Question

Unit rates and proportions unit test
Which ratio is equivalent to 9/78?
A: 3/26
B: 3/18
C: 1/8
D: 1/3

Answer 1

To find an equivalent ratio to \( \frac{9}{78} \), we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of \( 9 \) and \( 78 \) is \( 9 \).

Now, divide both the numerator and denominator by \( 9 \):

\[
\frac{9 \div 9}{78 \div 9} = \frac{1}{8.6667}
\]

However, since we're looking for an option presented, let’s simplify \( \frac{9}{78} \) step by step:

- First, note that \( 78 = 9 \times 8.6667 \) could help deduce a ratio.
- Alternatively, we can reduce this by factoring another common divisor (in simpler terms):
\[
\text{From } \frac{9}{78}, divide both by 3,
\frac{9 \div 3}{78 \div 3} = \frac{3}{26}
\]

So, the equivalent ratio of \( \frac{9}{78} \) is \( \frac{3}{26} \).

The correct answer is:

A: \( \frac{3}{26} \)