Question

a jeweler put these gemstones out on display today.
gemstone quantity
diamonds 2
emeralds 5
rubies 1
(a) build a diagram to show the ratio of diamonds to all gemstones shown.
select
1 1
drag to build the diagram.
select gemstones that are not diamonds

Explanation:

Step1: Calculate total gemstones

First, find the total number of gemstones. Diamonds: 2, Emeralds: 5, Rubies: 1. So total = \(2 + 5 + 1 = 8\).

Step2: Determine diamond and non - diamond counts

Diamonds are 2, so non - diamonds are \(8 - 2=6\). The ratio of diamonds to all gemstones is \(2:8\) (or simplified, but for the diagram, we can represent the parts). The top "Select" should be for the total number of parts (8), but looking at the diagram structure, the lower left "Select" is for diamonds. Since diamonds are 2, and the small boxes are 1 each, we need 2 for diamonds. The "Gemstones that are not diamonds" would be \(8 - 2 = 6\), but in the diagram's current small boxes (each 1), the top "Select" is for the whole, and the lower left is for diamonds. Wait, the diagram has a top node, then two nodes below: one for diamonds (with 1 and 1, so we can drag to make it 2) and one for non - diamonds. Wait, the problem says "build a diagram to show the ratio of diamonds to all gemstones". So the total number of gemstones is 8, diamonds are 2, non - diamonds are 6. But the diagram has a top "Select" (maybe the total number of units, but the lower left is for diamonds. Let's re - express: the ratio of diamonds to all gemstones is \(2:8\), which can be represented as 2 parts (diamonds) to 8 parts (total). But the diagram has a structure where the top is the whole, and below are diamonds and non - diamonds. So the lower left "Select" (for diamonds) should be set to 2 (since diamonds are 2), and the top "Select" (the whole) would be 8, but maybe the diagram is using a part - part - whole model. Wait, the small boxes below the top have 1 and 1, and we can drag to add more. Wait, the problem is about building a diagram (like a tape diagram or ratio diagram). The number of diamonds is 2, total gemstones is \(2 + 5+1 = 8\). So the ratio of diamonds to all gemstones is \(2:8\). So in the diagram, the "diamonds" part should have 2 units, and the "all gemstones" is the whole. Wait, the diagram structure: the top node is the whole (all gemstones), then it splits into diamonds and non - diamonds. So first, calculate total gemstones: \(2 + 5+1=8\). Diamonds: 2, non - diamonds: \(8 - 2 = 6\). So for the diamonds part (the lower left "Select"), we need to have 2 (since each small box is 1, we drag to make it 2). The "Gemstones that are not diamonds" would be 6, but in the diagram's current state, the lower left is for diamonds. So the lower left "Select" (the one connected to "1 1") should be set to 2 (by dragging the blue arrows to add more 1s, making it 2). The top "Select" is for the total number of gemstones (8), but maybe the diagram is using the number of gemstones as the total. Wait, maybe I misread. Let's start over:

1. Calculate total gemstones: \(2\) (diamonds) \(+ 5\) (emeralds) \(+ 1\) (rubies) \(= 8\).
2. The ratio of diamonds to all gemstones is \(2:8\). So in the diagram, the part representing diamonds should have 2 units, and the part representing all gemstones is the whole. But the diagram has a top "Select" (maybe the number of units in the whole), and below are diamonds and non - diamonds. The lower left "Select" is for diamonds. So we need to set the diamonds part to 2 (since there are 2 diamonds) and the total (top) to 8. But looking at the diagram's interface, the small boxes below the top have 1 and 1, and we can drag to add more. So for the diamonds part (the left - most of the two lower boxes), we drag to add one more 1 (since it has 1 and 1, wait no, the two boxes below the top: one is for diamonds, one is for non - diamonds. The diamonds box has "1 1" with blue arrows to add/remove. So we need 2 for diamonds, so we can leave it as 2 (since it's already 1 + 1 = 2? Wait, the initial diamonds box has two 1s? Wait, the image shows the diamonds part with two 1s (the two small boxes with 1 and 1)? No, the image shows the diamonds part (the left - hand box below the top) with "1" and a blue arrow, and the right - hand box (non - diamonds) with "1" and a blue arrow. Wait, maybe I misinterpret. Let's re - calculate:

Total gemstones: \(2\) (diamonds) \(+\ 5\) (emeralds) \(+\ 1\) (rubies) \(=\ 8\).

Ratio of diamonds to all gemstones: \(2:8\).

So in the diagram, the "diamonds" segment should have 2 units, and the "all gemstones" is the whole (8 units). The diagram's structure: the top is the whole (8), split into diamonds (2) and non - diamonds (6). So the lower left "Select" (for diamonds) should be set to 2 (by dragging the blue arrow to have 2 units, since each unit is 1). The top "Select" (the whole) would be 8, but maybe the diagram is using the number of gemstones as the count. So the steps are:

1. Calculate total gemstones: \(2 + 5+1 = 8\).
2. Determine the number of diamonds: 2.
3. In the diagram, the "diamonds" part (lower left) should have 2 (so we can drag the blue arrow to add one more 1, making it 2), and the top "Select" (the whole) is 8, but maybe the diagram is a ratio diagram where the top is the total number of gemstones (8) and the two lower parts are diamonds (2) and non - diamonds (6).

But since the problem is about building the diagram, and the answer is about what to select: the lower left "Select" (for diamonds) should be 2, and the top "Select" (the whole) is 8. But looking at the options (the "Select" dropdowns), maybe the lower left "Select" (diamonds) is set to 2, and the top "Select" is 8. But the problem is in the diagram - building, so the key is that the number of diamonds is 2, total is 8. So the "diamonds" part of the diagram should have 2 units, and the whole (all gemstones) is 8 units.

Answer:

For the lower left "Select" (diamonds), we need to have 2 (so drag to make it 2 units), and the top "Select" (all gemstones) is 8. But since the diagram - building is interactive, the answer is that the number of diamonds is 2, total gemstones is 8, so the ratio diagram for diamonds to all gemstones has 2 parts (diamonds) and 8 parts (total). So in the diagram, the "diamonds" segment should be 2, and the whole is 8.