Adding and subtracting fractions

In summary: Since they are all put together by "addition", you can arrange as9-3+2 +1/5 - 3/10 + 2/3Dealing with the whole numbers separately,8 + 1/5 -3/10 + 2/3Using some number familiarity, see that common denominator there should be 30...8 + 6/30 - 9/30 +20/30
  • #1
chwala
Gold Member
2,674
352
Homework Statement
Kindly see the attachment below:
Relevant Equations
basic adding/subtracting
1623228694312.png


now a bit confusing here, i always use Bodmas in that case,
##9\frac {1}{5}##-[##3\frac {3}{10}##+##2\frac {2}{3}]##...[1] is this correct and what if i re arrange to
##9\frac {1}{5}##+##2\frac {2}{3}##-##3\frac {3}{10}##...[2]
input guys...cheers

i have seen my mistake [1] is wrong...
 
Last edited:
Physics news on Phys.org
  • #2
As far as I'm concerned the expression is ambiguous. I'm not convinced there is a universal standard for pluses and minuses.
 
  • #3
perok hello, meaning what...i would like to get your opinion.
the negative sign applies to ##3\frac{3}{10}##, that's how i learned ...
 
  • #4
Meaning I don't consider it a well-defined mathematical expression.
 
  • #5
The way I know it is (9+1/5)-(3+3/10)+(2+2/3).
 
  • Like
Likes hmmm27 and SammyS
  • #6
I don't see how this could be confusing or ambiguous. Just imagine a practical problem.

You have ##9\frac{1}{5}## liters of water in a bucket. Remove ##3\frac{3}{10}## liters from the bucket and add ##2\frac{2}{3}## liters. What is the new volume of water in the bucket?

Say I slightly change the problem. You have ##9\frac{1}{5}## liters of water in a bucket. Add ##3\frac{3}{10}## liters to the bucket and remove ##2\frac{2}{3}## liters. What is the new volume of water in the bucket? Do you apply the negative sign to the fraction part? Of course you do. It wouldn't make sense otherwise. If you remove the whole part, you also remove the fraction part.

This type of fraction notation is defined as a mixed numeral.
 
Last edited:
  • Like
Likes chwala, DaveE, jim mcnamara and 4 others
  • #7
When I was a kid in elementary school (more than 50 years ago), teachers used to say "fractions (rational number) should only be used to report numbers smaller than one". Thus, if we had 7/5, we were forced to write ##1\frac{2}{5}##. This "saved" the rule we have been given. Casio calculators include this feature and keep alive this old stuff.
 
  • #8
Gordianus said:
When I was a kid in elementary school (more than 50 years ago), teachers used to say "fractions (rational number) should only be used to report numbers smaller than one". Thus, if we had 7/5, we were forced to write ##1\frac{2}{5}##. This "saved" the rule we have been given. Casio calculators include this feature and keep alive this old stuff.
Why would they say that? They're both valid notations, aren't they?
 
  • Like
Likes SammyS
  • #9
This happened in elementary school. Teachers weren't aware 7/5 is a valid rational number. Moreover, the idea of a "rational number" wasn't popular at that level. We only had "fractions" that, as I already said, were reserved for numbers smaller than one. But this is history.
 
  • Like
Likes chwala and DaveE
  • #10
Delta2 said:
The way I know it is (9+1/5)-(3+3/10)+(2+2/3).
Yes. This is an expression that involves what are called mixed fractions. Your interpretation is exactly how I see the problem as well.
Gordianus said:
This happened in elementary school. Teachers weren't aware 7/5 is a valid rational number.
Elementary school teachers who teach mathematics, or even plain old arithmetic, aren't always much up to speed in mathematics. 7/5 is an example of an improper fraction. It certainly is a rational number, and there's no definition that I'm aware of that requires rational numbers to have numerators that are less than their denominators.
 
  • Like
Likes jim mcnamara, Delta2 and chwala
  • #11
  • Like
Likes chwala
  • #12
chwala said:
Homework Statement:: Kindly see the attachment below:
Relevant Equations:: basic adding/subtracting

View attachment 284247

now a bit confusing here, i always use Bodmas in that case,
##9\frac {1}{5}##-[##3\frac {3}{10}##+##2\frac {2}{3}]## is this correct and what if i re arrange to
##9\frac {1}{5}##+##2\frac {2}{3}##-##3\frac {3}{10}##
input guys...cheers

i have seen my mistake the first fraction is wrong...
To say what has already been said slightly differently. BODMAS or no BODMAS it is always true that ##9\frac{1}{5} =\frac{46}{5}##, ##3\frac{3}{10}=\frac{33}{10}## and ##2\frac{2}{3}=\frac{8}{3}##.

