Another Expression: evaluate (3 + 1/4) - (4 + 4/5) + (1 + 5/6) in fraction form

[Probability]

OK I admit I don't seem to be mastering the technique required to do these expressions for some reason, I am really trying.

I am asked to evaluate this expression in fraction form;

(3 + 1/4) - (4 + 4/5) + (1 + 5/6)

I now I can just keep doubling the denominators until I find the LCM, which I know is 60 for this example, but I would of liked to be able to have worked through the expression like in my previous example and evaluate it, but this example I am really struggling with, and the very closest workout I have had on paper is;

(3 - 4 + 1) + (1/4 - 4/5 + 5/6) = 1/4 x 5/5 - 4/5 + 4/4 + 5/6 x 5/5 = 5/20 - 8/20 + 20/30 = 17/30

I think the problem is in bold here 5/6 somehow I think I need to increase this to get my denominator 6 = 10 = 60, but I need to keep the numerator 20, so I feel stuck at this point!!

I don't like cheating and using MathCad is a last resort if I can evaluate the expression, however MathCad gives an answer of 113/60, my calculator gives an answer of 17/60.

Am I correct in thinking my problem is the fraction 5/6 or am I completing missing the point in this expression?

Edited to add information.

I got to the understanding that I knew there was a problem with the fraction 5/6, I tried equivalent fractions but clearly missed the one I needed, i.e. 5/12. There is a lot to be said for understanding the times tables up to say 12 x 12, and using those for visual representation when struggling to think the problem through mentally.

So I have the correct, or one of the few correct solutions to this expression;

(3+(1/4)) - (4+(4/5)) + (1(5/6)) = (3 - 4 + 1) + (1/4) - (4/5) + (5/6) = (1/4) x (5/5) - (4/5) + (4/4) + (5/12) x (4/5) = (5/20) - (8/20) + (20/60) = 17/60

It is worth pointing out that (5/6) and (5/12) are NOT equivalent fractions, but (5/12) is an alternative to (5/6), which is why I was seriously struggling to see the problem.

 

[Probability]

Geeeeshhh buddy, you talk more than 4 women
sitting together playing Bingo

Go step by step:

3 + 1/4 = 12/4 + 1/4 = 13/4

4 + 4/5 = 20/5 + 4/5 = 24/5

1 + 5/6 = 6/6 + 5/6 = 11/6

So you're now at:
13/4 - 24/5 + 11/6

Now convert using LCM 60:

13/4 = 195/60
24/5 = 288/60
11/6 = 110/60

Take over, Rover!

I can follow you up to 13/4, 24/5 and 11/6. If I divide your 195/60 etc I can see they are equal to the fractions, how you achieved the large numbers, 195, 288 and 110 is beyond me at the moment.

 

[ksdhart2]

From what I've been seeing in the past three or so threads, the bulk of your struggles with adding and subtracting fractions appears to be in converting to the lowest common denominator. The main trick here lies in the fact that anything times 1 is itself. In your problems, this comes down to an exercise of finding the missing number. We'll borrow a concept from algebra and call that unknown number x.

We know the fraction we start with and the fraction we end with must be equal. Thus, the only possible number we can multiply by is 1. Next, we'll use the divisive identity, which states that anything divided by itself is 1. So, the problem is then:

\(\displaystyle \displaystyle \frac{13}{4} \cdot \frac{x}{x}=\frac{195}{60}\)

In other words, you multiplied 4 by the unknown number x to get 60. Working backwards, what is the value of x? Then, what number must you multiply the numerator by? Repeat for the other two fractions.

 

[Deleted member 4993]

I can follow you up to 13/4, 24/5 and 11/6. If I divide your 195/60 etc I can see they are equal to the fractions, how you achieved the large numbers, 195, 288 and 110 is beyond me at the moment.

You are somehow missing the process of converting the denominators to LCM!

13/4 - 24/5 + 11/6 ← we need to convert all the denominators to 60 (LCM)

first denominator is 4 → to convert to 60 we must multiply by 60/4 = 15

second denominator is 5 → to convert to 60 we must multiply by 60/5 = 12

third denominator is 6 → to convert to 60 we must multiply by 60/6 = 60

13/4 - 24/5 + 11/6

= 13/4 *(15/15) - 24/5 * (12/12) + 11/6 * (10/10)

= (13*15)/(4 *15) - (24 * 12)/(5 * 12) + (11 * 10)/(6 * 10)

Continue....

A suggestion - use paper & pencil and write these down instead of just staring at the screen......

 

[Probability]

From what I've been seeing in the past three or so threads, the bulk of your struggles with adding and subtracting fractions appears to be in converting to the lowest common denominator. The main trick here lies in the fact that anything times 1 is itself. In your problems, this comes down to an exercise of finding the missing number. We'll borrow a concept from algebra and call that unknown number x.

