21. Higher Orcler Thinking Explain why multiplying $$ 37.4 imes 0.1 $$ gives a product that is less than 37.4 .

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21. Higher Orcler Thinking Explain why multiplying $$ 37.4 	imes 0.1 $$ gives a product that is less than 37.4 .

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Multiplying $$ 37.4 	imes 0.1 $$ 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, $$ 37.4 	imes 0.1 = 3.74 $$.
   - 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 $$ 37.4 	imes 0.1 = 3.74 $$ 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.
Multiplying 37.4 by 0.1 gives a smaller product because 0.1 is less than 1, so it reduces the original number.

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

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