Not too sure about this method of;

[Probability]

determining the value of;

(5/8 - 1/4 + 2/5) = 5 x 5 - 10 x 1 + 8 x 2

The confusion stems around the - 1/4

The numerator 5 and the denominator 5 make up the 5 x 5.

I think the numerator 5 - + 5 which equals 5 - 5 seems to have been added to make - 10

The 1 is the numerator from the 1/4 I think

and the 8 comes from the 5/8 denominator and the 2 from the 2/5 numerator, making 8 x 2

I end up with;

5 x 5 - 10 x 1 + 8 x 2
40

8 x 5 = 40

What I don't understand is why has the denominator 4 from the 1/4 been missed out?

 

[ksdhart2]

Okay, so I'm afraid I don't fully understand most of what you wrote, but I think the core problem you're attempting to understand is this:

5/8 - 1/4 + 2/5 = (5 x 5 - 10 x 1 + 8 x 2)/40

As you know, when adding or subtracting fractions, you need to find a common denominator to proceed. And while working with the lowest common denominator is advised for simplicity's sake, it's not required. Do you know how to find the lowest common denominator? What is the lowest common denominator of 4, 5, and 8? Once you get that, you need to convert each of the fractions to have that denominator. So, if we define the variable x as the lowest common denominator of 4, 5, and 8, then your task is to determine...

5/8 = ?/x ; 1/4 = ?/x ; 2/5 = ?/x

Now add and subtract the numerators as appropriate and you'll find the expected answer.

 

[Probability]

keep it simple, use the LCM which is 40:
25/40 - 10/40 + 16/40 = 31/40

I think I have got it now!

(5/8 - 1/4 + 2/5) = 5 x 8 from the denominators.

5 x 8 = 40 LCM

then 5 x 5 cross multiplication.

LCM 40/- 4 = - 10

so we have = 5 x 5 - 10 and

8 x 2

it's a little confusing but ends up as 5 x 5 - 10 + 8 x 2 / 40

It's knowing how to work out fractions when there are three or more together that is confusing.

Thanks for all the help.

 

[Ishuda]

determining the value of;

(5/8 - 1/4 + 2/5) = 5 x 5 - 10 x 1 + 8 x 2

The confusion stems around the - 1/4

The numerator 5 and the denominator 5 make up the 5 x 5.

I think the numerator 5 - + 5 which equals 5 - 5 seems to have been added to make - 10

The 1 is the numerator from the 1/4 I think

and the 8 comes from the 5/8 denominator and the 2 from the 2/5 numerator, making 8 x 2

I end up with;

5 x 5 - 10 x 1 + 8 x 2
40

8 x 5 = 40

What I don't understand is why has the denominator 4 from the 1/4 been missed out?

As Denis said, keep it simple
5/8 = (5/8) * (5/5) = (5 * 5)/40
-1/4 =-(1/4) * (10/10) = - (10/40)
2/5 = (2/5) * (8/8) = (2 * 8)/40
or
25/40 - 10/40 + 16/40 = (25-10+16)/40=31/40

 

[Probability]

I can see Denis way of explaining it and it works on that example, however when I apply that logic to other similar expressions I cannot achieve the correct answers for some reason, there must be a technique/method of determining these types of fractions I am not aware of.

Look at this example, I know the answer is 47/63. I can input the fractions into my calculator and it works, but on paper I cannot achieve the same answer?

(2/9) - (1/7) + (2/3)= Find the LCM of the three denominators, which is 63.

Multiply out the fractions. 3 x 2 - 9 x 1 + 9 x 2 = - 36
63 63

For some reason I am just not seeing this!!

I tried splitting up the fractions and came up with this;

(-1/7) + (2/3) = (-3/21) + (14/21) = (11/21)

(11/21) - (2/9) = 57/63

I'm looking for 47/63

I can't see what I am doing incorrect!!

 

[Deleted member 4993]

I can see Denis way of explaining it and it works on that example, however when I apply that logic to other similar expressions I cannot achieve the correct answers for some reason, there must be a technique/method of determining these types of fractions I am not aware of.

