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Lesson 2: Adding & subtracting negative fractions

# Adding fractions with different signs

Use a number line to add fractions with different signs.  Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation? • Well if you want to do it without a number line then you just have to do the math. What I mean is that you have to first know how to add and subtract fractions and you have to learn how to learn how to add and subtract mixed fractions, also you have to learn how to add and subtract integers. So yeah it takes a long time to do this kind of math to learn how solve a problem without a number line. Understand?
• gimme up votes lets REACH 1 MILL! this is a target lets complete it lets goo and kids study hard ! • Seems a bit much for one equation, is there any simpler/faster way to do it? •  Yes, you can do just do the math without the visualization alone, the number line is just for better understanding. It is a bit complicated, but it is the fastest and most simple way to handle the question if you understand the math to it.

3 1/8 + 3/4 +(-2 1/6) = x
Let's solve for x.

``x = 3 1/8 + 3/4 - 2 1/6 [delete the ()]x = 3 1/8 + 6/8 - 2 1/6 [adjust the fractions for addition]x = 25/8 + 6/8 - 2 1/6 [convert into improper fraction]x = 31/8 - 2 1/6 [do the addition]x = 31/8 - 13/6 [convert into improper fraction]x = 93/24 - 52/24 [adjust the fractions for subtraction]x = 41/24``

or...

``x = 1 17/24``
• When I worked through this problem, I left them as mixed numbers and didn’t convert them to improper fractions. I came to the same answer (41/24 or 1&17/24). Did you convert them for a reason other than preference? Thanks • Yes, the "short way" of doing this problem is just working on the fractions of the mixed numbers (1/8+3/4-1/6) and subtracting the numbers (3-2). The reason this method works is because, in reality, 1&17/24 is the same as 1+17/24 (and this goes for all mixed numbers). Sal converted the mixed numbers mostly because of preference, but it is easier to convert to improper fractions when the problem would result in a negative fraction.
For example:
3&1/8 - 3/4 -2&1/6
See, now the fractions added up would result in a negative fraction (-19/24) and then you would still have to subtract 19/24 from 1. So, you would have to convert 1 to 24/24 and subtract. By converting all the mixed numbers into improper fractions, the sum of all the improper fractions is the final answer.
In conclusion, both methods work (Sal's method is the one taught in schools, normally) and, depending on the question (whether the fractions of the mixed numbers come out negative), one can work faster than the other.
• I tried to follow the lesson and I came to -11/6 instead of -13/6.
Could we get a clarification on this or I missed a step?
Look forward to her from you guys! example 6. -2 = -12/6 + 1/6= -11/6 • this is so confusing and there is so much to remember • Is it the same principle but with fractions?🤔 • crazy • Why do we have to do so much work • what are the steps
(1 vote) • Well, the first step would be to simplify the equation. For example, if I had the problem
-6 3/7 - -(2 7/9) - 8 3/10
then I could simplify it to:
-6 3/7 + 2 2/5 - 8 3/10
Then, you add the fractions together, and the first step for that is to find the common denominator. So, the common denominator of 7, 5, and 10, (the denominators), would be 70, and change the denominators to 70, and multiply the numerators by the number you multiplied the denominator by.
Here's an example, using our above equation;
-6 3/7 + 2 2/5 - 8 3/10
So, we change the denominators to 70, so our equation would be:
-6 3/70 + 2 2/50 - 8 3/70
But now our numerator wouldn't look right, so we have to multiply the numerators by the number we multiplied the denominator by.
So, for -6 3/70 to go from 7 to 70, we would have to multiply by 10, so we multiply 3 by to to get 30, so from:
-6 3/7 to
-6 30/70
The actual value of the fraction stays the same, though this format makes it easier to add/subtract.
So, if we repeat this process, our equation will be
-6 30/70 + 2 28/70 - 8 21/70
Now we do the actual addition. Let's focus on the whole numbers first.
So -6 + 2 - 8
What is 6 to the left of 2? -4! And what is 8 to the left of -4? -12! You can use a number line to help you out. So, the sum of all the whole numbers is 12.
Now let's do the fractions:
-30/70 + 28/70 - 21/70 = -23/70
Make sure you include all the minuses and plusses that were in the equation.
The last step is to add the two products.
-12 + -23/70 = -12 23/70
You then simplify, but this specific fraction is already simplified, so our final answer was:
-12 23/70

I know this looks long and like a bore to read through, but I still hope this helps you! Have a good day!😁