Select all ratios equivalent to 4:5.
Understand the Problem
The question is asking to identify which of the given ratios (5:4, 11:1, and 20:25) are equivalent to the ratio of 4:5. To solve it, we will compare each provided ratio to 4:5 by cross-multiplying or simplifying the ratios.
Answer
The ratio equivalent to $4:5$ is $20:25$.
Answer for screen readers
The ratios equivalent to $4:5$ are: $20:25$.
Steps to Solve
- Set Up the Ratios for Comparison
We are given the ratio $4:5$. We need to compare this with the ratios $5:4$, $11:1$, and $20:25$.
- Convert Ratios to Fraction Form
Convert the given ratios to fractions:
- For $4:5$, it is $\frac{4}{5}$.
- For $5:4$, it is $\frac{5}{4}$.
- For $11:1$, it is $\frac{11}{1}$.
- For $20:25$, it simplifies as follows: $$ \frac{20}{25} = \frac{20 \div 5}{25 \div 5} = \frac{4}{5} $$
- Compare Each Ratio
Now we compare each ratio's fraction with $\frac{4}{5}$:
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Compare $\frac{5}{4}$ with $\frac{4}{5}$: $$ 5 \times 5 \quad \text{vs} \quad 4 \times 4 $$ This results in $25 \neq 16$, so $5:4$ is not equivalent.
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Compare $\frac{11}{1}$ with $\frac{4}{5}$: $$ 11 \times 5 \quad \text{vs} \quad 4 \times 1 $$ This results in $55 \neq 4$, so $11:1$ is not equivalent.
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Compare $\frac{4}{5}$ with itself: $$ 4 \times 25 \quad \text{vs} \quad 5 \times 20 $$ This gives $100 = 100$, confirming that $20:25$ is equivalent.
- Conclusion of Comparisons
Based on the comparisons, only the ratio $20:25$ is equivalent to $4:5$.
The ratios equivalent to $4:5$ are: $20:25$.
More Information
The ratio $20:25$ simplifies to $4:5$ because both numbers can be divided by 5. Recognizing equivalent ratios is important in various applications such as cooking, scaling recipes, and mathematics.
Tips
- Confusing the order of numbers when comparing ratios, leading to incorrect results. Always ensure to maintain the proper sequence when comparing ratios.
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