Answer :
Sure, I'd be happy to help you understand how to find the equivalent ratio!
Davina counted 12 parrots out of 20 birds. We need to determine which given ratio is equivalent to this.
1. Find the ratio of parrots to total birds:
We start by writing the ratio of parrots to total birds:
[tex]\[
\text{Ratio} = \frac{\text{parrots}}{\text{total birds}} = \frac{12}{20}
\][/tex]
2. Simplify the ratio:
To simplify the ratio [tex]\( \frac{12}{20} \)[/tex], we need to find the greatest common divisor (GCD) of 12 and 20. The GCD of 12 and 20 is 4.
Now, divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{12 \div 4}{20 \div 4} = \frac{3}{5}
\][/tex]
So, the simplified ratio of parrots to total birds is [tex]\( \frac{3}{5} \)[/tex].
3. Match with the given options:
Let's look at our choices:
- [tex]\( 2:3 \)[/tex]
- [tex]\( 3 \text{ to } 2 \)[/tex]
- [tex]\( \frac{5}{3} \)[/tex]
- [tex]\( 3 \text{ to } 5 \)[/tex]
The simplified ratio [tex]\( \frac{3}{5} \)[/tex] matches with the option [tex]\( 3 \text{ to } 5 \)[/tex].
Therefore, the equivalent ratio to 12 parrots out of 20 birds is:
[tex]\[ 3 \text{ to } 5 \][/tex]
Davina counted 12 parrots out of 20 birds. We need to determine which given ratio is equivalent to this.
1. Find the ratio of parrots to total birds:
We start by writing the ratio of parrots to total birds:
[tex]\[
\text{Ratio} = \frac{\text{parrots}}{\text{total birds}} = \frac{12}{20}
\][/tex]
2. Simplify the ratio:
To simplify the ratio [tex]\( \frac{12}{20} \)[/tex], we need to find the greatest common divisor (GCD) of 12 and 20. The GCD of 12 and 20 is 4.
Now, divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{12 \div 4}{20 \div 4} = \frac{3}{5}
\][/tex]
So, the simplified ratio of parrots to total birds is [tex]\( \frac{3}{5} \)[/tex].
3. Match with the given options:
Let's look at our choices:
- [tex]\( 2:3 \)[/tex]
- [tex]\( 3 \text{ to } 2 \)[/tex]
- [tex]\( \frac{5}{3} \)[/tex]
- [tex]\( 3 \text{ to } 5 \)[/tex]
The simplified ratio [tex]\( \frac{3}{5} \)[/tex] matches with the option [tex]\( 3 \text{ to } 5 \)[/tex].
Therefore, the equivalent ratio to 12 parrots out of 20 birds is:
[tex]\[ 3 \text{ to } 5 \][/tex]
