Which of the following expressions is equivalent to 0.12 ×0.7 ? Choose 1 answer: (A) 12 ×7÷10 (B) 12 ×7÷100 (c) 12 ×7÷1,000 (D) 12 ×7÷10,000

Question

Which of the following expressions is equivalent to  0.12 ×0.7 ? Choose 1 answer: (A)  12 ×7÷10 (B)  12 ×7÷100 (c)  12 ×7÷1,000 (D)  12 ×7÷10,000

Bytelearn · Accepted Answer

Convert to Fractions: First, let's express 0.12 and 0.7 as fractions to make it easier to see which expression is equivalent. 0.12 can be written as 12/100 because there are two decimal places, moving the decimal two places to the right turns 0.12 into 12. 0.7 can be written as 7/10 because there is one decimal place, moving the decimal one place to the right turns 0.7 into 7. Now, we multiply these two fractions: (12/100) × (7/10).Multiply Fractions: Next, we multiply the numerators together and the denominators together: (12 × 7) / (100 × 10). This simplifies to 84 / 1000.Compare Answer Choices: Now, we look at the answer choices to see which one matches our expression 84 / 1000. (A) 12 × 7 ÷ 10 = 84 ÷ 10 = 8.4, which is not equivalent to 0.12 × 0.7. (B) 12 × 7 ÷ 100 = 84 ÷ 100 = 0.84, which is not equivalent to 0.12 × 0.7. (C) 12 × 7 ÷ 1,000 = 84 ÷ 1,000 = 0.084, which is not equivalent to 0.12 × 0.7. (D) 12 × 7 ÷ 10,000 = 84 ÷ 10,000 = 0.0084, which is not equivalent to 0.12 × 0.7.Simplify Further: We can see that none of the answer choices exactly match our simplified expression 84 / 1000. However, we can simplify our expression further by dividing both the numerator and the denominator by 10 to see if it matches any of the answer choices: 84 / 1000 = (84 ÷ 10) / (1000 ÷ 10) = 8.4 / 100.Compare with Answer Choices: Now, we compare this new expression 8.4 / 100 with the answer choices: (A) 12 × 7 ÷ 10 = 84 ÷ 10 = 8.4, which is not equivalent to 8.4 / 100. (B) 12 × 7 ÷ 100 = 84 ÷ 100 = 0.84, which is not equivalent to 8.4 / 100. (C) 12 × 7 ÷ 1,000 = 84 ÷ 1,000 = 0.084, which is not equivalent to 8.4 / 100. (D) 12 × 7 ÷ 10,000 = 84 ÷ 10,000 = 0.0084, which is not equivalent to 8.4 / 100.Identify Correct Answer: Upon reviewing the steps, it appears there has been a mistake. The correct simplification of 84 / 1000 does not require dividing by 10 again. The correct equivalent expression for 0.12 × 0.7 is indeed 84 / 1000, which matches the expression in option (C) 12 × 7 ÷ 1,000. Therefore, the correct answer is (C) 12 × 7 ÷ 1,000.

Which of the following expressions is equivalent to $\newline$ $0.12 \times 0.7$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $12 \times 7 \div 10$ $\newline$ (B) $12 \times 7 \div 100$ $\newline$ (C) $12 \times 7 \div 1,000$ $\newline$ (D) $12 \times 7 \div 10,000$

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