Questions: Determine whether the statement makes sense or does not make sense, and explain your reasoning. I can solve x/9=4/6 by using the cross-products principle or by multiplying both sides by 18, the least common denominator. Choose the correct answer below. A. The statement does not make sense. Multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation. However, the value of the missing quantity in a proportion cannot be found by using the cross-products principle if only three of the numbers are known. B. The statement makes sense. If three of the numbers in a proportion are known, the value of the missing quantity can be found by using the cross-products principle. Alternatively, multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation. C. The statement does not make sense. If three of the numbers in a proportion are known, the value of the missing quantity can be found by using the cross-products principle. However, the terms on both sides of the equation would need to be multiplied by 6 * 4=24, and not 18, to eliminate the fractions in the equation. D. The statement makes sense. If two of the numbers in a proportion are known, the value of the missing quantities can be found by using the cross-products principle. Alternatively, multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation.

Determine whether the statement makes sense or does not make sense, and explain your reasoning. I can solve x/9=4/6 by using the cross-products principle or by multiplying both sides by 18, the least common denominator. Choose the correct answer below. A. The statement does not make sense. Multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation. However, the value of the missing quantity in a proportion cannot be found by using the cross-products principle if only three of the numbers are known. B. The statement makes sense. If three of the numbers in a proportion are known, the value of the missing quantity can be found by using the cross-products principle. Alternatively, multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation. C. The statement does not make sense. If three of the numbers in a proportion are known, the value of the missing quantity can be found by using the cross-products principle. However, the terms on both sides of the equation would need to be multiplied by 6 * 4=24, and not 18, to eliminate the fractions in the equation. D. The statement makes sense. If two of the numbers in a proportion are known, the value of the missing quantities can be found by using the cross-products principle. Alternatively, multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation.
Transcript text: Determine whether the statement makes sense or does not make sense, and explain your reasoning. I can solve $\frac{x}{9}=\frac{4}{6}$ by using the cross-products principle or by multiplying both sides by 18 , the least common denominator. Choose the correct answer below. A. The statement does not make sense. Multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation. However, the value of the missing quantity in a proportion cannot be found by using the cross-products principle if only three of the numbers are known. B. The statement makes sense. If three of the numbers in a proportion are known, the value of the missing quantity can be found by using the cross-products principle. Alternatively, multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation. C. The statement does not make sense. If three of the numbers in a proportion are known, the value of the missing quantity can be found by using the cross-products principle. However, the terms on both sides of the equation would need to be multiplied by $6 \cdot 4=24$, and not 18 , to eliminate the fractions in the equation. D. The statement makes sense. If two of the numbers in a proportion are known, the value of the missing quantities can be found by using the cross-products principle. Alternatively, multiplying the terms on both sides of the equation by the least common denominator will eliminate the fractions in the equation.
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Solution

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Solution Steps

Solution Approach

The statement makes sense because both methods described are valid for solving the given proportion. The cross-products principle can be used to find the missing value when three numbers in a proportion are known. Additionally, multiplying both sides by the least common denominator (18 in this case) will eliminate the fractions, allowing for a straightforward solution.

Step 1: Set Up the Equation

We start with the equation given in the problem: \[ \frac{x}{9} = \frac{4}{6} \] This can be simplified to: \[ \frac{x}{9} = \frac{2}{3} \]

Step 2: Solve for \( x \)

To eliminate the fraction, we can multiply both sides of the equation by 9: \[ x = 9 \cdot \frac{2}{3} \] Calculating the right side gives: \[ x = 6 \]

Final Answer

Thus, the solution to the equation is \[ \boxed{x = 6} \]

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