2/3 of the flowers in a garden were roses .5/12 of the roses were yellow and the rest were red.what fraction of the flowers were red?

.5/12 = 1/24

2/3 = 16/24

1 - 16/24 - 1/24 = ?

To find the fraction of the flowers that were red, we need to first determine the fraction of flowers that were roses and then subtract the fraction of yellow roses from it.

1. Let's start by finding the fraction of flowers that were roses. We know that 2/3 of the flowers were roses. Therefore, the fraction of the flowers that were roses is 2/3.

2. Next, we need to find the fraction of roses that were yellow. We are told that 5/12 of the roses were yellow.

3. To find the fraction of the flowers that were yellow roses, we multiply the fraction of roses (2/3) by the fraction of yellow roses (5/12):

(2/3) * (5/12) = 10/36

4. Now, to find the fraction of the flowers that were red, we subtract the fraction of yellow roses (10/36) from the fraction of roses (2/3):

(2/3) - (10/36)

To simplify this subtraction, we need to find the least common denominator (LCD) of 3 and 36, which is 36. So, we have:

(24/36) - (10/36) = 14/36

5. Finally, the fraction of the flowers that were red is 14/36.

Therefore, the fraction of the flowers that were red is 14/36.

To find the fraction of flowers that were red, we need to determine the proportion of red roses out of the total number of flowers in the garden.

Let's break down the problem step by step:

1. Determine the fraction of roses in the garden. It is given that 2/3 of the flowers in the garden were roses. So, if we assume there are 3 parts in total, 2 of the 3 parts represent roses.

Therefore, the fraction of roses in the garden is 2/3.

2. Calculate the fraction of yellow roses out of the total number of roses. It is given that 5/12 of the roses were yellow.

Therefore, the fraction of yellow roses is 5/12.

3. Calculate the fraction of red roses. Since the question states that the remaining roses are red, subtract the fraction of yellow roses from the fraction of roses in the garden:

Fraction of red roses = Fraction of roses - Fraction of yellow roses

= 2/3 - 5/12.

To perform this subtraction, we need to find a common denominator. The least common multiple (LCM) of 3 and 12 is 12. So, we can rewrite the equation as:

Fraction of red roses = (8/12) - (5/12).

This simplifies to:

Fraction of red roses = 3/12.

4. Simplify the fraction. The fraction 3/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3. This results in:

Fraction of red roses = 1/4.

Therefore, 1/4 of the flowers in the garden were red roses.