Question
Use cross multiplication to decide whether the following proportion is true or false. \( \frac{4}{15}=\frac{8}{75} \) Is the proportion true or false? true false
Ask by Kirk Summers. in the United Arab Emirates
Mar 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The proportion is false.
Solution
1. Write the proportion:
\[
\frac{4}{15}=\frac{8}{75}
\]
2. Cross multiply:
\[
4 \times 75 \quad \text{and} \quad 15 \times 8
\]
3. Calculate the products:
\[
4 \times 75 = 300 \quad \text{and} \quad 15 \times 8 = 120
\]
4. Compare the products:
\[
300 \neq 120
\]
Since the cross products are not equal, the proportion is false.
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Simplify this solution Beyond the Answer
Let’s cross-multiply: \(4 \times 75\) gives us \(300\). Now, \(15 \times 8\) gives us \(120\). Since \(300\) is not equal to \(120\), this proportion is false! Proportions can seem tricky, but remember—if the cross products don’t match, it’s a no-go! In real-life applications, proportions are super handy! For example, if you’re cooking and you need to double a recipe, checking the proportions of ingredients ensures that you maintain the same taste and texture. So, whether you're in the kitchen or solving math problems, knowing how to verify proportions will come in handy!