We know the fraction we start with and the fraction we end with must be equal. Thus, the only possible number we can multiply by is 1. Next, we'll use the divisive identity, which states that anything divided by itself is 1. So, the problem is then:

\(\displaystyle \displaystyle \frac{13}{4} \cdot \frac{x}{x}=\frac{195}{60}\)

In other words, you multiplied 4 by the unknown number x to get 60. Working backwards, what is the value of x? Then, what number must you multiply the numerator by? Repeat for the other two fractions.

It's all fairly new stuff that I will have to spend time learning, please bare with me thanks.

 

[Probability]

You are somehow missing the process of converting the denominators to LCM!

13/4 - 24/5 + 11/6 ← we need to convert all the denominators to 60 (LCM)

first denominator is 4 → to convert to 60 we must multiply by 60/4 = 15

second denominator is 5 → to convert to 60 we must multiply by 60/5 = 12

third denominator is 6 → to convert to 60 we must multiply by 60/6 = 60

13/4 - 24/5 + 11/6

= 13/4 *(15/15) - 24/5 * (12/12) + 11/6 * (10/10)

= (13*15)/(4 *15) - (24 * 12)/(5 * 12) + (11 * 10)/(6 * 10)

Continue....

A suggestion - use paper & pencil and write these down instead of just staring at the screen......

Are you saying above what Denis has shown me in a later post using algebra, i.e. 4n = 13.60 etc ...

 

[Probability]

Don't worry, it's simple. Let's take the 13/4:
we want to change the 4 to 60, right?
To do so means a new numerator, right?

Let n be new numerator.
So we want 13/4 = n/60
Solve for n:
4 * n = 13 * 60 (this process is known as cross-multiplication)
4n = 780
n = 780 / 4 = 195

Got it?

Thanks Denis, yes got it. No women at bingo required

 

[lookagain]

I am asked to evaluate this expression in fraction form;

(3 + 1/4) - (4 + 4/5) + (1 + 5/6)

This problem is not geared to be done the way it was shown to you by others
in this thread, because the work is needlessly cumbersome.


(3 + 1/4) - (4 + 4/5) + (1 + 5/6) =

3 - 4 + 1 + 1/4 - 4/5 + 5/6 =

1/4 - 4/5 + 5/6

The L.C.M. is 60.


\(\displaystyle \dfrac{1(15)}{4(15)} \ - \ \dfrac{4(12)}{5(12)} \ + \ \dfrac{5(10)}{6(10)} \ =\)


\(\displaystyle \dfrac{15}{60} \ - \ \dfrac{48}{60} \ + \ \dfrac{50}{60} \ =\)


\(\displaystyle \dfrac{15 - 48 + 50}{60} \ =\)


And continue...

 

[Probability]

This problem is not geared to be done the way it was shown to you by others
in this thread, because the work is needlessly cumbersome.


(3 + 1/4) - (4 + 4/5) + (1 + 5/6) =

3 - 4 + 1 + 1/4 - 4/5 + 5/6 =

1/4 - 4/5 + 5/6

The L.C.M. is 60.


\(\displaystyle \dfrac{1(15)}{4(15)} \ - \ \dfrac{4(12)}{5(12)} \ + \ \dfrac{5(10)}{6(10)} \ =\)


\(\displaystyle \dfrac{15}{60} \ - \ \dfrac{48}{60} \ + \ \dfrac{50}{60} \ =\)


\(\displaystyle \dfrac{15 - 48 + 50}{60} \ =\)


And continue...

17/60

Thanks. I have nearly finished the first section of the book I am practicing, then I am going to go through that section again until I am confident with the whole arithmetic in there. I'll return to this method soon.

 

[Ishuda]

I can follow you up to 13/4, 24/5 and 11/6. If I divide your 195/60 etc I can see they are equal to the fractions, how you achieved the large numbers, 195, 288 and 110 is beyond me at the moment.

Sometimes, the following technique may be of use [technique picked up from an earlier post by someone else]: Starting with the expression by Denis
13/4 - 24/5 + 11/6
let
X = 13/4 - 24/5 + 11/6
Multiply through by the first denominator
4 X = 4*(13/4) - 4*(24/5) + 4*(11/6) = 13 - 96/5 + 2*(11/3) = 13 - 96/5 + 22/3
Now multiply through by the first remaining denominator
5*(4 X) = 20 X = 65 - 5*(96/5) + 5*(22/3) = 65 - 96 + 55/3 = -31 + 110/3
and finally the remaining denominator
3*(20 X) = 60 X = 3*(-31) + 3*(110/3) = -93 + 110 = 17
or
X = 17/60

 

[Probability]

This is all very good stuff guys and it is very appreciated, but we must remember I am learning the basics and missing out loads of steps in worked examples is not really good for me at the moment. When I am working with fractions I think I need the basics first before the advanced stuff. Thanks.