To convert division to multiplication in fractions, you invert the divisor (the second fraction) and change the division symbol to a multiplication symbol. This process is sometimes referred to as "reciprocating" the second fraction.
Understanding the Process
When dividing fractions, you're essentially asking how many times the second fraction (the divisor) fits into the first fraction (the dividend). Converting to multiplication by the reciprocal provides an easier way to calculate this.
Steps for Converting Division to Multiplication
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Identify the divisor: This is the fraction you are dividing by. It's the fraction to the right of the division symbol.
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Invert the divisor (find its reciprocal): Flip the divisor fraction so that the numerator becomes the denominator and the denominator becomes the numerator.
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Change the division to multiplication: Replace the division symbol (÷) with a multiplication symbol (×).
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Multiply the fractions: Multiply the first fraction (the dividend) by the reciprocal of the second fraction.
Example
Let's say you want to divide 1/2 by 1/4:
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Problem: 1/2 ÷ 1/4
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Invert the divisor (1/4): The reciprocal of 1/4 is 4/1.
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Change to multiplication: 1/2 × 4/1
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Multiply: (1 × 4) / (2 × 1) = 4/2 = 2
Therefore, 1/2 ÷ 1/4 = 2.
Key Takeaway
The provided reference states: "When we divide fractions, we actually turn the division problem into a multiplication problem by turning the divisor (the second fraction) upside down (switching its numerator with its denominator) and changing the division symbol to a multiplication symbol at the same time." This perfectly summarizes the process of converting fraction division to multiplication.