It follows that ##9\frac{1}{5}-3\frac{3}{10}+2\frac{2}{3}=\frac{46}{5}-\frac{33}{10}+\frac{8}{3}##.
 
  • Like
Likes chwala
  • #13
Delta2 said:
The way I know it is (9+1/5)-(3+3/10)+(2+2/3).
Yes This is the one. Nothing about the expression is ambiguous.
 
Last edited by a moderator:
  • Like
Likes Delta2
  • #14
Keith_McClary said:
I can only refer you to Wikipedia:
b02604576272c50868105415b2135b59bd3b71d2
Basic Pre-Algebra stuff

Something that can be done is like this:
a-b+c
a+(-b)+c
Sometimes this helps but is often not necessary.
 
  • Like
Likes chwala
  • #15
chwala said:
Homework Statement:: Kindly see the attachment below:
Relevant Equations:: basic adding/subtracting

View attachment 284247

now a bit confusing here, i always use Bodmas in that case,
##9\frac {1}{5}##-[##3\frac {3}{10}##+##2\frac {2}{3}]##...[1] is this correct and what if i re arrange to
##9\frac {1}{5}##+##2\frac {2}{3}##-##3\frac {3}{10}##...[2]
input guys...cheers

i have seen my mistake [1] is wrong...

9_1/5 - 3_3/10+ 2_2/3

Convert each mixed fraction to an improper fraction.

9_1/5 = 46/5

3_3/10= 33/10

2_2/3 = 8/3

We now have (46/5) - (33/10) + (8/3).

LDC = 10

Take it from here.
 
  • Like
Likes chwala
  • #16
Some variations are possible as long as no property is violated.

(9+1/5)-(3+3/10)+(2+2/3)
or
9&1/5-3&3/10+2&2/3

Since they are all put together by "addition", you can arrange as
9-3+2 +1/5 - 3/10 + 2/3

Dealing with the whole numbers separately,
8 + 1/5 -3/10 + 2/3

Using some number familiarity, see that common denominator there should be 30...
8 + 6/30 - 9/30 +20/30

Now handle the fractions addition,...
8+17/30
 
  • Like
Likes chwala and nycmathguy
  • #17
In my reply which cannot be edited now, the LCD should be 30 not 10. It is a typo.
 
  • #18
UPDATED REPLY

9_1/5 - 3_3/10+ 2_2/3

Convert each mixed fraction to an improper fraction.

9_1/5 = 46/5

3_3/10= 33/10

2_2/3 = 8/3

We now have (46/5) - (33/10) + (8/3).

LDC = 30

Take it from here.
 
  • Like
Likes chwala

Related to Adding and subtracting fractions

What are fractions?

Fractions are numbers that represent a part of a whole. They are written as one number on top of another, with a line in between, such as 1/2 or 3/4.

How do you add fractions?

To add fractions, you first need to make sure they have the same denominator (the bottom number). Then, you can simply add the numerators (the top numbers) and keep the denominator the same. For example, 1/4 + 3/4 = 4/4 or 1.

How do you subtract fractions?

Subtracting fractions follows the same process as adding. You need to make sure they have the same denominator, and then you can subtract the numerators while keeping the denominator the same. For example, 5/6 - 1/6 = 4/6 or 2/3.

What do you do if the fractions have different denominators?

If the fractions have different denominators, you need to find a common denominator by finding the lowest common multiple of the two denominators. Then, you can convert the fractions to have the same denominator and follow the same process as adding or subtracting.

Can fractions be simplified?

Yes, fractions can be simplified by dividing the numerator and denominator by their greatest common factor. This means finding the largest number that can divide evenly into both the numerator and denominator. For example, 8/12 can be simplified to 2/3 by dividing both numbers by 4.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
9
Views
652
  • Precalculus Mathematics Homework Help
Replies
4
Views
812
  • Precalculus Mathematics Homework Help
Replies
14
Views
418
  • Precalculus Mathematics Homework Help
2
Replies
39
Views
2K
  • Precalculus Mathematics Homework Help
Replies
5
Views
887
  • Precalculus Mathematics Homework Help
Replies
21
Views
871
  • Precalculus Mathematics Homework Help
Replies
11
Views
765
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
3
Views
915
  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
Back
Top