Write the ratio as a fraction in simplest 45 to 27

The Correct Answer and Explanation is:

To simplify the ratio 45 to 27 as a fraction, we first express it as a fraction:

[
\frac{45}{27}
]

Step 1: Find the Greatest Common Divisor (GCD)

The next step is to find the greatest common divisor (GCD) of 45 and 27. The GCD is the largest number that divides both 45 and 27 without leaving a remainder.

The factors of 45 are: 1, 3, 5, 9, 15, and 45.
The factors of 27 are: 1, 3, 9, and 27.

The largest common factor between 45 and 27 is 9. Therefore, the GCD of 45 and 27 is 9.

Step 2: Simplify the Fraction

To simplify the fraction, we divide both the numerator and the denominator by the GCD, which is 9:

[
\frac{45}{27} = \frac{45 \div 9}{27 \div 9} = \frac{5}{3}
]

Step 3: Verify the Simplified Fraction

The fraction (\frac{5}{3}) is in its simplest form because 5 and 3 do not have any common factors other than 1.

Step 4: Convert Back to a Ratio

Now that we have simplified the fraction, we can express it back as a ratio. The simplified ratio of 45 to 27 is:

[
5:3
]

Final Answer:

The ratio 45 to 27 simplifies to ( \frac{5}{3} ) or ( 5:3 ).

Explanation:

A ratio compares two quantities. In this case, we started with the ratio 45 to 27, which means we are comparing 45 units to 27 units. By simplifying the ratio, we make it easier to understand the relationship between the two numbers. The process of simplifying involves finding the greatest common divisor (GCD) of the two numbers and dividing both the numerator and the denominator by that GCD. This step ensures that the ratio is expressed in the simplest possible form.