How do you find the product of 710×58107​×85​?

To find the product of the fractions \(\frac{7}{10} \times \frac{58}{107} \times \frac{8}{5}\), follow these steps:

1. **Multiply the numerators (the top numbers) together:**
   \[
   7 \times 58 \times 8
   \]

2. **Multiply the denominators (the bottom numbers) together:**
   \[
   10 \times 107 \times 5
   \]

### Step-by-Step Calculation:

#### Numerator:
\[
7 \times 58 \times 8
\]

First, calculate \(7 \times 58\):
\[
7 \times 58 = 406
\]

Next, multiply the result by 8:
\[
406 \times 8 = 3248
\]

#### Denominator:
\[
10 \times 107 \times 5
\]

First, calculate \(10 \times 107\):
\[
10 \times 107 = 1070
\]

Next, multiply the result by 5:
\[
1070 \times 5 = 5350
\]

### Form the Fraction:
\[
\frac{3248}{5350}
\]

### Simplify the Fraction:
To simplify \(\frac{3248}{5350}\), find the greatest common divisor (GCD) of 3248 and 5350.

Using the Euclidean algorithm, the GCD of 3248 and 5350 is 2.

Divide both the numerator and the denominator by their GCD:
\[
\frac{3248 \div 2}{5350 \div 2} = \frac{1624}{2675}
\]

Therefore, the product of \(\frac{7}{10} \times \frac{58}{107} \times \frac{8}{5}\) is:
\[
\frac{1624}{2675}
\]

Would you like more details or have any questions?

Here are 8 related questions for further practice:

1. What is \(\frac{3}{7} \times \frac{14}{9} \times \frac{5}{6}\)?
2. How do you multiply \(\frac{11}{15} \times \frac{5}{8} \times \frac{9}{10}\)?
3. What is the product of \(\frac{2}{9} \times \frac{27}{14} \times \frac{8}{11}\)?
4. How do you simplify \(\frac{6}{13} \times \frac{4}{7} \times \frac{7}{10}\)?
5. What is the result of \(\frac{5}{8} \times \frac{16}{3} \times \frac{2}{11}\)?
6. How do you multiply \(\frac{9}{11} \times \frac{7}{5} \times \frac{4}{9}\)?
7. What is \(\frac{12}{15} \times \frac{5}{14} \times \frac{2}{9}\)?
8. How do you find the product of \(\frac{10}{21} \times \frac{7}{4} \times \frac{3}{5}\)?

**Tip:** When multiplying multiple fractions, consider simplifying any common factors across numerators and denominators before performing the multiplication. This will make the arithmetic simpler and reduce the chance of errors.

Learn how to calculate the product of fractions 7/10 × 58/107 × 8/5 step-by-step. This problem involves multiplying fractions and simplifying the result. Suitable for students in Grades 6-8.

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