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What numbers should go where the 2 and 4 are in the table

Let's analyze the given table to determine the missing values.

The table shows the amounts of yellow paint (in quarts) and red paint (in quarts) for different-sized batches of the same shade of orange paint. We can use the ratios of yellow paint to red paint to solve for the missing numbers. The ratio should remain constant across all rows, as the mixture must maintain the same proportions to produce the same shade of paint.

### Step 1: Find the ratio of yellow to red paint for the known quantities
In the first row, we have:
\[
\frac{\text{yellow paint}}{\text{red paint}} = \frac{5}{6}
\]
This is the ratio of yellow to red paint.

### Step 2: Use the ratio to find the missing values
Now, we'll apply this ratio to the rows where the red paint values are missing.

#### Row 2:
- We know the yellow paint is \( \frac{5}{4} \) quarts, and we need to find the corresponding red paint.
- Set up the equation:
  \[
  \frac{\frac{5}{4}}{x} = \frac{5}{6}
  \]
  Solving for \( x \):
  \[
  x = \frac{6 \times \frac{5}{4}}{5} = \frac{6 \times 5}{4 \times 5} = \frac{6}{4} = 1.5
  \]
  So, the missing red paint value in the second row is 1.5 quarts.

#### Row 4:
- We know the yellow paint is \( \frac{15}{4} \) quarts, and we need to find the corresponding red paint.
- Set up the equation:
  \[
  \frac{\frac{15}{4}}{x} = \frac{5}{6}
  \]
  Solving for \( x \):
  \[
  x = \frac{6 \times \frac{15}{4}}{5} = \frac{6 \times 15}{4 \times 5} = \frac{90}{20} = 4.5
  \]
  So, the missing red paint value in the fourth row is 4.5 quarts.

### Final Answer:
- The missing value in the second row for red paint is 1.5 quarts.
- The missing value in the fourth row for red paint is 4.5 quarts.

Let me know if you'd like any more details or have further questions!

Here are 5 related questions:
1. What is the concept of ratio and proportion in mathematics?
2. How do you solve proportion problems using cross-multiplication?
3. How can we convert fractions to decimals when solving ratio problems?
4. What other real-life examples use proportional relationships like paint mixtures?
5. How do you verify if two ratios are equivalent?

**Tip**: Always check your ratio units (like quarts or liters) to ensure they match across all rows when solving proportion tables!

What numbers should go where the 2 and 4 are in the table?

Learn how to complete a ratio table by finding missing values for yellow and red paint quantities to maintain the same shade of orange paint. This problem covers the concept of ratios and proportions, using the ratio of 5:6 to solve for missing quantities. Suitable for Grade 6 students.

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