Solving "division under division," more formally known as dividing fractions, involves a specific process. The key is to remember that dividing by a fraction is the same as multiplying by its reciprocal.
Here's the step-by-step method:
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Rewrite the Problem: Express the "division under division" as a fraction divided by another fraction. For example: (a/b) / (c/d).
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Find the Reciprocal: Identify the second fraction (the divisor) and find its reciprocal. The reciprocal is found by flipping the numerator and the denominator. So, the reciprocal of (c/d) is (d/c).
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Change Division to Multiplication: Replace the division sign with a multiplication sign. Now the problem looks like: (a/b) * (d/c).
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Multiply the Fractions: Multiply the numerators together and the denominators together: (a d) / (b c).
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Simplify (if possible): Reduce the resulting fraction to its simplest form.
Example:
Let's say you want to solve: (1/2) / (3/4)
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Rewrite: The problem is already in the correct format.
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Reciprocal: The reciprocal of (3/4) is (4/3).
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Change to Multiplication: (1/2) * (4/3)
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Multiply: (1 4) / (2 3) = 4/6
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Simplify: 4/6 simplifies to 2/3.
Therefore, (1/2) / (3/4) = 2/3.
In Summary:
To solve a division problem where one fraction is divided by another, you multiply the first fraction by the reciprocal of the second fraction. This simplifies the process and allows you to arrive at the correct answer.
