Today ill show you how to solve subtraction with addition of fractions.If you are among the people that always get it hard to solve this kind of mathematics do not worry i will guide you on how to do that.
Fraction is one those mathematics that time time give some student problems especially when its come to expression and simplification.I believe you still remember that any number that has up and bottom number is knowing as fraction.
Also, before you start to solving this, find the L.C.M first , secondly, obtain the equivalent fractions..if only the bottom number are not the same.
When your borrowing take place, you have:
4 - 1 = 3
5 - 1 = 4
6 - 1 = 5
7 - 1 = 6
1 - 1 = 0 but you should not include the 0
3 - 1 = 2 etc.....
The above examples means you should borrow only 1 number.
Examples
Simplify the following using equivalent fractions method
5 1
(a. ) -------- - -----------
8 4
1 3 13
(b) --------- - -------- + -----------
2 4 16
3 2
(c) 5 ------ - 2 --------
5 3
Solution
5 1
(a. ) -------- - -----------
8 4
The L.C.M of 8 and 4 is 8
Equivalent fractions
5 5 x 1 5
-------- = --------- = ---------
8 8 x 1 8
1 1 x 2 2
--------- = --------------= -------
4 4 x 2 8
5 - 2
= --------------
8
3
-----------
8
Building an equivalent fractions means,to make the two denominators to become the same.
1 3 13
(b) --------- - -------- + -----------
2 4 16
The L.C.M of 2, 4 and 16 = 16
1 1 x 8 8
----------- = ----------- = --------
2 2 x 8 16
3 3 x 4 12
----------- = ------------ = ---------
4 4 x 4 16
13 13 x 1 13
---------- = ------------- = ---------
16 16 x 1 16
8 + 13 - 12
= -------------------------- rule of BODMAS ( Addition before subtraction )
16
21 - 12
= ---------------
16
9/16
3 2
(c) 5 ------ - 2 --------
5 3
3 2
= ( 5 - 2 ) + ---------- - ---------
5 3
The L.C.M of 5 and 3 = 15
3 3 x 3 9
--------- = ----------- = -----------
5 5 x 3 15
2 2 x 5 10
------------ = ------------- = --------------
3 3 x 5 15
9 + 10 - 10
= 2 + -------------------- we borrow 1 from 3
15
19 - 10
= 2 + ----------------
15
9
= 2+ --------
15
then
3
9
= 2 ----------
15
5
3
= 2 -----------
5
If you observed the last example, you'll notice that, i had apply borrowing method by removing 1 from 3 to sort 9.Also, follow my own method and you are good to go...
Now solve these
Simplify the following using equivalent fractions method
2 1
(i.) ------ - -------
3 4
1 1 1
(ii) 4 ----- - 1------- + 1 ---------
4 3 12
1
(iii) 3 - ---------
3
3 1 3
(iv) 2 ------- + 1 ------- - 1 --------
4 2 8
Always remember to look for the L.C.M , after that you obtain an equivalent fractions, please if you have questions, put them in the comment box.
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