What are 3 equivalent ratios for 12 to 9?

Step 1
To find alternative ratios, you can divide both sides by a common factor (this will simplify it) or multiply them both by the same factor.
So, for ${\displaystyle 12:9}$, we can divide both sides by 3:
${\displaystyle \frac{12}{3}:\frac{9}{3}=4:3}$
Or we can multiply both sides by any number, as long as it is the same for both:
e.g. by 2
${\displaystyle 12\times 2:9\times 2=24:18}$
e.g. by ${\displaystyle 1\frac{1}{3}}$
${\displaystyle 12\times 1\frac{1}{3}:9\times 1\frac{1}{3}=16:12}$
So, three equivalent ratios (of the many possibilities) are:
$4:3$
${\displaystyle 24:18}$
${\displaystyle 16:12}$
Hope this helps; let me know if I can do anything else.

Step 1 
The ratio 12 to 9 is given to us here, and we are requested to write its three comparable ratios. First let us find its equivalent fractions which can be converted into the ratios easily. 
The ratio 12 to 9 can be written in fractional form by considering 12 as the numerator and 9 as the denominator as ${\displaystyle \frac{12}{9}}$. Let us see if it has common factors, so we get, 
${\displaystyle \Rightarrow \frac{12}{9}=\frac{3\times s4}{3\times 3}}$ 
${\displaystyle \Rightarrow \frac{12}{9}=\frac{4}{3}}$ 
Therefore, the simplest form of the fraction ${\displaystyle \frac{12}{9}}$ is ${\displaystyle \frac{4}{3}}$ 
Now, if the simplest forms of two or more fractions are equal, they are said to be equivalent.
So, ${\displaystyle \frac{4}{3}}$ is an equivalent fraction of ${\displaystyle \frac{12}{9}}$. We multiply the numerator and denominator with a number other than 0 to find equivalent fractions. So let us find two more equivalent fractions. 
1) ${\displaystyle \frac{4}{3}=\frac{4\times s5}{3\times 5}=\frac{20}{15}}$ 
2) ${\displaystyle \frac{4}{3}=\frac{4\times 6}{3\times 6}=\frac{24}{18}}$ 
Therefore, ${\displaystyle \frac{4}{3},\frac{20}{15}}$ and ${\displaystyle \frac{24}{18}}$ are the three equivalent fractions of ${\displaystyle \frac{12}{9}}$. We know that a fraction of the form ${\displaystyle \frac{a}{b}}$ is written in the ratio form as ${\displaystyle a:b}$. Hence, we have ${\displaystyle 4:3,20:15}$ and ${\displaystyle 24:18}$ as the three equivalent ratios of ${\displaystyle 12:9}$

Step 1 By dividing the numerator and denominator of the provided ratio by three, we can obtain the first ratio. This yields $\frac{12}{9}=\frac{12÷3}{9÷3}$ $=\frac{4}{3}$ The second ratio can then be calculated by multiplying the first ratio by two. This yields $\frac{4}{3}=\frac{4\times 2}{3\times 2}$ $=\frac{8}{6}$ Then, the third ratio can be obtained if we will multiply the simplified ratio by 4. This yields $\frac{4}{3}=\frac{4\times 4}{3\times 4}$ $=\frac{16}{12}$ Hence, the 3 equivalent ratios for $\frac{12}{9}$ are $\frac{4}{3},\frac{8}{6}$, and $\frac{16}{12}$