A picture frame is 6 1/2 inches wide. The ratio of the length of the frame to the width is 3:2. What is the length of the frame in inches?

3/2 = x/6.5

Cross multiply and solve for x.

To find the length of the frame, we need to use the given ratio and the width of the frame.

The ratio of the length to the width is 3:2. This means that the length is 3 parts and the width is 2 parts.

Since we know that the width is 6 1/2 inches, we can divide it into 2 parts:

6 1/2 inches ÷ 2 = 3 1/4 inches per part

Now, we can use this value to find the length:

Length = 3 parts × 3 1/4 inches per part

To multiply these values, convert the mixed number 3 1/4 to an improper fraction:

3 1/4 = 4/4 + 1/4 = 5/4

Length = 3 × 5/4 inches

To multiply fractions, multiply the numerators together and multiply the denominators together:

Length = (3 × 5)/(4 × 1) = 15/4

Since we have an improper fraction, we can convert it back to a mixed number:

15/4 = 3 3/4

Therefore, the length of the frame is 3 3/4 inches.

To solve this problem, we need to find the length of the picture frame.

Let's start by understanding the given information. We are told that the width of the picture frame is 6 1/2 inches, or 6.5 inches.

Next, we're given the ratio of the length of the frame to the width, which is 3:2. This means that the length is 3 parts and the width is 2 parts.

To find the length, we can set up a proportion using the ratio:

Length / Width = 3 / 2

Let's substitute the known values:

Length / 6.5 = 3 / 2

Now, we can cross-multiply to solve for the length:

2 * Length = 3 * 6.5

2 * Length = 19.5

Divide both sides by 2 to isolate the Length:

Length = 19.5 / 2

Length = 9.75

Therefore, the length of the picture frame is 9.75 inches.