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Course: Arithmetic>Unit 18

Lesson 10: Adding & subtracting negative fractions

Adding and subtracting fractions with negatives

Use the properties of addition to strategically add and subtract fractions with negatives and unlike denominators. We can rewrite the subtraction as adding the opposite so that the addition properties will apply. Created by Sal Khan.

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• I don’t get this, help!
• Basically, we're trying to find out 3/7 - (-7/3)- 11/3
Something minus a negative is basically an addition problem. Ex. 2 - (-2) = 2+2=4.
He changed the minus negative to a plus.
3/7 + 7/3 - 11/3
He then turned it into this.
3/7 + 7+-11/3. The denominator will stay the same.
He then evaluated the problem.
Now we have 3/7 + -4/3
He then found the LCM, 21.
?/21 + ?/21
He evaluated the problem again.
9/21 + -28/21

Therefore,
3/7 - (-7/3)- 11/3 = -19/21

Hope this helped! Have a great rest of your day!
• 2024 new year same me!!
• I am in 6 th grade and I am trying out for AGS 2 next year
Wish me Luck!
• Wish You Luck!
• I get that 3/7 - (-7/3) equals 3/7 + 7/3 but why does he still put parantheses.
• --a is harder to read, hence the parenthesis - (-a)
(1 vote)
• this doesnt make sense at all. how did he get 21?
im so confused
(1 vote)
• 21 is the common denominator of 3 and 7,
• I understand the positive*positive thing but why are we making all the signs vice versa what is the use
• Multiplying different signs make negative and same signs make positive. Unless you multiply with 0 then you'll end up with nothing
• ඞඞඞ i don't understand this
(1 vote)
• When, you add, let's say something positive and negative like:
9+(-28), it's the same thing as subtracting 9-28. If you wish to do the math like standard without thinking about a number line you can do it like this:
09
- 28
-------

And, you subtract the digits out normally, there are two methods: positive 9 ones - 8 ones gives you a POSITIVE 1 one.
0 tens - 2 tens gives you -2 tens. So, what number forms when you have (-2) tens and 1 POSITIVE one, -19 ones! Because (-2) tens is equal to -20 ones. (-20 ones) + 1 one = -19 ones.

Another way to think about it is, regroup the 2 tens and 8 ones you are subtracting into 1 ten and 18 ones. You then subtract the units (0 tens - 1 tens) and (9 ones) - (18 ones):
09 ------> 0 ones + 9 ones
-28 -----> - (1 ten) +18 ones
---- ------
(-1 tens) + (-9 ones)

(-1 tens) = (-10 ones)+(-9 ones) = (-19) ones.

We add the negative digits together because we're looking for the total amount of ones we have.
(1 vote)
• wait why did he switch -11/3 to +11/3 couldnt he have solved it with minus sign.

Can someone help
(1 vote)
• I can do the common denominators and all, but I just have trouble figuring whether the fraction will be positive or you subtract or add the numerators. How does that work, exactly?
(1 vote)