Here is your equation that you need to solve:
[tex]\frac{2}{66}+\frac{9}{88}+\frac{1}{8}[/tex]
The first thing you'd probably notice is that the bottom number isn't the same. The bottom part of a fraction([tex]\frac{a}{b}[/tex]) is called the denominator where the top part of a fraction is called the numerator.
In this question, you are going to be adding fractions. The first step you need to do when adding fractions is making sure that the denominator is the same. As you've probably noticed, they aren't the same. That means you have to change them by finding the least common multiple(LCM). You can do that by finding their prime factors, also the prime numbers that are multiplied to make that number.
8- 2, 2, 2
66- 2, 3, 11
88- 2, 2, 2, 11
Since the factors for 8 are the same, they don't need to be included. Now you need to multiply the factors of 66 and 88 that aren't the same.
[tex]2 \times 2 \times 2 \times 3 \times 11 \rightarrow 264[/tex]
That means the denominator of all three numbers has to be 234.
Change the fractions:
[tex]\frac{2}{66} \rightarrow \times 4 \rightarrow \frac{2 \times 4}{66 \times 4} \rightarrow \frac{8}{264}[/tex]
[tex]\frac{9}{88} \rigtharrow \times 3 \rightarrow \frac{9 \times 3}{88 \times 3} \rightarrow \frac{27}{264}[/tex]
[tex]\frac{1}{8} \rightarrow \times 33 \rightarrow \frac{1 \times 33}{8 \times 33} \rightarrow \frac{33}{264}[/tex]
Now that all the fractions have been changed, here is your new equation:
[tex]\frac{8}{264}+ \frac{27}{264}+ \frac{33}{264}[/tex]
Now all you need to do is add the numerators. Also keep in mind: when adding fractions, the denominator does NOT change.
[tex]\frac{8}{264}+ \frac{27}{264}+ \frac{33}{264} = \frac{68}{264}[/tex]
Now you have your answer. However it can be simplified:
[tex]\frac{68}{264} \rightarrow \frac{68 \div 4}{264 \div 4} \rightarrow \frac{17}{66}[/tex]
Your answer is [tex]\bf\frac{17}{66}[/tex]
