Certainly! To express the ratio [tex]\( 9 : 4 \)[/tex] in its simplest form, let's go through the steps together.
1. Identify the numerator and denominator of the ratio:
- The ratio is given as [tex]\( 9 : 4 \)[/tex].
- Here, the numerator is 9, and the denominator is 4.
2. Simplification of the ratio:
- We need to find the greatest common divisor (GCD) of 9 and 4 to simplify the ratio.
- The GCD of 9 and 4 is 1 (since 9 and 4 have no common factors other than 1).
3. Divide both the numerator and the denominator by their GCD:
- Dividing the numerator 9 by the GCD 1, we get [tex]\( \frac{9}{1} = 9 \)[/tex].
- Dividing the denominator 4 by the GCD 1, we get [tex]\( \frac{4}{1} = 4 \)[/tex].
4. Form the simplified ratio:
- After dividing by the GCD, the ratio remains [tex]\( 9 : 4 \)[/tex].
Thus, the ratio [tex]\( 9 : 4 \)[/tex] is already in its simplest form, and it can't be reduced any further. Therefore, the simplest form of the ratio is [tex]\( 9 : 4 \)[/tex].
