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

drag to build the diagram.

choose one choose one

(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 their quantities. The quantity of diamonds is 3 and emeralds is 4. So the ratio of diamonds to emeralds is \( 3:4 \). We can represent this using a tape diagram where we have two parts, one for diamonds and one for emeralds. We can divide the diagram such that the length for diamonds is 3 units and for emeralds is 4 units (or use the given 1 - unit blocks and repeat them 3 times for diamonds and 4 times for emeralds).

Step 1: Determine the ratio

The quantity of diamonds \( = 3 \), quantity of emeralds \( = 4 \), so the ratio of diamonds to emeralds is \( 3:4 \).

Step 2: Build the diagram

We can use the blocks to represent the ratio. For the top "Choose one", we can select a way to label the ratio (e.g., "Diamonds : Emeralds"). Then, for the bottom left (representing diamonds), we use 3 of the 1 - unit blocks (or adjust the multiplier to get 3) and for the bottom right (representing emeralds), we use 4 of the 1 - unit blocks. (Since it's a drag - and - drop, we would set the number of blocks for diamonds to 3 and for emeralds to 4, with the ratio label as "Diamonds : Emeralds" at the top.)

Part (b)

The ratio of two quantities is the comparison of their amounts. Here, we need the ratio of the number of diamonds to the number of emeralds. From the table, the number of diamonds is 3 and the number of emeralds is 4. So we write the ratio as the number of diamonds first, then the number of emeralds.

Step 1: Identify the quantities

Number of diamonds \( = 3 \), Number of emeralds \( = 4 \).

Step 2: Write the ratio

The ratio of diamonds to emeralds is \( 3:4 \).

Answer:

(Part a Diagram Explanation):
For the diagram, label the top as "Diamonds : Emeralds", use 3 units (blocks) for diamonds and 4 units (blocks) for emeralds.