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$As a fraction in simplest terms, what would you multiply the first number by to get the second? First number: 27 Second number: 15 27*◻=15$

As a fraction in simplest terms, what would you multiply the first number by to get the second? $\newline$ First number: $27$ Second number: $15$ $\newline$ $27 \cdot \square=15$

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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:

27

Second number:

15

\newline

27 \cdot \square=15

Identify Operation: Identify the operation needed to find the fraction. $\newline$ To find the fraction that you would multiply by $27$ to get $15$ , you need to divide $15$ by $27$ . $\newline$ Calculation: $15 \div 27$
Calculate Division: Simplify the fraction. $\newline$ Divide both the numerator $15$ and the denominator $27$ by their greatest common divisor (GCD). The GCD of $15$ and $27$ is $3$ . $\newline$ Calculation: $(15 \div 3) / (27 \div 3) = 5 / 9$
Simplify Fraction: Check the result. $\newline$ Multiplying the simplified fraction by the first number should give the second number. $\newline$ Calculation: $27 \times \left(\frac{5}{9}\right) = \left(\frac{27}{9}\right) \times 5 = 3 \times 5 = 15$

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