To find which ratio is equivalent to \( \frac{9}{78} \), we can simplify \( \frac{9}{78} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 9 and 78 is 9. So, we divide both by 9:
\[ \frac{9 \div 9}{78 \div 9} = \frac{1}{8.67} \]
However, none of the provided answers are \( \frac{1}{8.67} \). Instead, let's simplify it correctly step by step and see what we get next.
First, let's check the simplified form if any of the provided options are equivalent:
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Check \( \frac{3}{26} \):
- Cross-multiplying: \[ 3 \times 78 = 234 \quad \text{and} \quad 26 \times 9 = 234. \] This means \( \frac{3}{26} \) is indeed equivalent to \( \frac{9}{78} \).
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The other options:
- \( \frac{1}{8} \): Cross-multiply \( 1 \times 78 \) and \( 8 \times 9 \):
- \( 78 \neq 72 \) (not equivalent).
- \( \frac{3}{18} \): Cross-multiply \( 3 \times 78 \) and \( 18 \times 9 \):
- \( 234 \neq 162 \) (not equivalent).
- \( \frac{1}{3} \): Cross-multiply \( 1 \times 78 \) and \( 3 \times 9 \):
- \( 78 \neq 27 \) (not equivalent).
- \( \frac{1}{8} \): Cross-multiply \( 1 \times 78 \) and \( 8 \times 9 \):
Thus, the equivalent ratio to \( \frac{9}{78} \) is:
\[ \frac{3}{26} \]
So the answer is \( \frac{3}{26} \).
1 answer