Select all ratios equivalent to 12:6.
Understand the Problem
The question is asking to identify which of the given ratios are equivalent to the ratio 12:6. This involves determining the ratios that simplify or reduce to the same value as 12:6.
Answer
The equivalent ratios to $12:6$ are $18:9$ and $10:5$.
Answer for screen readers
The equivalent ratios to ( 12:6 ) are ( 18:9 ) and ( 10:5 ).
Steps to Solve
- Simplify the original ratio
Start with the ratio ( 12:6 ).
To simplify, divide both the numerator and denominator by their greatest common divisor (GCD), which is 6:
$$ \frac{12 \div 6}{6 \div 6} = \frac{2}{1} $$
So, the simplified form of ( 12:6 ) is ( 2:1 ).
- Simplify the other ratios
Now, simplify each of the given ratios to see if they also reduce to ( 2:1 ).
-
For ( 18:9 ):
Divide both by 9:
$$ \frac{18 \div 9}{9 \div 9} = \frac{2}{1} $$
-
For ( 27:54 ):
Divide both by 27:
$$ \frac{27 \div 27}{54 \div 27} = \frac{1}{2} $$
This does not match.
-
For ( 70:48 ):
The GCD is 2, so divide by 2:
$$ \frac{70 \div 2}{48 \div 2} = \frac{35}{24} $$
This does not match.
-
For ( 10:5 ):
Divide both by 5:
$$ \frac{10 \div 5}{5 \div 5} = \frac{2}{1} $$
- Collect the equivalent ratios
After simplifying, the ratios equivalent to ( 12:6 ) are ( 18:9 ) and ( 10:5 ).
The equivalent ratios to ( 12:6 ) are ( 18:9 ) and ( 10:5 ).
More Information
Understanding ratios and how to simplify them is important in various fields, including cooking, budgeting, and scale modeling. Ratios represent the relationship between two quantities and can help in comparing them.
Tips
- Forgetting to simplify both parts of the ratio.
- Misidentifying the GCD, leading to wrong simplifications.
- Not converting ratios to the same or simplest form for comparison.
AI-generated content may contain errors. Please verify critical information
