Example 2.
Calculate the sum
.
Solution.
To find the sum of these fractions, you need to add up their whole parts, and bring the fractional parts to the lowest common denominator and add them up too. Let's find the lowest common denominator for the fractional parts:
24 = 2*2*2*3;
16 = 2*2*2*2.
Therefore, the least common denominator is 2*2*2*3*2=48.
3
23/24
+ 1
15/16
= 3 + 1 +
23/24
+
15/16
= 4 +
46/48
+
45/48
= 4
46+45/48
= 4
91/48
= 5
43/48
.
Answer: .
Example 3.
Calculate the sum
.
Solution.
To find the sum of these fractions, you need to add up their whole parts, and bring the fractional parts to the lowest common denominator and add them up too. Let's find the lowest common denominator for the fractional parts:
12 = 2*2*3;
20 = 2*2*5.
Therefore, the least common denominator is 2*2*3*5=60.
6
5/12
+ 2
19/20
= 6 + 2 +
5/12
+
19/20
= 8 +
25/60
+
57/60
= 8
25+57/60
= 8
82/60
= 9
22/60
= 9
11/30
.
Answer: .
Subtracting mixed fractions
To subtract mixed fractions, bring the fractional parts of the minuend and subtrahend to the lowest common denominator, and separately subtract the whole parts and subtract the fractional parts. If the fractional part of the minuend is less than the fractional part of the subtrahend, then the fractional part of the minuend must be converted into an improper fraction by reducing the whole part of the minuend by 1. Let's consider the subtraction of mixed fractions using examples.
Example 4.
Calculate the difference
.
Solution.
To find the difference between these fractions, you need to reduce the fractional parts to the least common denominator 16 and subtract the whole parts and the fractional parts separately:
5
7/8
- 4
3/16
= 5 - 4 +
7/8
-
3/16
= 1 +
14/16
-
3/16
= 1
14-3/16
= 1
11/16
.
Answer: .
Example 5.
Calculate the difference
Solution.
Let's find the least common denominator for fractional parts:
9 = 3*3;
6 = 2*3.
Therefore, the least common denominator is 3*3*2=18.
7
4/9
- 2
5/6
= 7 - 2 +
4/9
-
5/6
= 5 +
8/18
-
15/18
= 4 +
26/18
-
15/18
= 4
11/18
.
Answer: .
Example 6.
Calculate the difference
.
Solution.
Let's find the least common denominator for fractional parts:
12 = 2*2*3;
20 = 2*2*5.
Therefore, the least common denominator is 2*2*3*5=60.
1
1/12
-
19/20
= 1 +
1/12
-
19/20
= 1 +
5/60
-
57/60
=
65/60
-
57/60
=
8/60
=
2/15
.
Answer: .
Example 7.
Calculate the difference
.
Solution.
6 - 2
2/3
= 5 +
3/3
- 2
2/3
= 5 - 2 +
3/3
-
2/3
= 3
1/3
.
Answer: .