Look at this example, I know the answer is 47/63. I can input the fractions into my calculator and it works, but on paper I cannot achieve the same answer?

(2/9) - (1/7) + (2/3)= Find the LCM of the three denominators, which is 63.

Multiply out the fractions. 3 x 2 - 9 x 1 + 9 x 2 = - 36
63 63

For some reason I am just not seeing this!!

I tried splitting up the fractions and came up with this;

(-1/7) + (2/3) = (-3/21) + (14/21) = (11/21)

(11/21) - (2/9) = 57/63

I'm looking for 47/63

I can't see what I am doing incorrect!!

(2/9) - (1/7) + (2/3) → You need to make all the denominators same - in this case 63

(2/9) - (1/7) + (2/3)

= [(2*7)/(9*7)] - [(1*9)/(7*9)] + [(2*21)/(3*21)]

= (14/63) - (9/63) + (42/63)

= (14 - 9 + 42)/63

= 47/63

 

[Probability]

(2/9) - (1/7) + (2/3) → You need to make all the denominators same - in this case 63

(2/9) - (1/7) + (2/3)

= [(2*7)/(9*7)] - [(1*9)/(7*9)] + [(2*21)/(3*21)]

= (14/63) - (9/63) + (42/63)

= (14 - 9 + 42)/63

= 47/63

Thanks for replying, I can follow your solution through to the part where you advise [2*21]. I can see where that has been calculated from?

I assume you used the fraction 2/3 to calculate it, but can't see 2*? in the fractions that make 21?

 

[ksdhart2]

Yes, you're correct that the 2*21 came from the 2/3 term. You started with a denominator of 3, and you ended up with a denominator of 63. What did you do to the original denominator (3) to get 63? Now you must perform that same operation on the numerator to ensure the fraction is equal to what you started with.

 

[Probability]

Yes, you're correct that the 2*21 came from the 2/3 term. You started with a denominator of 3, and you ended up with a denominator of 63. What did you do to the original denominator (3) to get 63? Now you must perform that same operation on the numerator to ensure the fraction is equal to what you started with.

I understand some of what you say above, however I am no better off in my understanding. 2/3 does not have a common multiple, by example, 2 = 4,6,8,10,12,14,16,18,20,22,24.....

3 = 3,6,9,12,15,18,21,24.....

so yes I see 3 x 21 = 63, but I fail to understand how 2 x 21 is found from the above?

Edited;

Yes I think I have now understood, please confirm I have understood correctly then I can move on, same example;

(2/9) - (1/7) + (2/3) = (2/9) x (7/7) - (1/7) x (9/9) + (2/3) x (3/3) x (7/7) = (14/63) - (9/63) + (42/63) = 47/63

This method will take a bit of practicing if I have not got this right by a fluke

 

[ksdhart2]

I understand some of what you say above, however I am no better off in my understanding. 2/3 does not have a common multiple, by example, 2 = 4,6,8,10,12,14,16,18,20,22,24.....

3 = 3,6,9,12,15,18,21,24.....

so yes I see 3 x 21 = 63, but I fail to understand how 2 x 21 is found from the above?

Edited;

Yes I think I have now understood, please confirm I have understood correctly then I can move on, same example;

(2/9) - (1/7) + (2/3) = (2/9) x (7/7) - (1/7) x (9/9) + (2/3) x (3/3) x (7/7) = (14/63) - (9/63) + (42/63) = 47/63

This method will take a bit of practicing if I have not got this right by a fluke

Yes, the above is the correct process of adding and subtracting fractions. Good job.

 

[Bob Brown MSEE]

distribution

determining the value of;

(5/8 - 1/4 + 2/5) = X

Sometimes it's easier to solve for X.
You need to use the distribution property of multiplication.
a(b+c+d) = ab + ac + ad

Here we go....
(5/8 - 1/4 + 2/5) = X (given)
8(5/8 - 1/4 + 2/5) = 8X (multiply both sides by 8)
(5 - 2 + 16/5) = 8X (distribution)
5(5 - 2 + 16/5) = 40X (multiply both sides by 5)
(25 - 10 + 16) = 40X (distribution)
31 = 40X (add)
X = 31/40 (divide both sides by 40)