How many groups of 9/5 are in 1?
Understand the Problem
The question is asking how many times the fraction 9/5 fits into the whole number 1. To solve this, we can divide 1 by 9/5 or multiply 1 by the reciprocal of 9/5, which is 5/9.
Answer
The fraction \( \frac{9}{5} \) fits into 1 exactly \( \frac{5}{9} \) times.
Answer for screen readers
The fraction ( \frac{9}{5} ) fits into the whole number 1 exactly ( \frac{5}{9} ) times.
Steps to Solve
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Setting up the division To find out how many times the fraction ( \frac{9}{5} ) fits into 1, we need to divide 1 by ( \frac{9}{5} ): $$ 1 \div \frac{9}{5} $$
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Converting the division to multiplication Instead of dividing by a fraction, we can multiply by its reciprocal. The reciprocal of ( \frac{9}{5} ) is ( \frac{5}{9} ): $$ 1 \times \frac{5}{9} $$
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Carrying out the multiplication Now, multiply: $$ 1 \times \frac{5}{9} = \frac{5}{9} $$
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Interpreting the answer The result ( \frac{5}{9} ) means that ( \frac{9}{5} ) fits into 1 exactly ( \frac{5}{9} ) times.
The fraction ( \frac{9}{5} ) fits into the whole number 1 exactly ( \frac{5}{9} ) times.
More Information
This result shows the relationship between whole numbers and fractions, illustrating that even a smaller number (like 1) can accommodate fractions like ( \frac{9}{5} ) less than once.
Tips
Common mistakes include:
- Misunderstanding how to divide by a fraction. Remember to multiply by its reciprocal instead.
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