths this is represents 47 hundredths of the entire of the entire hole now what I'm curious about is I want to break up this fraction I want to write it as 40 over actually let me write it this way I want to write it as 4 over 10 plus plus something over 100 and I'll just write star plus star over 100 and my question to you is what is the star going to be equal to the star is equal to what and pause the video to try to figure it out all right so let's let's work this let's work this together so one thing that we could say immediately is we could say that 47 over 100 is equal to 40 hundredths 40 hundredths you see that over here 10 20 30 40 hundreds this is 10 20 30 40 hundredths plus one two three four five six seven hundredths plus seven hundredths now 40 hundredths is the same thing as four tenths 40 hundredths is the same thing as four tenths there's a bunch of ways we could think about it one is you could think about dividing this larger larger square into tenths so this would be 1/10 right over here that would be 1/10 this would be another tenth that's two tenths this would be three tenths now all I'm doing here is I'm dividing the larger thing into 10 into tenths I should say if I'm taking the larger if I'm taking the larger square instead of dividing it into hundreds I divided it into tenths so this would be four tenths so let me just do them 5/10 6/10 6/10 7/10 8/10 and 9/10 and then 10 tenths notice if you look at the orange lines I've divided my square not into 100 equal sections but into 10 equal sections and so you see these 40 hundredths that are in blue right over there that's the same thing as 1/10 2/10 3/10 and 4/10 so that is the 4/10 right over there another way you can think about it when you go from hundreds to tenths each ten hundredths each ten hundredths is are equal to 1/10 so you're dividing both the denominator by 10 when you go from hundredths to tenths and you would also divide the numerator by 10 going from hundredths to tenths so 40 divided by 10 is 4 100 divided by 10 is 10 so hopefully you're convinced that 40 hundredths is the same thing as 4 tenths but what's left over well we still have the 700s over here so 40 hundredths plus 7 hundredths is the same thing as 4 tenths plus 7 hundredths so the star right over here this is going to let me actually let me erase this the star right over here I could write that as 7 hundredths you see 47 hundredths which is all the stuff shaded in that's the same thing is the 4 tenths which is the same thing as 40 hundredths shaded in blue plus these 1 2 3 4 5 6 7 hundredths right over here 47 100 or 47 hundredths 4/10 plus 7 hundredths