Select all ratios equivalent to 8:7.
Understand the Problem
The question asks us to identify which provided ratios are equivalent to the ratio 8:7. We can do this by simplifying each ratio and comparing them to 8:7.
Answer
The only ratio equivalent to \( 8:7 \) is \( 24:21 \).
Answer for screen readers
The ratios equivalent to ( 8:7 ) are ( 24:21 ).
Steps to Solve
- Convert the given ratios to their simplest form
We need to compare each ratio to the ratio ( 8:7 ). Let's simplify each ratio:
- For ( 7:6 ), it is already in simplest form.
- For ( 24:21 ), we can simplify it:
$$ \text{GCD of } 24 \text{ and } 21 = 3 $$
Thus,
$$ \frac{24 \div 3}{21 \div 3} = \frac{8}{7} $$
- For ( 6:5 ), it is also in simplest form.
- Compare with the ratio ( 8:7 )
Now we compare each simplified ratio to ( 8:7 ):
- The simplified form of ( 7:6 ) is ( 7:6 ) (not equivalent to ( 8:7 )).
- The simplified form of ( 24:21 ) is ( 8:7 ) (equivalent).
- The simplified form of ( 6:5 ) is ( 6:5 ) (not equivalent).
- Identify equivalent ratios
Based on the comparisons, the only ratio that is equivalent to ( 8:7 ) is ( 24:21 ).
The ratios equivalent to ( 8:7 ) are ( 24:21 ).
More Information
The ratio ( 8:7 ) represents a proportional relationship between two quantities. In this instance, ( 24:21 ) simplifies to ( 8:7 ), showing that they are equivalent fractions.
Tips
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