Question

Select Proportional or Not Proportional to correctly classify each pair of ratios.

Proportional Not Proportional
78 and 4248

Answer 1

To determine if the ratios 78 and 4248 are proportional, we can check if they can be expressed as a fraction that simplifies to the same value.

To do this, we'll first create a fraction from the two numbers:

\[
\frac{78}{4248}
\]

Next, we can simplify this fraction. Both 78 and 4248 can be divided by their greatest common divisor (GCD).

Finding the GCD of 78 and 4248:

1. The prime factorization of 78 is \(2 \times 3 \times 13\).
2. The prime factorization of 4248 can be determined:

4248 ÷ 2 = 2124
2124 ÷ 2 = 1062
1062 ÷ 2 = 531
531 ÷ 3 = 177
177 ÷ 3 = 59 (since 59 is prime)

So, the prime factorization of 4248 is \(2^3 \times 3^2 \times 59\).

Now, we can find the GCD:

- The GCD of 78 and 4248 is \(2^1 \times 3^1 = 6\).

Now we divide both 78 and 4248 by their GCD:

\[
\frac{78 ÷ 6}{4248 ÷ 6} = \frac{13}{708}
\]

Since \(13\) and \(708\) do not share any common factors other than \(1\), we cannot simplify further. Therefore, the ratio \( \frac{78}{4248} \) does not equal a simple ratio that would imply proportionality.

### Conclusion:
The pairs \( 78 \) and \( 4248 \) are classified as **Not Proportional**.