Math Problem Statement
Solution
From the image, we are solving a ratio table problem. The goal is to fill in the missing entries in the table based on proportional relationships.
The table appears as follows:
Column 1 | Column 2 |
---|---|
1 | 32 |
? | 32 |
58 | ? |
60 | ? |
100 | 100 |
Let us compute step-by-step:
1. Find the ratio factor:
From the first row:
- : The ratio is .
This ratio applies to the entire table.
2. Fill in the missing entries:
-
Row 2, Column 1: What number gives 32 in Column 2?
-
Row 3, Column 2: 58 scaled by :
-
Row 4, Column 2: 60 scaled by :
-
Row 5, Column 1: To get 100 in Column 2, divide:
Updated Table:
Column 1 | Column 2 |
---|---|
1 | 32 |
1 | 32 |
58 | 1856 |
60 | 1920 |
3.125 | 100 |
Would you like further clarification or detailed explanations for any specific row? Here are some related questions for practice:
- What is the importance of identifying the ratio in a proportional relationship?
- How can you verify if two values in a table are proportional?
- Can you think of a real-world example where ratio tables are helpful?
- What happens if one of the values in a ratio table is negative?
- How would you compute ratios if decimals are introduced?
Tip: Always start by finding the ratio or scaling factor between corresponding entries! This simplifies solving ratio tables efficiently.
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Math Problem Analysis
Mathematical Concepts
Ratios
Proportional Relationships
Scaling
Formulas
Scaling factor = value in one column / corresponding value in another column
Missing value = known value × scaling factor
Theorems
Proportionality in ratio tables
Suitable Grade Level
Grades 6-8