31. Communicate and Justify Which is greater, $$ \frac{4}{7} imes \frac{1}{4} $$ or $$ \frac{4}{7} imes \frac{1}{6} $$ ? Explain,

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31. Communicate and Justify Which is greater, $$ \frac{4}{7} 	imes \frac{1}{4} $$ or $$ \frac{4}{7} 	imes \frac{1}{6} $$ ? Explain,

UpStudy AI · Accepted Answer

To determine which expression is greater between $$ \frac{4}{7} \times \frac{1}{4} $$ and $$ \frac{4}{7} \times \frac{1}{6} $$, let's evaluate each step by step.

1. **Calculate Each Expression:**

- **First Expression:** 
     $$
     \frac{4}{7} \times \frac{1}{4} = \frac{4 \times 1}{7 \times 4} = \frac{4}{28} = \frac{1}{7}
     $$
     
   - **Second Expression:** 
     $$
     \frac{4}{7} \times \frac{1}{6} = \frac{4 \times 1}{7 \times 6} = \frac{4}{42} = \frac{2}{21}
     $$

2. **Compare the Results:**
   
   - $$ \frac{1}{7} $$ versus $$ \frac{2}{21} $$

To compare these fractions easily, let's express them with a common denominator:

- $$ \frac{1}{7} = \frac{3}{21} $$
   - $$ \frac{2}{21} $$ remains the same.

Now, it’s clear that:
   $$
   \frac{3}{21} > \frac{2}{21}
   $$
   
3. **Conclusion:**

Since $$ \frac{1}{7} $$ (which is equivalent to $$ \frac{3}{21} $$) is greater than $$ \frac{2}{21} $$, the first expression $$ \frac{4}{7} \times \frac{1}{4} $$ is **greater** than $$ \frac{4}{7} \times \frac{1}{6} $$.

**Final Answer:**

$$ \frac{4}{7} \times \frac{1}{4} $$ is greater than $$ \frac{4}{7} \times \frac{1}{6} $$ because $$ \frac{1}{4} $$ is larger than $$ \frac{1}{6} $$, and multiplying both by $$ \frac{4}{7} $$ preserves the inequality.
$$ \frac{4}{7} \times \frac{1}{4} $$ is greater than $$ \frac{4}{7} \times \frac{1}{6} $$ because $$ \frac{1}{4} $$ is larger than $$ \frac{1}{6} $$.

Communicate and Justify Which is
greater, or ? Explain,

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