Write the ratio 36:9 as a fraction in simplest form
The Correct Answer and Explanation is :
To convert the ratio ( 36:9 ) into a fraction in simplest form, we can follow these steps:
- Understand the Ratio: The ratio ( 36:9 ) means that for every 36 units of one quantity, there are 9 units of another. We can express this ratio as a fraction: [
\frac{36}{9}
] - Simplify the Fraction: To simplify the fraction, we need to divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). The GCD of 36 and 9 is 9.
- Perform the Division:
- Divide the numerator by the GCD:
[
36 \div 9 = 4
] - Divide the denominator by the GCD:
[
9 \div 9 = 1
]
- Write the Simplified Fraction: After simplifying, we get:
[
\frac{4}{1}
]
This means that the ratio ( 36:9 ) in simplest form is ( \frac{4}{1} ).
- Interpret the Result: The fraction ( \frac{4}{1} ) indicates that for every 1 unit of the second quantity (9 in the original ratio), there are 4 units of the first quantity (36 in the original ratio). This simplified form is useful in various applications, such as cooking, budgeting, or comparing quantities, as it provides a clearer understanding of the relationship between the two values.
In summary, the ratio ( 36:9 ) can be simplified to the fraction ( \frac{4}{1} ) by dividing both the numerator and denominator by their GCD, which helps clarify the proportional relationship between the two quantities.