Adding mixed fractions to whole numbers: 6 - (3/2) = 9/2 how?

[Illvoices]

Hello colleagues in my recent problem I was faced to add a whole number to a fraction. Now as I was balancing the equation I noticed that the teacher answered like so...

6- 3/2=
9/2

Tell me how is this possible guys. I didn't want to type in the whole equation in b/c it would take to long to type, but I thought you had to subtract instead of multiply and divide like so.

6*3=18
18/2=9
Add the denominator 9/2

 

[Deleted member 4993]

Hello colleagues in my recent problem I was faced to add a whole number to a fraction. Now as I was balancing the equation I noticed that the teacher answered like so...

6- 3/2=
9/2

Tell me how is this possible guys. I didn't want to type in the whole equation in b/c it would take to long to type, but I thought you had to subtract instead of multiply and divide like so.

6*3=18
18/2=9
Add the denominator 9/2

\(\displaystyle 6 \ - \ \dfrac{3}{2}\)

= \(\displaystyle \dfrac{6 \ * \ 2}{2} \ - \ \dfrac{3}{2}\)

= \(\displaystyle \dfrac{12}{2} \ - \ \dfrac{3}{2}\)

= \(\displaystyle \dfrac{12 \ - \ 3}{2} \)

= \(\displaystyle \dfrac{9}{2} \)

 

[Illvoices]

O understand now Khan thank you for the reply. It looks like I was tackling this the wrong way.

 

[j-astron]

It's important that you understand why and not just how. Numerators (the top) of fractions can only be added or subtracted if those fractions have a common denominator (the bottom). Because (in this case) you are literally asking "how many halves" do I have? Six wholes is twelve halves. I hope this helps.

 

[melis]

You should think of 6 as a fraction, so it would be 6/1, and to add or subtract fractions you need to get a common denominator. In this case it would be 2, so 6/1 would become 12/2 and 12/2-3/2=9/2