Question

which of these division problems have the same quotient as 12.3 divided by 0.4? check all that apply.

123 \div 4
1.23 \div 0.4
1,230 \div 40
123 \div 0.04

Explanation:

Represent the original division as a fraction

Using the Decimal Division and Equivalent Expressions knowledge points

$$ 12.3 \div 0.4 = \frac{12.3}{0.4} $$

Analyze the first option

Using the Equivalent Expressions knowledge point

$$ \frac{12.3 \times 10}{0.4 \times 10} = \frac{123}{4} = 123 \div 4 $$

Analyze the second option

Using the Decimal Division knowledge point

$$ 1.23 \div 0.4 = \frac{1.23}{0.4} eq \frac{12.3}{0.4} $$

Analyze the third option

Using the Equivalent Expressions knowledge point

$$ \frac{12.3 \times 100}{0.4 \times 100} = \frac{1230}{40} = 1,230 \div 40 $$

Analyze the fourth option

Using the Decimal Division knowledge point

$$ 123 \div 0.04 = \frac{123}{0.04} = \frac{12.3 \times 10}{0.4 \times 0.1} eq \frac{12.3}{0.4} $$

Answer:

• (A) \(123 \div 4\) (Correct answer)
• (B) \(1.23 \div 0.4\)
• (C) \(1,230 \div 40\) (Correct answer)
• (D) \(123 \div 0.04\)