What is the ratio as a fraction in simplest form 30 to 18
The Correct Answer and Explanation is:
To simplify the ratio 30 to 18, we need to express it as a fraction and then simplify it.
Step 1: Write the ratio as a fraction.
The ratio 30 to 18 can be written as:3018\frac{30}{18}1830
Step 2: Simplify the fraction.
To simplify this fraction, we need to find the Greatest Common Divisor (GCD) of 30 and 18. The GCD is the largest number that divides both numbers exactly.
- The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.
- The factors of 18 are: 1, 2, 3, 6, 9, 18.
The greatest common factor between 30 and 18 is 6. Now, we divide both the numerator and the denominator of the fraction by 6:3018=30÷618÷6=53\frac{30}{18} = \frac{30 \div 6}{18 \div 6} = \frac{5}{3}1830=18÷630÷6=35
Step 3: Final Answer.
So, the simplified form of the ratio 30 to 18 is:53\frac{5}{3}35
This is the ratio in its simplest form.
Explanation:
The process of simplifying fractions involves finding the greatest common divisor (GCD) of the numbers in the ratio, and then dividing both the numerator and the denominator by that number. In this case, the GCD of 30 and 18 is 6, so dividing both by 6 gives us the ratio of 5 to 3.
In real-world terms, simplifying ratios helps to express the relationship between two quantities in the simplest, most understandable form. For example, if you’re mixing two ingredients in a ratio of 30 to 18, simplifying it to 5 to 3 makes the proportions easier to work with, whether you’re baking or mixing chemicals.
