Math Problem Statement

Find equivalent ratios for the ratio relationship of 2 cups of water to 3 cups of flour.

Solution

The problem asks for equivalent ratios based on the ratio of 2 cups of water to 3 cups of flour, and it requires filling out the table for equivalent ratios.

Given the base ratio of 2:3 (water:flour), we can multiply both the numerator and denominator by the same number to generate equivalent ratios. Let's create a few examples and populate the table:

  • Multiply by 2:
    2×2=4cups of water,3×2=6cups of flour2 \times 2 = 4 \quad \text{cups of water}, \quad 3 \times 2 = 6 \quad \text{cups of flour}
    Ratio: 4:6

  • Multiply by 3:
    2×3=6cups of water,3×3=9cups of flour2 \times 3 = 6 \quad \text{cups of water}, \quad 3 \times 3 = 9 \quad \text{cups of flour}
    Ratio: 6:9

  • Multiply by 4:
    2×4=8cups of water,3×4=12cups of flour2 \times 4 = 8 \quad \text{cups of water}, \quad 3 \times 4 = 12 \quad \text{cups of flour}
    Ratio: 8:12

Here’s how the table should look:

Cups of WaterCups of FlourRatio
232:3
464:6
696:9
8128:12

Would you like more equivalent ratios or further clarification?

Here are 5 follow-up questions:

  1. How would the ratio change if you doubled both values again?
  2. What happens to the proportion if we reduce both water and flour?
  3. Can you simplify the ratio 4:6 further?
  4. What other real-life situations use ratios like this?
  5. How can you express the relationship as a fraction instead of a ratio?

Tip: Always multiply both parts of a ratio by the same factor to keep the relationship equivalent.

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Multiplication

Formulas

Equivalent Ratio Formula: (Original Ratio) * (Multiplication Factor) = Equivalent Ratio

Theorems

Proportionality Theorem

Suitable Grade Level

Grades 5-7