(a) [tex]\frac{4}{3} + \frac{3}{4}[/tex] (b) [tex]\frac{7}{4} + \frac{1}{7}[/tex] (c) [tex]\frac{1}{6} + \frac{11}{12}[/tex] (d) [tex]3\frac{2}{3} + 1\frac{3}{8}[/tex]
Answer (1)
To solve the given fractions, we will add them together by finding a common denominator for each pair.
(a) 3 4 + 4 3
First, find the least common denominator (LCD) of 3 and 4, which is 12.
Convert 3 4 to 12 16
Convert 4 3 to 12 9
Now add the fractions: 12 16 + 12 9 = 12 25 = 2 12 1
(b) 4 7 + 7 1
The LCD of 4 and 7 is 28.
Convert 4 7 to 28 49
Convert 7 1 to 28 4
Now add them: 28 49 + 28 4 = 28 53 = 1 28 25
(c) 6 1 + 12 11
The LCD of 6 and 12 is 12.
Convert 6 1 to 12 2
12 11 stays the same.
Now add them: 12 2 + 12 11 = 12 13 = 1 12 1
(d) 3 3 2 + 1 8 3
First, convert the mixed numbers to improper fractions:
3 3 2 = 3 11
1 8 3 = 8 11
Find the LCD of 3 and 8, which is 24.
Convert 3 11 to 24 88
Convert 8 11 to 24 33
Add them: 24 88 + 24 33 = 24 121 = 5 24 1
Therefore, the answers for each part are:
(a) 2 12 1
(b) 1 28 25
(c) 1 12 1
(d) 5 24 1
