Question
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Dividen of fraction \( \frac{8}{20} \div \frac{1}{8}= \) \( \frac{4}{5} \div \frac{1}{10}= \) \( \frac{14}{2} \div \frac{1}{4}= \) \( \frac{9}{10} \div \frac{1}{5}= \) \( \frac{1}{2} \div \frac{1}{4}= \)

Ask by Allan Zimmerman. in Samoa
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

1. \( \frac{16}{5} \) 2. 8 3. 28 4. \( \frac{9}{2} \) 5. 2

Solution

1. \( \frac{8}{20} \div \frac{1}{8} \) Rewrite as multiplication by the reciprocal: \[ \frac{8}{20} \times \frac{8}{1} \] Multiply numerators and denominators: \[ \frac{8 \times 8}{20 \times 1} = \frac{64}{20} \] Simplify by dividing numerator and denominator by 4: \[ \frac{64 \div 4}{20 \div 4} = \frac{16}{5} \] 2. \( \frac{4}{5} \div \frac{1}{10} \) Rewrite as multiplication by the reciprocal: \[ \frac{4}{5} \times \frac{10}{1} \] Multiply: \[ \frac{4 \times 10}{5 \times 1} = \frac{40}{5} = 8 \] 3. \( \frac{14}{2} \div \frac{1}{4} \) First simplify \(\frac{14}{2}\): \[ \frac{14}{2} = 7 \] Then: \[ 7 \div \frac{1}{4} = 7 \times \frac{4}{1} = 28 \] 4. \( \frac{9}{10} \div \frac{1}{5} \) Rewrite as multiplication by the reciprocal: \[ \frac{9}{10} \times \frac{5}{1} \] Multiply: \[ \frac{9 \times 5}{10 \times 1} = \frac{45}{10} = \frac{9}{2} \] 5. \( \frac{1}{2} \div \frac{1}{4} \) Rewrite as multiplication by the reciprocal: \[ \frac{1}{2} \times \frac{4}{1} \] Multiply: \[ \frac{1 \times 4}{2 \times 1} = \frac{4}{2} = 2 \]

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Extra Insights

To divide fractions, you multiply by the reciprocal of the divisor. For example, to solve \( \frac{8}{20} \div \frac{1}{8} \), you convert it to \( \frac{8}{20} \times \frac{8}{1} = \frac{64}{20} \), which simplifies to \( \frac{16}{5} \). This method applies to each calculation consistently! For \( \frac{1}{2} \div \frac{1}{4} \), you’re effectively asking how many fourths fit into a half! By rewriting as \( \frac{1}{2} \times \frac{4}{1} = \frac{4}{2} \), you find it equals \( 2 \), because two quarters make a half! It's all about understanding those delicious relationships between fractions!

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