Full solution

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

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First number:

57 \quad

Second number:

78

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57 \cdot \square=78

Find Fraction for $57$ : First, we need to find the fraction that, when multiplied by $57$ , gives us $78$ . To do this, we set up the equation $57 \times x = 78$ , where $x$ is the fraction we are looking for.
Solve for x: Next, we solve for $x$ by dividing both sides of the equation by $57$ . This gives us $x = \frac{78}{57}$ .
Calculate x Value: Now we perform the division to find the value of x. Calculating $78$ divided by $57$ gives us $x = 1.36842105263$ .
Express $x$ as Fraction: However, we need to express $x$ as a fraction in simplest terms. To do this, we can write both numbers as fractions with a common denominator and then simplify. The fraction $\frac{78}{57}$ can be simplified by finding the greatest common divisor (GCD) of $78$ and $57$ and dividing both the numerator and the denominator by this number.
Simplify Fraction: The GCD of $78$ and $57$ is $3$ . We divide both the numerator and the denominator by $3$ to simplify the fraction. So, $\frac{78}{57}$ simplifies to $\left(\frac{78}{3}\right) / \left(\frac{57}{3}\right)$ .
Simplify Fraction: The GCD of $78$ and $57$ is $3$ . We divide both the numerator and the denominator by $3$ to simplify the fraction. So, $\frac{78}{57}$ simplifies to $\left(\frac{78}{3}\right) / \left(\frac{57}{3}\right)$ .Performing the division, we get $\left(\frac{78}{3}\right) / \left(\frac{57}{3}\right) = \frac{26}{19}$ . This is the fraction in simplest terms that we were looking for.