Question
8. Between which two whole numbers will the product be found? \[ 3 \times 3 \frac{1}{7}= \]
Ask by Bates Mcguire. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product is between 9 and 10.
Solution
To find between which two whole numbers the product of \( 3 \times 3 \frac{1}{7} \) lies, let's perform the calculation step by step.
1. **Convert the Mixed Number to an Improper Fraction:**
\( 3 \frac{1}{7} = \frac{3 \times 7 + 1}{7} = \frac{21 + 1}{7} = \frac{22}{7} \)
2. **Multiply by 3:**
\( 3 \times \frac{22}{7} = \frac{66}{7} \)
3. **Convert the Improper Fraction to a Mixed Number:**
\( \frac{66}{7} = 9 \frac{3}{7} \)
4. **Determine the Whole Numbers Between Which the Product Lies:**
\( 9 \frac{3}{7} \) is greater than 9 but less than 10.
**Answer:**
The product is between 9 and 10.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the product of \(3 \times 3 \frac{1}{7}\), first convert the mixed number into an improper fraction. That would give you \(3 \frac{1}{7} = \frac{22}{7}\). Now, multiplying \(3\) by \(\frac{22}{7}\) gives you \(\frac{66}{7}\). To find whole numbers, divide \(66\) by \(7\), which is approximately \(9.42857\). Thus, the product will lie between \(9\) and \(10\). To check your understanding, consider estimating the multiplication. Since \(3\) is close to \(3.14\) (which is \(\pi\)), you could think about multiples of \(3\). For instance, around \(3 \times 3\) is \(9\), while \(3 \times 4\) inches toward \(12\). So, tweaking to decimals can clarify the range: \(9 < 9.42857 < 10\).
