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## 7th grade (Eureka Math/EngageNY)

### Course: 7th grade (Eureka Math/EngageNY) > Unit 2

Lesson 2: Topic B: Multiplication and division of integers and rational numbers- Why a negative times a negative is a positive
- Why a negative times a negative makes sense
- Signs of expressions
- Multiplying positive & negative numbers
- Dividing positive and negative numbers
- Multiplying negative numbers
- Dividing negative numbers
- One-step equations with negatives (multiply & divide)
- Multiplying negative numbers review
- Dividing negative numbers review
- Rewriting decimals as fractions: 2.75
- Write decimals as fractions
- Rewriting decimals as fractions challenge
- Fraction to decimal: 11/25
- Worked example: Converting a fraction (7/8) to a decimal
- Fraction to decimal with rounding
- Converting fractions to decimals
- Multiplying positive and negative fractions
- Multiplying positive and negative fractions
- Dividing negative fractions
- Dividing positive and negative fractions
- Negative signs in fractions
- Negative signs in fractions
- Negative signs in fractions (with variables)
- Dividing mixed numbers
- Dividing mixed numbers with negatives
- Simplifying complex fractions
- Expressions with rational numbers
- Simplify complex fractions
- Equivalent expressions with negative numbers (multiplication and division)
- Equivalent expressions with negative numbers (multiplication and division)
- Why dividing by zero is undefined
- Dividing by zero

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# Rewriting decimals as fractions: 2.75

CCSS.Math:

Here's an example of how we convert a decimal to a simplified fraction. Over time this will become second nature to you. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- How would you turn a fraction who's denominator is in the ones place like, 1 over 8 into a decimal?(17 votes)
- If you're familiar with division using decimals, set it up similarly to that.

EXAMPLE:

1 divided by 8 (This is what 1/8 means, technically.)

8 goes into 1 no times, so we create a decimal point and go to the tenth's place.

8 goes into 10 (which is technically 1.0) one time, leaving a 2 (which is 0.2) remaining.

Add another zero after the decimal and repeat:

8 goes into 20 (which is .20) 2 times, which leaves 4 (read 0.04) as remainder.

Put an extra zero at the end one last time:

8 goes into 40 a total of five times, with no remainder, we're done!

So with all those added zeroes left of the decimal, we get 8 goes into one... 0.125 times!

(If you weren't able to get it on you own, 1/8 = 0.125) I hope this helps!

Also, if you're still having trouble, the next video in this playlist does a great job of showing this visually:

http://www.khanacademy.org/video/converting-fractions-to-decimals?playlist=Developmental%20Math(32 votes)

- I can't really understand him.(8 votes)
- It just makes sense when you read these?(5 votes)

- if the problem is 3.05 will you put 0/10(5 votes)
- atcually, with 3.05 you round to the nearset tenth so the real answer is 1/10(8 votes)

- how does this rounding work exactly? I watched the video a few times and still doesn't make sense...(6 votes)
- Here are some examples of fractions that need to be rounded: Example 1: The fraction 5/9 won't divide evenly — it ends in a repeating decimal. Change 5/9 to a decimal by dividing 5 by 9. If you choose to round to three decimal places, look one digit beyond the third decimal place, which is 5.To round off a decimal number, you limit the number of decimal places that the number holds. If the division ends in a repeating decimal, you can stop after a certain number of decimal places and round off.(6 votes)

- I Don't Understand The
**Simpliflying Process**?(5 votes)- Assuming that you still dont understand, the simpliflying process is quite simple. Lets say we have a fraction of 6/21. We need to find the biggest common factor between the 2 numbers, if there is one. 6 can be divided by 2, but not 21. Because everything we do the the top, we need to do the bottom, and everything we do to the bottom we do to the top. 6 can be divided by 3, and so can 21. So, we divide 6 by 3, and get 2. We divide 21 by 3 and get 7. Our simplified answer is 2/7.(8 votes)

- What is 7/10 equal to as a decimal.(5 votes)
- 0.7

This is because "10" has one zero, which means one decimal place, and 7 is just how many of the 0.1's you need.(5 votes)

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this is the all mighty kirby(7 votes) - Not sure I understand the simplification process entirely..

When Sal says you find the lowest number that both are divisible by, firstly, how does he know that so quickly (and how do you work it out) and second, when he says 25, can you not go lower? Are not 100 and 75 both divisible by 5 which is lower?(6 votes)- well first of all sal is an completed school and i think he went to college

and say u have this problem

8/16

u can divide both by 4 but the lowest possible number would be 2 probably if u divide 8/16 by 4 u get 2/4

u can still simplify so if u did 8/16 by 2 u get 4/8 BUT Wait u can still simplify that by 2

so basically u need a number that will simplify another number until it cant be simplified(2 votes)

- _

On my homework my teacher gave me, it has 0.3(the three is repeated) and I have to turn that into a fraction in simplest terms. How would I convert that?(4 votes)- If the three repeats forever, it is 1/3. Try doing 1 divided by 3 on a calculator. You might get something like 0.3333333334.(6 votes)

- I just listen to this at x2 speed and it still is not fast enough sometimes...(6 votes)

## Video 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.