Math Problem Statement

Complete the ratio table with missing values based on proportional relationships.

Solution

To solve the ratio table, we need to determine the relationships between the numbers in the columns and complete any missing values.

Given Table:

1    | ?
2    | 48
3    | ?
4    | 64
6    | 96

The pattern suggests proportional relationships between the rows. The ratio of numbers in one column to another should remain constant. Let’s solve:

  1. Find the ratio:

    • Look at row 2: 48÷2=2448 \div 2 = 24. The ratio is 1:241:24.
  2. Use this ratio to find the missing values:

    • For 1:241:24, multiply by 11: 1×24=241 \times 24 = 24 (value for row 1, column 2).
    • For 3:243:24, multiply by 33: 3×24=723 \times 24 = 72 (value for row 3, column 2).

Completed Table:

1    | 24
2    | 48
3    | 72
4    | 64
6    | 96

Would you like a detailed breakdown of the proportional calculations or help with a similar problem?

Here are five follow-up questions to expand your understanding:

  1. What is the proportional relationship between the first and second columns?
  2. How can you verify your ratio calculations?
  3. How would the table change if one of the given values were incorrect?
  4. Can you create your own ratio table based on a different multiplier?
  5. What real-world scenarios use proportional relationships like this?

Tip: Always check for a consistent ratio by dividing values from corresponding rows to confirm the proportional relationship.

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportional Relationships

Formulas

Value = Ratio × Multiplier

Theorems

Proportionality Theorem

Suitable Grade Level

Grade 6-7