Sure, let's find the ratio for each part and reduce them to their lowest terms.
### Part (a): 35 and 65
To find the ratio in its simplest form, we need to divide both numbers by their greatest common divisor (GCD).
1. Find the GCD of 35 and 65:
- The factors of 35 are 1, 5, 7, and 35.
- The factors of 65 are 1, 5, 13, and 65.
- The common factors are 1 and 5.
- The greatest common divisor (GCD) is 5.
2. Divide both numbers by the GCD:
- [tex]\( \frac{35}{5} = 7 \)[/tex]
- [tex]\( \frac{65}{5} = 13 \)[/tex]
So, the ratio of 35 to 65 in its lowest terms is 7:13.
### Part (b): 2 meters and 300 centimeters
First, we need to ensure both quantities are in the same units. We'll convert 300 centimeters to meters.
1. Convert 300 centimeters to meters:
- [tex]\( 300 \, \text{cm} = 300 \, \text{cm} \div 100 = 3 \, \text{meters} \)[/tex]
Now we have 2 meters and 3 meters.
2. Find the GCD of 2 and 3:
- The factors of 2 are 1 and 2.
- The factors of 3 are 1 and 3.
- The common factor is 1.
- The greatest common divisor is 1.
Since the GCD is 1, the ratio is already in its lowest terms.
So, the ratio of 2 meters to 3 meters is 2:3.
In summary:
- The ratio of 35 to 65 in its lowest terms is 7:13.
- The ratio of 2 meters to 300 centimeters (or 2 meters to 3 meters) in its lowest terms is 2:3.
