Select all ratios equivalent to 5:4.
Understand the Problem
The question is asking to identify which ratios among the given options are equivalent to the ratio of 5:4. This will involve comparing each ratio to see if they can be simplified or converted to 5:4.
Answer
The equivalent ratio to \( 5:4 \) is \( 60:48 \).
Answer for screen readers
The equivalent ratio to ( 5:4 ) is ( 60:48 ).
Steps to Solve
- Understanding the Target Ratio
The given target ratio is ( 5:4 ). This means that for every 5 parts of one quantity, there are 4 parts of another. We will compare each candidate ratio to see if they can be simplified to ( 5:4 ).
- Analyzing the First Ratio (60:48)
To determine if ( 60:48 ) is equivalent to ( 5:4 ), we can simplify it.
- First, find the greatest common divisor (GCD) of 60 and 48. The GCD is 12.
- Now divide both numbers by 12: $$ \frac{60 \div 12}{48 \div 12} = \frac{5}{4} $$ Thus, ( 60:48 ) simplifies to ( 5:4 ).
- Analyzing the Second Ratio (11:7)
Next, we check ( 11:7 ).
- Since 11 and 7 share no common factors other than 1, this ratio cannot be simplified to ( 5:4 ). Thus, ( 11:7 ) is not equivalent to ( 5:4 ).
- Analyzing the Third Ratio (9:1)
Finally, consider ( 9:1 ).
- Similar to ( 11:7 ), there are no common factors to simplify ( 9:1 ) to ( 5:4 ). Thus, ( 9:1 ) is also not equivalent to ( 5:4 ).
The equivalent ratio to ( 5:4 ) is ( 60:48 ).
More Information
The ratio of ( 5:4 ) represents a proportional relationship where the first quantity is slightly larger than the second. When comparing ratios, finding a common divisor helps determine equivalence.
Tips
- Failing to simplify ratios correctly by not finding the GCD.
- Assuming two ratios are equivalent without simplifying both to a common form.
