How many 2/5 are in 1?
Understand the Problem
The question is asking how many times the fraction 2/5 fits into the whole number 1. This can be solved by dividing 1 by 2/5, which is equivalent to multiplying 1 by the reciprocal of 2/5 (which is 5/2). This will give us the quantity of 2/5 in 1.
Answer
The fraction $ \frac{2}{5} $ fits into 1 a total of $ \frac{5}{2} $ or $ 2 \frac{1}{2} $ times.
Answer for screen readers
The fraction $ \frac{2}{5} $ fits into 1 a total of $ \frac{5}{2} $ or $ 2 \frac{1}{2} $ times.
Steps to Solve
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Identify the operation
To find out how many times the fraction $ \frac{2}{5} $ fits into the whole number 1, we need to divide 1 by $ \frac{2}{5} $. -
Set up the division
We can express the division as:
$$ 1 \div \frac{2}{5} $$ -
Multiply by the reciprocal
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $ \frac{2}{5} $ is $ \frac{5}{2} $. Therefore, we rewrite the division as:
$$ 1 \times \frac{5}{2} $$ -
Perform the multiplication
Now calculate the multiplication:
$$ 1 \times \frac{5}{2} = \frac{5}{2} $$ -
Convert to a mixed number (if needed)
The fraction $ \frac{5}{2} $ can also be expressed as a mixed number:
$$ \frac{5}{2} = 2 \frac{1}{2} $$
This means $ \frac{2}{5} $ fits into 1 two and a half times.
The fraction $ \frac{2}{5} $ fits into 1 a total of $ \frac{5}{2} $ or $ 2 \frac{1}{2} $ times.
More Information
This problem illustrates how fractions can be manipulated by using their reciprocals, which is a fundamental skill in understanding division with fractions. It also shows how to convert between improper fractions and mixed numbers.
Tips
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Ignoring the reciprocal
Many students forget to multiply by the reciprocal of the fraction when dividing. Always remember that dividing by a fraction is the same as multiplying by its reciprocal.
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