About this video
Sal writes 2.75 as a simplified fraction by breaking it into place values: 2 ones, 7 tenths and 5 hundredths. He rewrites 7/10 as 70/100, adds to get 2 and 75/100, then divides top and bottom by 25 to get 2 and 3/4.
You'll be able to
- explain what each digit after the decimal point is worth (tenths, hundredths).
- rewrite a decimal like 2.75 as a mixed number.
- simplify a fraction by dividing the numerator and denominator by their greatest common factor.
Key words
- tenths place
- The first place after the decimal point; a digit there is worth that many tenths.
- hundredths place
- The second place after the decimal point; a digit there is worth that many hundredths.
- common denominator
- A shared bottom number that lets you add fractions.
- simplified fraction
- A fraction where top and bottom have no common factor except 1.
- mixed number
- A whole number and a fraction together, like 2 3/4.
Transcript
Write 2.75 as a simplified fraction. So once you get some practice here. You're going to find it pretty straightforward to do. But we're really going to think through it and get the intuition for why this makes sense. So if we were to write this down, the 2, that literally just represents two 1's, I'll just write it down like that.
Then we have the 7 in another color. We have a 7 one place to the right of the decimal. It's in the tenths place, with a T-H-S at the end. So it literally represents 7 over 10. And then finally, we have the 5 in the hundredths place, so it represents 5 over 100.
Now, if I want to write this as a simplified fraction, or really as a mixed number, I have to merge these fraction parts right here. And to add two fractions, you have to have a common denominator. And to figure out the common denominator, you just have to think about the least common multiple of 10 and 100.
And that's 100. 100 is divisible by both 100 and 10. So let's get this 10 to be 100. So we can do that by multiplying it by 10. So when you multiply something by 10, you add a zero at the end of it. But you can't just do that to the denominator. We also have to do that to the numerator.
So we multiplied the denominator by 10. Let's also multiply the numerator by 10. 7 times 10 is 70, or 70 over 100. It's the exact same thing as 7/10. Now we can add these two. What is 70 plus 5? 70 plus 5 is 75. And our denominator is 100, so this can be rewritten as 2 and 75/100.
And we saw that in the last video, you would read this as two and seventy-five hundredths. Now we aren't in a completely simplified fraction yet because 75 and 100 have common factors. And the largest number that goes into both, if you're familiar with quarters, is 25.
Three quarters is $0.75, four quarters is 100 cents, or four quarters is $1.00. So you divide both of them by 25. So 75 divided by 25 is 3, and 100 divided by 25 is 4. So as a simplified mixed number, this becomes 2 and 3/4. And after you do a lot of practice here, and you just see a lot of numbers like this, it will be almost second nature for you to say, oh, 2.75 is the same thing as 2 and 75/100, is the same thing as 2 and 3/4.
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