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Evaluate the following expression:

[tex]\[ \frac{8}{9} + \frac{1}{6} \][/tex]

A. [tex]\( 1 \frac{1}{18} \)[/tex]

B. [tex]\( \frac{3}{5} \)[/tex]

C. [tex]\( \frac{4}{27} \)[/tex]

D. [tex]\( \frac{9}{54} \)[/tex]


Sagot :

Let's solve the problem step-by-step to add the fractions [tex]\(\frac{8}{9}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex].

1. Find a common denominator:
To add two fractions, we need a common denominator. The denominators we have are 9 and 6. We need to find the least common multiple (LCM) of 9 and 6. The LCM of 9 and 6 is 18.

2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{8}{9}\)[/tex]:
[tex]\[ \frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18} \][/tex]
- For [tex]\(\frac{1}{6}\)[/tex]:
[tex]\[ \frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18} \][/tex]

3. Add the two fractions:
[tex]\[ \frac{16}{18} + \frac{3}{18} = \frac{16 + 3}{18} = \frac{19}{18} \][/tex]

4. Convert the improper fraction to a mixed number:
[tex]\[ \frac{19}{18} = 1 \frac{1}{18} \][/tex]
This mixed number consists of a whole number part and a fractional part:
- The whole number part is 1.
- The fractional part is [tex]\(\frac{1}{18}\)[/tex].

Therefore, after adding [tex]\(\frac{8}{9}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex], we get the result:

[tex]\[ 1 \frac{1}{18} \][/tex]