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21. Higher Orcler Thinking Explain why multiplying \( 37.4 \times 0.1 \) gives a product that is less than 37.4 .

Ask by Bartlett Lambert. in the United States
Jan 23,2025

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Multiplying 37.4 by 0.1 gives a smaller product because 0.1 is less than 1, so it reduces the original number.

Solution

Multiplying \( 37.4 \times 0.1 \) results in a product that is less than 37.4 because of the fundamental properties of multiplication involving fractions less than one. Here's a detailed explanation: 1. **Understanding the Multiplier (0.1):** - The number 0.1 is equivalent to the fraction \( \frac{1}{10} \) or 10%. - When you multiply a number by a fraction less than 1, you are effectively taking a part of that number. 2. **Scaling Down the Original Number:** - Multiplying by 0.1 scales the original number down to 10% of its value. - Mathematically, \( 37.4 \times 0.1 = 3.74 \). - Here, 3.74 is clearly less than 37.4 because you are taking only one-tenth of the original amount. 3. **Conceptual Perspective:** - Think of \( 37.4 \) as a whole. Multiplying by 0.1 means you are finding a portion of that whole. - Just as taking 10% of a pie gives you a smaller slice compared to the entire pie, multiplying by 0.1 gives you a smaller value compared to the original number. 4. **Visual Representation:** - Imagine you have 37.4 units of something (like dollars). - If you take 10% of it, you are left with \( 37.4 \times 0.1 = 3.74 \) units. - This operation reduces the amount because you're only considering a fraction of the whole. 5. **General Principle:** - In multiplication, any number multiplied by a factor between 0 and 1 decreases in value. - Conversely, multiplying by a factor greater than 1 increases the original number. **Conclusion:** Multiplying 37.4 by 0.1 gives a smaller product because 0.1 represents a fraction (10%) of the original number. This operation scales the original value down, resulting in a product that is one-tenth of 37.4.

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When you multiply any positive number by a fraction (like \(0.1\), which is equivalent to \( \frac{1}{10} \)), the result will always be less than the original number. This is because you are essentially dividing the original number into smaller parts. In this case, \(37.4\) divided by \(10\) results in \(3.74\), which is certainly less than \(37.4\). Additionally, it's important to grasp that multiplying by a decimal shrinks the value; think of it as taking a fraction of something, which naturally results in a smaller quantity. Just like sharing your pizza with more friends means you'll each get a smaller slice! So, \(37.4 \times 0.1\) equals \(3.74\), showing that fractional multiplication leads to a smaller outcome.

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