Question

1. select all the quotients that are reasonable estimates for 472 ÷ 6. 450 ÷ 5 480 ÷ 6 500 ÷ 5 450 ÷ 3 1,200 ÷ 6 = 200

Explanation:

Step1: Calculate 472 ÷ 6

First, we know that \( 6\times78 = 468 \), and \( 472 - 468 = 4 \), so \( 472\div6\approx78.67 \).

Step2: Analyze each option

• For \( 450\div5 \): Calculate \( 450\div5 = 90 \). The difference between 90 and 78.67 is \( |90 - 78.67| = 11.33 \).
• For \( 480\div6 \): Calculate \( 480\div6 = 80 \). The difference between 80 and 78.67 is \( |80 - 78.67| = 1.33 \).
• For \( 500\div5 \): Calculate \( 500\div5 = 100 \). The difference between 100 and 78.67 is \( |100 - 78.67| = 21.33 \).
• For \( 450\div3 \): Calculate \( 450\div3 = 150 \). The difference between 150 and 78.67 is \( |150 - 78.67| = 71.33 \).
• For \( 1200\div6 = 200 \): The difference between 200 and 78.67 is \( |200 - 78.67| = 121.33 \).

We are looking for reasonable estimates. The quotient of \( 480\div6 = 80 \) is closest to \( 472\div6\approx78.67 \) among these options. Also, we can think about rounding 472 to 480 (since 480 is a multiple of 6), so \( 480\div6 \) is a reasonable estimate.

Answer:

The reasonable estimate is \( 480\div6 \) (the option with \( 480\div6 \)).