Question

11. \( \frac{5}{8} \cdot \frac{3}{5} \cdot \frac{4}{5} \)

Ask by Crawford Garrett. in the United States
Jan 23,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The final answer is \( \frac{3}{10} \).

Solution

To solve the multiplication of the fractions \( \frac{5}{8} \cdot \frac{3}{5} \cdot \frac{4}{5} \), follow these steps: 1. **Multiply the Numerators Together:** \[ 5 \times 3 \times 4 = 60 \] 2. **Multiply the Denominators Together:** \[ 8 \times 5 \times 5 = 200 \] 3. **Form the New Fraction:** \[ \frac{60}{200} \] 4. **Simplify the Fraction:** - Find the greatest common divisor (GCD) of 60 and 200, which is 20. - Divide both the numerator and the denominator by 20: \[ \frac{60 \div 20}{200 \div 20} = \frac{3}{10} \] **Final Answer:** \[ \frac{3}{10} \]

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Mind Expander

To tackle the multiplication of fractions like \( \frac{5}{8} \cdot \frac{3}{5} \cdot \frac{4}{5} \), just remember that you can multiply the numerators together and the denominators together. So, we have: Numerator: \( 5 \cdot 3 \cdot 4 = 60 \) Denominator: \( 8 \cdot 5 \cdot 5 = 200 \) Now, we combine these to get \( \frac{60}{200} \). Simplifying this fraction by dividing both the numerator and the denominator by 20 gives us \( \frac{3}{10} \). A quick tip: remember that when multiplying fractions, you can look for opportunities to simplify before multiplying. For instance, in this case, the \( 5 \) in the numerator of \( \frac{5}{8} \) and \( \frac{3}{5} \) cancels out, which helps to simplify the calculation, making it easier and faster! If you love to explore fractions further, there are plenty of fun worksheets and manipulatives that can help visualize how fractions work. Look for fraction circles or bars that allow you to see and compare different fractional parts in an engaging way — it's a great way to solidify your understanding while having some hands-on fun!

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