Trying to learn the correct notation for fractions

Casio

Member
2 4/7 + 1 3/5 = 4 6/35 This is easy on a calculator, but I would like to understand how to do it without using calculators.

First I separate the integers from the fractions;

4/7 + 3/5 = Then find the LCM, which I get to be 35

2 4/7 + 1 3/5 = 4/7 + 3/5 = 21/35 2 + 1 20/35 = 3 41/35

Now I know that the answer above can be further cancelled and I don't know whether this method is correct or not, but here goes;

3 x 13 + 2 / 35 = 41/35 but then 3 x 35 + 41 / 35 = 4 6/35

Does my work seen OK or am I not getting the notation correct?

Thanks

SuperSonic4

Well-known member
MHB Math Helper
2 4/7 + 1 3/5 = 4 6/35 This is easy on a calculator, but I would like to understand how to do it without using calculators.

First I separate the integers from the fractions;

4/7 + 3/5 = Then find the LCM, which I get to be 35

2 4/7 + 1 3/5 = 4/7 + 3/5 = 21/35 2 + 1 20/35 = 3 41/35

Now I know that the answer above can be further cancelled and I don't know whether this method is correct or not, but here goes;

3 x 13 + 2 / 35 = 41/35 but then 3 x 35 + 41 / 35 = 4 6/35

Does my work seen OK or am I not getting the notation correct?

Thanks
You've got your fractions and their integers mixed up: $\frac{21}{35} = \frac{3}{5}$ which goes with 1 instead of 2 so you've swapped them around. The method is largely good although I don't understand a couple of steps that I've put in bold above. You'd end up with $2 \frac{20}{35} + 1\frac{21}{35} = 2 + \frac{20}{35} + 1 + \frac{21}{35}$. Thanks to the order of addition not mattering you still end up with the right answer though.

(with mixed fractions you can split them with addition signs since they're sums: $a + \frac{b}{c} = a\frac{b}{c}$ - if I go off topic for a moment the latter can also mean $a \times \frac{b}{c}$ which is why it should be avoided where it's not clear)

In this case I you look at the fractional parts as you've done:

For simple fractions I find it easier to convert to improper fractions then combine them. In your case:
$2\frac{4}{7} + 1\frac{3}{5} = \frac{14+4}{7} + \frac{5+3}{5} = \frac{18}{7} + \frac{8}{5}$ and then add them using the LCM and cancel where necessary

$\frac{18}{7} + \frac{8}{5} = \frac{90}{35} + \frac{56}{35} = \frac{146}{35}$. That last fraction is irreducible and I'd be inclined to leave it like that, sure it looks nasty but it's clearer than it's mixed equivalent.

If you do want to make it a mixed fraction then $\frac{146}{35} = \frac{140+6}{35} = \frac{140}{35} + \frac{6}{35} = 4\frac{6}{35}$

Hope that's clear

edit: drat, too slow

Casio

Member
You've got your fractions and their integers mixed up: $\frac{21}{35} = \frac{3}{5}$ which goes with 1 instead of 2 so you've swapped them around. The method is largely good although I don't understand a couple of steps that I've put in bold above. You'd end up with $2 \frac{20}{35} + 1\frac{21}{35} = 2 + \frac{20}{35} + 1 + \frac{21}{35}$. Thanks to the order of addition not mattering you still end up with the right answer though.

(with mixed fractions you can split them with addition signs since they're sums: $a + \frac{b}{c} = a\frac{b}{c}$ - if I go off topic for a moment the latter can also mean $a \times \frac{b}{c}$ which is why it should be avoided where it's not clear)

In this case I you look at the fractional parts as you've done:

For simple fractions I find it easier to convert to improper fractions then combine them. In your case:
$2\frac{4}{7} + 1\frac{3}{5} = \frac{14+4}{7} + \frac{5+3}{5} = \frac{18}{7} + \frac{8}{5}$ and then add them using the LCM and cancel where necessary

$\frac{18}{7} + \frac{8}{5} = \frac{90}{35} + \frac{56}{35} = \frac{146}{35}$. That last fraction is irreducible and I'd be inclined to leave it like that, sure it looks nasty but it's clearer than it's mixed equivalent.

If you do want to make it a mixed fraction then $\frac{146}{35} = \frac{140+6}{35} = \frac{140}{35} + \frac{6}{35} = 4\frac{6}{35}$

Hope that's clear

edit: drat, too slow
I have a lot of practice to do and yes I appreciate there are many routes to the correct answer, and people will find the way that suits them best.

I see what you have said now about me putting the integers with the wrong fractions, I never thought about keeping them with the same fraction I just didn't know.

Thanks for your input and help I just have to keep practicing

Don't know what happend to CB's reply, he must have removed it for some reason?

Casio

SuperSonic4

Well-known member
MHB Math Helper
I have a lot of practice to do and yes I appreciate there are many routes to the correct answer, and people will find the way that suits them best.

I see what you have said now about me putting the integers with the wrong fractions, I never thought about keeping them with the same fraction I just didn't know.
No problem. In this case it doesn't matter because you're adding the fractions but it would matter if you wanted to do anything else with them (subtract, multiply or divide) so I find it's good practice to keep them together.

Thanks for your input and help I just have to keep practicing

Don't know what happend to CB's reply, he must have removed it for some reason?

Casio
If you've any other questions feel free to post them here or in a new topic. It may be easier for you to use LaTeX then typing out SUP and SUB tags for fractions . There's a link in my sig

Casio

Member
No problem. In this case it doesn't matter because you're adding the fractions but it would matter if you wanted to do anything else with them (subtract, multiply or divide) so I find it's good practice to keep them together.

If you've any other questions feel free to post them here or in a new topic. It may be easier for you to use LaTeX then typing out SUP and SUB tags for fractions . There's a link in my sig