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$As a fraction in simplest terms, what would you multiply the first number by to get the second? First number: 42 Second number: 67 42*◻=67$

As a fraction in simplest terms, what would you multiply the first number by to get the second? $\newline$ First number: $42$ Second number: $67$ $\newline$ $42 \cdot \square=67$

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Convert between exponential and logarithmic form: rational bases

Full solution

Q. As a fraction in simplest terms, what would you multiply the first number by to get the second?

\newline

First number:

42

Second number:

67

\newline

42 \cdot \square=67

Set up equation: Set up the equation to find the fraction. $\newline$ To find the fraction that you would multiply by the first number $42$ to get the second number $67$ , you can set up the equation as follows: $\newline$ $42 \times (\text{fraction}) = 67$ $\newline$ Let's denote the fraction as $\frac{x}{y}$ , where $x$ and $y$ are integers and the fraction is in simplest terms. $\newline$ So, the equation becomes: $\newline$ $42 \times \left(\frac{x}{y}\right) = 67$
Solve for fraction: Solve for the fraction $x/y$ . To solve for $x/y$ , we need to isolate the fraction on one side of the equation. We can do this by dividing both sides of the equation by $42$ : $(42 \cdot (x/y)) / 42 = 67 / 42$ Simplifying the left side, we get: $x/y = 67 / 42$
Simplify fraction: Simplify the fraction $\frac{67}{42}$ . To simplify the fraction, we need to find the greatest common divisor (GCD) of $67$ and $42$ and divide both the numerator and the denominator by the GCD. However, since $67$ is a prime number and $42$ is not a multiple of $67$ , the GCD of $67$ and $42$ is $1$ . Therefore, the fraction $\frac{67}{42}$ is already in its simplest terms.

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