\begin{tabular}{c|} Find the product. \ Simplify the response. \ $$ \frac{10}{15} imes \frac{4}{7}= $$\end{tabular}

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\begin{tabular}{c|} Find the product. \ Simplify the response. \ $$ \frac{10}{15} 	imes \frac{4}{7}= $$\end{tabular}

UpStudy AI · Accepted Answer

To find and simplify the product of the two fractions $$ \frac{10}{15} $$ and $$ \frac{4}{7} $$, follow these steps:

1. **Multiply the Numerators and Denominators:**
   
   $$
   \frac{10}{15} \times \frac{4}{7} = \frac{10 \times 4}{15 \times 7} = \frac{40}{105}
   $$

2. **Simplify the Fraction:**
   
   To simplify $$ \frac{40}{105} $$, find the greatest common divisor (GCD) of 40 and 105.

- **Factors of 40:** 1, 2, 4, 5, 8, 10, 20, 40
   - **Factors of 105:** 1, 3, 5, 7, 15, 21, 35, 105
   - **Common Factors:** 1, 5

The GCD of 40 and 105 is **5**.

3. **Divide Both Numerator and Denominator by the GCD:**
   
   $$
   \frac{40 \div 5}{105 \div 5} = \frac{8}{21}
   $$

So, the simplified product is:

$$
\frac{10}{15} \times \frac{4}{7} = \frac{8}{21}
$$
The product simplifies to $$ \frac{8}{21} $$.

Find the product.

Simplify the response.

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