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
┌─────┬─────┐
│ 1 │ 1 │
└─────┴─────┘
choose one choose one

drag to build the diagram.

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

Explanation:

Part (a)

To build the ratio diagram for diamonds to emeralds, we first identify the quantities. Diamonds have a quantity of 3 and emeralds have a quantity of 4. The ratio of diamonds to emeralds is \( 3:4 \). So we can represent this with a tape diagram where we have two parts, one for diamonds (length corresponding to 3) and one for emeralds (length corresponding to 4), or using unit blocks. If we use unit blocks, we can have 3 blocks for diamonds and 4 blocks for emeralds. But since the initial diagram has a 1:1 part, we can scale it. However, a simple way is to show the number of diamonds and emeralds. So the top choice could be "Ratio of Diamonds to Emeralds", then the bottom left is "Diamonds" with 3 units (or blocks) and bottom right is "Emeralds" with 4 units (or blocks). But since the drag - and - drop is about building the diagram with the given 1 - 1 blocks, we can think of the ratio \( 3:4 \), so we need to have 3 of one type (diamonds) and 4 of the other (emeralds). So the top dropdown can be labeled as "Diamonds to Emeralds", the bottom left as "Diamonds (3)" and bottom right as "Emeralds (4)" (or using the number of blocks, like 3 blocks for diamonds and 4 blocks for emeralds).

Part (b)

Step 1: Identify the quantities

From the table, the quantity of diamonds is 3 and the quantity of emeralds 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 the ratio is \( 3:4 \).

Answer:

(a) (Top: "Diamonds to Emeralds", Bottom Left: "Diamonds (3)", Bottom Right: "Emeralds (4)" - or appropriate drag - and - drop representation with 3 units for diamonds and 4 units for emeralds)
(b) \( 3:4 \)