Question

a jeweler put these gemstones out on display today.

gemstone	quantity
emeralds	4
diamonds	3

(a) build a diagram to show the ratio of diamonds to emeralds.

choose one dropdown
├─ 1 1
│ ├─ left arrow button
│ └─ right arrow button
│ └─ drag to build the diagram.
├─ choose one dropdown
└─ choose one dropdown

(b) write the ratio of diamonds to emeralds.
□ : □

Explanation:

Part (a)

To build the diagram for the ratio of diamonds to emeralds, we first find the ratio of diamonds to emeralds. The number of diamonds is 3 and the number of emeralds is 4. So the ratio of diamonds to emeralds is \(3:4\). For the diagram, we can think of it as groups. The top box can represent the "diamond - emerald" group concept, and the bottom two boxes represent the number of diamonds and emeralds respectively. So we would set the top dropdown (if it's about the type of ratio representation, maybe "Ratio of Diamonds to Emeralds"), and the bottom left (diamonds) as 3 and bottom right (emeralds) as 4. But since it's a drag - build, we can structure it to show 3 parts for diamonds and 4 parts for emeralds, with the ratio relationship.

Part (b)

Step 1: Identify the quantities

We know from the table that the number of diamonds (\(n_d\)) is 3 and the number of emeralds (\(n_e\)) is 4.

Step 2: Write the ratio

The ratio of diamonds to emeralds is written as the number of diamonds followed by a colon and then the number of emeralds, so it is \(3:4\).

Answer:

For part (b), the ratio of diamonds to emeralds is \(\boldsymbol{3:4}\)