1584:946

Here's a clear, step-by-step solution to simplify the ratio 1584:946 (aimed at a 6th-grade level).

1. Recognize the task

• We are asked to simplify the ratio by finding the greatest common divisor (GCD) of 1584 and 946, and then dividing both numbers by that GCD.

2. Use the Euclidean algorithm to find the GCD

• 1584 = 946 × 1 + 638
• 946 = 638 × 1 + 308
• 638 = 308 × 2 + 22
• 308 = 22 × 14 + 0

Since the last nonzero remainder is 22, the GCD is 22.

3. Divide both terms by the GCD

• 1584 ÷ 22 = 72
• 946 ÷ 22 = 43

4. State the simplified ratio

• 1584:946 simplifies to 72:43

5. Optional checks

• 72 × 22 = 1584 and 43 × 22 = 946, so the division is correct.
• If you want a decimal sense: 72/43 ≈ 1.674, so the ratio is about 1.674:1.

Answer: 72:43