Question The ratio of small dogs to large dogs at the pet store is two to three. There are 45 dogs at the pet store. Represent the ratio with a tape diagram.
To represent the ratio of small dogs to large dogs at the pet store using a tape diagram, you can divide a tape into two parts. One part should be labeled "small dogs" and the other part should be labeled "large dogs."
Since the ratio of small dogs to large dogs is two to three, we can divide the tape into 5 equal parts.
The first two parts will represent the small dogs, and the remaining three parts will represent the large dogs.
Here is a representation of the ratio using a tape diagram:
Small Dogs Large Dogs
-------------------|---------------------|---------------------
Each part of the tape diagram represents 9 dogs since there are 45 dogs at the pet store (5 parts x 9 dogs = 45 dogs).
So, the first two parts represent 18 small dogs, and the remaining three parts represent 27 large dogs.
To represent the ratio of small dogs to large dogs at the pet store with a tape diagram, you would create two sections for small dogs and three sections for large dogs. Since the ratio is 2 to 3, each of the sections would be equal in length.
Let's assume that each section represents an equal number of dogs.
Start by drawing five equal sections in a horizontal line.
|----|----|----|----|----|
The first two sections represent small dogs, and the next three sections represent large dogs.
|----|----|----|----|----|
Small Small Large Large Large
Since there are 45 dogs at the pet store, we need to divide them into two parts: small dogs and large dogs.
To do this, we divide the line into five equal parts, each representing 9 dogs (since 45 divided by 5 is 9).
|----|----|----|----|----|
9 9 9 9 9
So, the diagram represents the ratio of small dogs to large dogs at the pet store as 2 to 3.
To represent the ratio of small dogs to large dogs at the pet store with a tape diagram, we can draw two separate rectangles to represent the two parts of the ratio.
First, let's label the rectangles as "Small Dogs" and "Large Dogs." Since the ratio of small dogs to large dogs is 2 to 3, we can divide the first rectangle into two equal parts and the second rectangle into three equal parts.
Next, we fill in each part of the rectangles according to the ratio. To do this, we need to find the value of each part of the ratio. Since we know that there are a total of 45 dogs at the pet store, we can divide this number into two parts based on the ratio.
Let's set up an equation to represent the ratio:
2x + 3x = 45
5x = 45
x = 9
Now, we can calculate the value of each part of the ratio:
Small Dogs: 2x = 2 * 9 = 18
Large Dogs: 3x = 3 * 9 = 27
Finally, we can draw the tape diagram:
Small Dogs Large Dogs
___________ _______________
| | | |
| | | |
| | | |
| | | |
| | | |
|___________| |_______________|
Here, we divide the Small Dogs rectangle into two equal parts, where each part represents 9 dogs. Similarly, we divide the Large Dogs rectangle into three equal parts, where each part represents 9 dogs.
After counting the parts, we have:
- 2 parts in the Small Dogs rectangle, which represents 2 x 9 = 18 small dogs.
- 3 parts in the Large Dogs rectangle, which represents 3 x 9 = 27 large dogs.
Therefore, the tape diagram shows a ratio of 18 small dogs to 27 large dogs, which satisfies the given ratio of 2:3.