To determine the ratio of 90 cm to 1.5 meters, follow these steps:
1. Convert meters to centimeters:
Since 1 meter is equal to 100 centimeters, multiply 1.5 meters by 100 to convert it to centimeters.
[tex]\[
1.5 \text{ meters} \times 100 = 150 \text{ centimeters}
\][/tex]
2. Write the ratio in terms of centimeters:
We need to find the ratio of 90 cm to 150 cm. The ratio is thus written as:
[tex]\[
\frac{90 \text{ cm}}{150 \text{ cm}}
\][/tex]
3. Simplify the ratio:
To simplify the ratio, find the greatest common divisor (GCD) of 90 and 150.
- The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- The factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
- The greatest common factor is 30.
4. Divide both terms by the GCD:
[tex]\[
\frac{90 \div 30}{150 \div 30} = \frac{3}{5}
\][/tex]
5. Write the simplified ratio:
[tex]\[
90 \text{ cm} : 150 \text{ cm} = 3 : 5
\][/tex]
Therefore, the ratio of 90 cm to 1.5 meters simplifies to [tex]\(3 : 5\)[/tex].
Thus, the correct answer is:
b) [tex]\(3 : 5\)[/tex]
