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Answer :
- Check each proportion by cross-multiplying.
- For $\frac{18}{48}=\frac{20}{50}$, $18 \times 50 = 900$ and $48 \times 20 = 960$, which are not equal.
- For $\frac{10}{25}=\frac{40}{100}$, $10 \times 100 = 1000$ and $25 \times 40 = 1000$, which are equal.
- For $\frac{25}{45}=\frac{75}{135}$, $25 \times 135 = 3375$ and $45 \times 75 = 3375$, which are equal.
- For $\frac{24}{30}=\frac{20}{25}$, $24 \times 25 = 600$ and $30 \times 20 = 600$, which are equal.
- The false proportion is $\boxed{\frac{18}{48}=\frac{20}{50}}$.
### Explanation
1. Understanding Proportions
We are given four proportions and need to determine which one is false. A proportion is an equation stating that two ratios are equal. To check if a proportion is true, we can cross-multiply and see if the products are equal.
2. Checking Proportion 1
Let's check the first proportion: $\frac{18}{48}=\frac{20}{50}$. Cross-multiplying, we get $18 \times 50 = 900$ and $48 \times 20 = 960$. Since $900 \neq 960$, this proportion is false.
3. Checking Proportion 2
Let's check the second proportion: $\frac{10}{25}=\frac{40}{100}$. Cross-multiplying, we get $10 \times 100 = 1000$ and $25 \times 40 = 1000$. Since $1000 = 1000$, this proportion is true.
4. Checking Proportion 3
Let's check the third proportion: $\frac{25}{45}=\frac{75}{135}$. Cross-multiplying, we get $25 \times 135 = 3375$ and $45 \times 75 = 3375$. Since $3375 = 3375$, this proportion is true.
5. Checking Proportion 4
Let's check the fourth proportion: $\frac{24}{30}=\frac{20}{25}$. Cross-multiplying, we get $24 \times 25 = 600$ and $30 \times 20 = 600$. Since $600 = 600$, this proportion is true.
6. Conclusion
Therefore, the false proportion is $\frac{18}{48}=\frac{20}{50}$.
### Examples
Proportions are used in everyday life to scale recipes, convert currencies, and understand maps. For example, if a recipe calls for 2 cups of flour for 4 servings, you can use a proportion to determine how much flour you need for 10 servings. Understanding proportions helps in making accurate adjustments and decisions in various practical situations.
- For $\frac{18}{48}=\frac{20}{50}$, $18 \times 50 = 900$ and $48 \times 20 = 960$, which are not equal.
- For $\frac{10}{25}=\frac{40}{100}$, $10 \times 100 = 1000$ and $25 \times 40 = 1000$, which are equal.
- For $\frac{25}{45}=\frac{75}{135}$, $25 \times 135 = 3375$ and $45 \times 75 = 3375$, which are equal.
- For $\frac{24}{30}=\frac{20}{25}$, $24 \times 25 = 600$ and $30 \times 20 = 600$, which are equal.
- The false proportion is $\boxed{\frac{18}{48}=\frac{20}{50}}$.
### Explanation
1. Understanding Proportions
We are given four proportions and need to determine which one is false. A proportion is an equation stating that two ratios are equal. To check if a proportion is true, we can cross-multiply and see if the products are equal.
2. Checking Proportion 1
Let's check the first proportion: $\frac{18}{48}=\frac{20}{50}$. Cross-multiplying, we get $18 \times 50 = 900$ and $48 \times 20 = 960$. Since $900 \neq 960$, this proportion is false.
3. Checking Proportion 2
Let's check the second proportion: $\frac{10}{25}=\frac{40}{100}$. Cross-multiplying, we get $10 \times 100 = 1000$ and $25 \times 40 = 1000$. Since $1000 = 1000$, this proportion is true.
4. Checking Proportion 3
Let's check the third proportion: $\frac{25}{45}=\frac{75}{135}$. Cross-multiplying, we get $25 \times 135 = 3375$ and $45 \times 75 = 3375$. Since $3375 = 3375$, this proportion is true.
5. Checking Proportion 4
Let's check the fourth proportion: $\frac{24}{30}=\frac{20}{25}$. Cross-multiplying, we get $24 \times 25 = 600$ and $30 \times 20 = 600$. Since $600 = 600$, this proportion is true.
6. Conclusion
Therefore, the false proportion is $\frac{18}{48}=\frac{20}{50}$.
### Examples
Proportions are used in everyday life to scale recipes, convert currencies, and understand maps. For example, if a recipe calls for 2 cups of flour for 4 servings, you can use a proportion to determine how much flour you need for 10 servings. Understanding proportions helps in making accurate adjustments and decisions in various practical situations.
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