Dividing a fraction by a whole number involves converting the whole number into a fraction and then multiplying by the reciprocal of that fraction.
Here's a step-by-step breakdown:
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Convert the Whole Number to a Fraction: Write the whole number as a fraction by putting it over 1. For example, if you have the whole number 5, write it as 5/1.
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Find the Reciprocal of the Whole Number Fraction: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. So, the reciprocal of 5/1 is 1/5.
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Multiply the Original Fraction by the Reciprocal: Multiply the numerator of the original fraction by the numerator of the reciprocal, and the denominator of the original fraction by the denominator of the reciprocal.
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Simplify the Result: If possible, simplify the resulting fraction to its lowest terms.
Example:
Let's say you want to divide 1/2 by 4.
- Convert 4 to a fraction: 4/1
- Find the reciprocal of 4/1: 1/4
- Multiply 1/2 by 1/4: (1/2) * (1/4) = (1 * 1) / (2 * 4) = 1/8
- Simplify: 1/8 is already in its simplest form.
Therefore, 1/2 divided by 4 is 1/8.
Simplifying Before Multiplying
Sometimes, you can simplify before multiplying, which can make the calculation easier. If the numerator of one fraction and the denominator of the other share a common factor, you can divide both by that factor before multiplying. The reference mentions an example where simplification can occur to reduce the math involved. For example, consider a scenario where simplification can occur to reduce the math involved when multiplying by a reciprocal after turning the whole number into a fraction.
