What ratio is equivalent to 2/3?
Understand the Problem
The question is asking for a ratio that has the same value as 2/3. Ratios can be expressed in various equivalent forms, such as multiplying both the numerator and the denominator by the same number.
Answer
The equivalent ratio is $\frac{8}{12}$.
Answer for screen readers
One equivalent ratio for $\frac{2}{3}$ is $\frac{8}{12}$.
Steps to Solve
-
Identify the original ratio
The original ratio given is $\frac{2}{3}$. -
Choose a multiplier
Select a number to multiply both numerator and denominator. For example, let's use 4. -
Multiply numerator and denominator by the chosen number
Multiply both 2 and 3 by 4:
Numerator: $2 \times 4 = 8$
Denominator: $3 \times 4 = 12$ -
Write the new ratio
Combine the new numerator and denominator into a ratio:
The new ratio is $\frac{8}{12}$. -
Verify equivalence
Check if the original ratio $\frac{2}{3}$ is equivalent to the new ratio $\frac{8}{12}$ by simplifying.
Divide the numerator and denominator of $\frac{8}{12}$ by their GCD (which is 4):
$$ \frac{8 \div 4}{12 \div 4} = \frac{2}{3} $$
This confirms that $\frac{8}{12}$ is equivalent to $\frac{2}{3}$.
One equivalent ratio for $\frac{2}{3}$ is $\frac{8}{12}$.
More Information
Ratios are useful in various applications such as cooking, comparing quantities in geometry, and in finance to relate different values. The idea of equivalent ratios allows for flexibility in representation while maintaining the same relationship.
Tips
- Not simplifying the new ratio to check for equivalence. Always verify by reducing it back to see if it matches the original ratio.
