Answer :
To determine which ratio is equivalent to [tex]\( \frac{9}{10} \)[/tex], we compare each option:
1. The first ratio is [tex]\( \frac{9}{10} \)[/tex] itself.
2. The second ratio is [tex]\( \frac{30}{27} \)[/tex], which simplifies as follows:
[tex]$$\frac{30}{27} = \frac{10}{9}.$$[/tex]
Since [tex]\( \frac{10}{9} \neq \frac{9}{10} \)[/tex], this option is not equivalent.
3. The third ratio is [tex]\( \frac{27}{30} \)[/tex]. We simplify it by dividing the numerator and denominator by their greatest common divisor (which is 3):
[tex]$$\frac{27}{30} = \frac{27 \div 3}{30 \div 3} = \frac{9}{10}.$$[/tex]
This is exactly the ratio we are given.
4. The fourth ratio is [tex]\( \frac{27}{20} \)[/tex], which does not simplify to [tex]\( \frac{9}{10} \)[/tex].
Thus, the ratio in option 3, [tex]\( \frac{27}{30} \)[/tex], is equivalent to [tex]\( \frac{9}{10} \)[/tex].
The correct answer is option 3.
1. The first ratio is [tex]\( \frac{9}{10} \)[/tex] itself.
2. The second ratio is [tex]\( \frac{30}{27} \)[/tex], which simplifies as follows:
[tex]$$\frac{30}{27} = \frac{10}{9}.$$[/tex]
Since [tex]\( \frac{10}{9} \neq \frac{9}{10} \)[/tex], this option is not equivalent.
3. The third ratio is [tex]\( \frac{27}{30} \)[/tex]. We simplify it by dividing the numerator and denominator by their greatest common divisor (which is 3):
[tex]$$\frac{27}{30} = \frac{27 \div 3}{30 \div 3} = \frac{9}{10}.$$[/tex]
This is exactly the ratio we are given.
4. The fourth ratio is [tex]\( \frac{27}{20} \)[/tex], which does not simplify to [tex]\( \frac{9}{10} \)[/tex].
Thus, the ratio in option 3, [tex]\( \frac{27}{30} \)[/tex], is equivalent to [tex]\( \frac{9}{10} \)[/tex].
The correct answer is option 3.
