Answer:
This is very detailed as I wish to make some principles about fractions clear.
3
5
12
Explanation:
This question boils down to
3
2
3
−
1
4
A fractions structure is that of:
count
size indicator of what you are counting
→
numerator
denominator
You can not directly add or subtract the counts (numerators) unless the size indicators (denominators) are the same.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider
3
2
3
Write as
3
+
2
3
Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way something looks without changing its true value
[
3
×
1
]
+
2
3
[
3
×
3
3
]
+
2
3
9
3
+
2
3
=
11
3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting it all together
3
2
3
−
1
4
→
11
3
−
1
4
But the size indicators are not the same. I chose to make them become 12
11
3
−
1
4
→
[
11
3
×
1
]
−
[
1
4
×
1
]
→
[
11
3
×
4
4
]
−
[
1
4
×
3
3
]
→
44
12
−
3
12
Now we may subtract the counts
→
44
−
3
12
=
41
12
But this is the same as
12
12
+
12
12
+
12
12
+
5
12
=
1
2
+
2
1
2
+
2
1
2
+
5
12
=
3
5
12
Explanation: