How many groups of 1/2 are in 8?
Understand the Problem
The question is asking how many times the fraction 1/2 can be grouped to reach the whole number 8. This requires dividing 8 by 1/2, which is the same as multiplying 8 by the reciprocal of 1/2, or 2.
Answer
16
Answer for screen readers
The final answer is 16.
Steps to Solve
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Identify the operation To determine how many times the fraction $\frac{1}{2}$ can be grouped to get to 8, we need to divide 8 by $\frac{1}{2}$.
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Set up the division The division is set up as follows: $$ 8 \div \frac{1}{2} $$
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Change the division to multiplication Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $\frac{1}{2}$ is 2. Therefore, we rewrite the problem: $$ 8 \div \frac{1}{2} = 8 \times 2 $$
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Perform the multiplication Now we perform the multiplication: $$ 8 \times 2 = 16 $$
The final answer is 16.
More Information
This result means that the fraction $\frac{1}{2}$ can be added together 16 times to sum up to 8. This is an example of how fractions can be used to reach whole numbers through multiplication and division.
Tips
- A common mistake is forgetting to multiply by the reciprocal when dividing by a fraction. Always remember that $a \div \frac{b}{c}$ can be rewritten as $a \times \frac{c}{b}$.
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