Select all statements that show correct reasoning for finding 15 divided 2/9 (multiple answers) A. Multiply 15 by 2, then divide by 9. B. Multiply 15 by 9, then divide by 2. C. Multiply 15 by , then multiply by 2. D. D. Multiply 15 by 9, then multiply by 1/2
The Correct Answer and Explanation is:
Correct Answers: B and D
Explanation
To find the solution for 15 divided by 2/9, it is essential to understand the principle of dividing by a fraction. Division by a fraction is equivalent to multiplication by that fraction’s reciprocal. The reciprocal of a fraction is found by inverting it, meaning the numerator and the denominator switch places.
First, identify the components of the problem: the dividend is 15, and the divisor is the fraction 2/9.
The initial step is to find the reciprocal of the divisor, 2/9. By inverting the fraction, the reciprocal is 9/2.
Next, the division operation (÷) is replaced with a multiplication operation (×), using the reciprocal. Therefore, the original expression 15 ÷ 2/9 is transformed into the equivalent expression 15 × 9/2.
Now, we can evaluate the new expression, 15 × 9/2. To multiply a whole number by a fraction, the whole number is multiplied by the numerator, and the result becomes the new numerator, while the denominator remains the same.
This gives us: (15 × 9) / 2.
This process directly corresponds to statement B: Multiply 15 by 9, then divide by 2. This is a correct method for solving the problem.
Furthermore, it is important to recognize that dividing by a number is the same as multiplying by its multiplicative inverse (or reciprocal). Dividing by 2 is mathematically identical to multiplying by 1/2. Applying this concept, the expression (15 × 9) / 2 can be rewritten as (15 × 9) × 1/2.
This interpretation matches statement D: Multiply 15 by 9, then multiply by 1/2. This also represents a correct sequence of operations.
Statement A is incorrect because it mistakenly multiplies by the numerator (2) and divides by the denominator (9), failing to use the reciprocal. Statement C is incomplete and does not represent a valid mathematical operation.thumb_upthumb_down
