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## 5th grade foundations (Eureka Math/EngageNY)

### Unit 3: Lesson 2

Topic B: Foundations- Adding fractions with like denominators
- Add fractions with common denominators
- Subtracting fractions with like denominators
- Subtract fractions with common denominators
- Adding mixed numbers with like denominators
- Subtracting mixed numbers with like denominators
- Add and subtract mixed numbers (no regrouping)

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# Subtracting mixed numbers with like denominators

Think of a mixed numbers as a number AND a fraction. You can subtract numbers....you can subtract fractions with like denominators. Therefore, you can subtract mixed numbers! Watch. Created by Sal Khan.

## Want to join the conversation?

- What if you have a problem like 5 1/8 - 3 3/8?(8 votes)
- Okay so, the add/sub is easy. But how do you properly simplify fractions? On the test every one of my wrong answers is because I don't do proper simplifying. I always fix my mistake the 2nd try but how do I make sure I know the proper way to simplify? Sorry for making this so confusing.(3 votes)
- If there’s a whole number greater than 1 that divides both the numerator and denominator evenly, your answer is not simplified. Continue to divide both numerator and denominator by the same whole number (greater than 1), until there’s no whole number greater than 1 that divides them both evenly. After this, your answer would be simplified.(5 votes)

- how do I add -1/6-5+2/5-1/15?(2 votes)
- The best way is to give all of the numbers a common denominator. On the three fractions you can see that the denominators are 6,5 and 15. All of these go into 30 so your first step would be to take the first fraction which is -1/6 and multiply that by 5/5 which would make it -5/30.

For the 2/5 fraction you would multiply by 6/6 and that would make it 12/30. and for the last fraction you would multiply it by 2/2 to make it 2/30.

This is allowed because any number over itself is just 1 and so you aren't changing the value of the fraction just the way it is represented. 1/15 is they same as 2/30. If you took a calculator and divided the numbers you would come up with the same result.

Lastly you need to represent the 5 as it's fractional equivalent with 30 in the denominator. To do that you just multiply 5 by 30/30 and get 150/30.

Now you have the numbers with common denominators of -5/30 - 150/30 +12/30 -2/30 . You combine the numerators while keeping the denominator at 30 and get -145/30. This can be further simplified to -29/6.(6 votes)

- So is the whole number component representing six 16/16's / six 4/4's (when reduced) ?(4 votes)
- I think you add the whole but just making sure do you add the whole(4 votes)
- can someone identify how to fraction time(3 votes)
- It takes 60 minutes to = 1 hour.

So, 1 minute = 1/60 hours.

30 minutes = 30/60 hours, or 1/2 hour.

Hope this helps.(2 votes)

- Well i think it's getting a little Easier for me.(3 votes)
- How would you subtract a mixed number and a normal fraction?

Example= 11 12/16- 4/12(3 votes) - what is 12 5/5-3 1/2(3 votes)
- I think there are 2 ways that are good to know.

Here is the first way.

Step 1, subtract the whole numbers.

12-3 = 9

Stp 2, subtract the fractions

5/5 - 1/2 = 5/10 = 1/2

Step 3 add the whole number and fraction together

9 1/2

Keep in mind, if the fraction is negative it lowers the whole number

The other way is to convert both into improper fractions, subtract those, then turn the new difference into a mixed number

12 5/5 - 3 1/2

65/5 - 7/2

130/10 - 35/10

95/10

9 1/2

The same works for addition as well, except you replace all subtractions with additions. Also, in this problem 12 5/5 = 13 since 5/5 is 1. So this could have been 13 - 3 1/2(1 vote)

- explain in another problem(2 votes)

## Video transcript

Let's figure out what 11 and
12/16 minus 5 and 8/16 is. And then we might have
to simplify it down to lowest terms. So the way I like to do these
is to kind of separate out the whole number
part of the mixed numbers from the
fractional part. So I can rewrite this
number right over here as 11 plus 12/16. And from that, I am
going to subtract-- and I'll put parentheses
here because I'm going to break this part open. I'm going to
subtract 5 plus 8/16. 5 and 8/16-- same
thing as 5 plus 8/16. But I have to remember,
I'm subtracting it. I'm subtracting
this whole thing. So I could rewrite it as--
I'll rewrite this part-- 11 plus 12/16. And I'm subtracting 5 plus 8/16. So I can distribute
the negative sign. So it's going to be minus
5, negative 1 times 5. And then negative 1
times positive 8/16. So it's going to be minus 8/16. And then I like to do the
whole number parts separately and then the fractional
parts separately. So let's do the
whole number parts. We have 11 minus 5. I'll write it here, 11 minus 5. We'll do that part. That's the whole number part. And then we have plus 12/16. Let me do this in pink maybe,
plus 12/16, minus 8/16. And 11 minus 5 is 6. And I have 6 plus. And then our denominators
are the same here, so we're going to get
something over 16. And 12 minus 8 is 4. So this is the same
thing as 6 plus 4 over 16, which is the
same thing as-- writing it as a mixed number-- 6 and 4/16. And this is the right quantity,
but we can simplify it. 4/16 can be simplified. Both the numerator and the
denominator are divisible by 4. They both have the factor 4. So let's divide both the
numerator and denominator by 4. Divided by 4. Divided by 4. Since we're dividing
by the same thing, we're not changing its quantity. And so this is
equal to-- we still have the whole number part,
6, but the fraction part is now 1, 1/4. So we get 6 and 1/4.