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Answer :
Let's solve the problem step-by-step:
1. Understanding the problem:
- Davina counted 12 parrots out of a total of 20 birds at the pet store.
- We need to find an equivalent ratio of parrots to birds.
2. Current ratio of parrots to birds:
- The ratio given is 12 parrots to 20 birds.
3. Simplify the ratio:
- To simplify the ratio, we divide both numbers by their greatest common divisor (GCD).
- The GCD of 12 and 20 is 4.
- Dividing both numbers by 4, we get:
[tex]\[
\frac{12 \div 4}{20 \div 4} = \frac{3}{5}
\][/tex]
- So the simplified ratio is [tex]\(3:5\)[/tex].
4. Equivalent ratio options given:
- [tex]\(2:3\)[/tex]
- [tex]\(3:2\)[/tex]
- [tex]\(\frac{5}{3}\)[/tex] (which is the same as 5:3)
- [tex]\(3:5\)[/tex]
5. Compare the simplified ratio with the options:
- We simplified the ratio to [tex]\(3:5\)[/tex].
- Let's see which option matches [tex]\(3:5\)[/tex]:
- [tex]\(2:3\)[/tex] is not equivalent to [tex]\(3:5\)[/tex].
- [tex]\(3:2\)[/tex] is not equivalent to [tex]\(3:5\)[/tex].
- [tex]\(\frac{5}{3}\)[/tex] is the same as 5:3 and is not equivalent to [tex]\(3:5\)[/tex].
- [tex]\(3:5\)[/tex] is exactly the same as our simplified ratio.
6. Conclusion:
- The equivalent ratio of parrots to birds at the pet store is [tex]\(3:5\)[/tex].
So, the answer is:
[tex]\[
3 : 5
\][/tex]
1. Understanding the problem:
- Davina counted 12 parrots out of a total of 20 birds at the pet store.
- We need to find an equivalent ratio of parrots to birds.
2. Current ratio of parrots to birds:
- The ratio given is 12 parrots to 20 birds.
3. Simplify the ratio:
- To simplify the ratio, we divide both numbers by their greatest common divisor (GCD).
- The GCD of 12 and 20 is 4.
- Dividing both numbers by 4, we get:
[tex]\[
\frac{12 \div 4}{20 \div 4} = \frac{3}{5}
\][/tex]
- So the simplified ratio is [tex]\(3:5\)[/tex].
4. Equivalent ratio options given:
- [tex]\(2:3\)[/tex]
- [tex]\(3:2\)[/tex]
- [tex]\(\frac{5}{3}\)[/tex] (which is the same as 5:3)
- [tex]\(3:5\)[/tex]
5. Compare the simplified ratio with the options:
- We simplified the ratio to [tex]\(3:5\)[/tex].
- Let's see which option matches [tex]\(3:5\)[/tex]:
- [tex]\(2:3\)[/tex] is not equivalent to [tex]\(3:5\)[/tex].
- [tex]\(3:2\)[/tex] is not equivalent to [tex]\(3:5\)[/tex].
- [tex]\(\frac{5}{3}\)[/tex] is the same as 5:3 and is not equivalent to [tex]\(3:5\)[/tex].
- [tex]\(3:5\)[/tex] is exactly the same as our simplified ratio.
6. Conclusion:
- The equivalent ratio of parrots to birds at the pet store is [tex]\(3:5\)[/tex].
So, the answer is:
[tex]\[
3 : 5
\][/tex]
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