Question
Fill in the blank to make equivalent rational expressions. \( \frac{7}{3 y}=\frac{\square}{18 y^{7}} \)
Ask by Guerrero Nichols. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The missing numerator is \( 42y^{6} \).
Solution
We need to determine the numerator in the expression
7/(3y) = (□)/(18y⁷).
To do this, we'll set up an equation and solve for the unknown numerator, which we'll call N.
Step 1: Write the equation:
7/(3y) = N/(18y⁷)
Step 2: Cross-multiply:
7 × (18y⁷) = N × (3y)
126y⁷ = 3yN
Step 3: Solve for N by dividing both sides by 3y:
N = (126y⁷)/(3y) = 42y⁶
Thus, the missing numerator is 42y⁶.
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Simplify this solution The Deep Dive
To find the missing value, we can cross-multiply. We set up the equation as follows: \( 7 \cdot 18 y^{7} = 3 y \cdot \square \) This simplifies to: \( 126 y^{7} = 3 y \cdot \square \) To isolate \(\square\), divide both sides by \(3y\): \(\square = \frac{126 y^{7}}{3y}\) When you simplify \(\frac{126}{3}\), you get \(42\). Therefore, the missing value is: \(42y^{6}\) So the complete expression is: \( \frac{7}{3 y}=\frac{42y^{6}}{18 y^{7}} \).
