unit12
Adding and Subtracting Mixed Numbers
1. Mixed numbers are part whole number and part fraction.
2. Adding and subtracting procedures:
A. Make sure all fractions have the same denominator (LCD).
B. Add or subtract fractions (watch out for carrying and borrowing).
C. Add or subtract the whole numbers.
D. If necessary, reduce your answer to lowest terms.
3. Adding and subtracting mixed numbers with like fractions
1~
3~
Carrying
5
+2~
-3
35
47
+2-4
7
Borrowing
7
I
6~5 = 5~5 + ~
= 5l5
5
-1~
7
-215 =
2~7
6g7
-21 5
Subtracting 4/5 from
2/5 is not possible.
Reduce
3~
6g777= 6 + 1~ = 7~
Borrowing
4
8=7+4
Note: To simplify the improper
fraction 9/7, divide 7 into 9. The
answer is 1 with a remainder of 2/7.
4
=74
-1~
4
-1~
~
614
4. Adding mixed numbers with unlike fractions
LCD is 12
LCD is 8
118 =
118
+212 = 2 + 2x4
1x4 = + 218
413 = 4
+
+3~4 -- 3 +
1 x4
3x4
3x3
4x3
3~8
= 4..i.
12
= +3.JL
12
711
12
13
Reduce
1
1
712=7+ 1 12= 8 12
5. Subtracting mixed numbers with unlike fractions
LCD is 6
2~3 = 2 +
-112 = 1 +
2x2
3x2
=
216
1x3
2x 3
= -1~ 6
LCD is 6
Borrowing
1
6
1
7
616 =
6-6 = 5-6 + -6 = 5-6
- 3~3 = 3 + 2x2
-31 6
3x2 = -31 6 =
11
6
Reduce
32
2~6 = 212