Answer:
[tex]\displaystyle \frac{8}{18} = \frac{4}{9}\ ,\ \displaystyle \frac{12}{27} = \frac{4}{9}[/tex]
Step-by-step explanation:
Equivalent Fractions
Two fractions are equivalent if they represent the same rational number, regardless of their expression. For example, the fraction 2/5 is equivalent to 10/25 since they both represent the number 0.4
To find if a given fraction is equivalent to another given fraction, we can simplify or amplify it until an equivalence is found or not. We can also simply perform the division and compare the results.
We must find out if the four choices are equivalent to the fraction 4/9. Let's start with the first one
[tex]\displaystyle \frac{20}{36} =\frac{5}{9}[/tex]
We simplified it by 4 and found it's not equivalent to 4/9. The fraction
[tex]\displaystyle \frac{8}{18} = \frac{4}{9}[/tex]
is equivalent to 4/9 when simplified by 2.
[tex]\displaystyle \frac{24}{45} = \frac{8}{15}[/tex]
This fraction was simplified by 3 and is not equivalent to 4/9. Finally
[tex]\displaystyle \frac{12}{27} = \frac{4}{9}[/tex]
Is equivalent to 4/9 when simplified by 3. Summarizing, these fractions are equivalent to 4/9
[tex]\boxed{\displaystyle \frac{8}{18} = \frac{4}{9}\ ,\ \displaystyle \frac{12}{27} = \frac{4}{9}}[/tex]
