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Taylor_1989
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Could someone show me the proof to why we use the reciprocal in fractions division. I ask this because it seem we are taught the how in math but never the why. Algebra proof would be best thanks.
A fraction is simplified when the greatest common factor (GCF) of the numerator and denominator is 1. To prove this, find the GCF of the numerator and denominator and divide both by it. If the result is a fraction with a numerator and denominator of 1, then the original fraction is simplified.
Yes, the most commonly used method is the "find a common denominator" method. This involves finding the least common multiple (LCM) of the denominators, converting both fractions to equivalent fractions with the LCM as the denominator, and then adding or subtracting the numerators. The resulting fraction can then be simplified if necessary.
The multiplication of fractions can be proved by multiplying the numerators and denominators separately, and then simplifying the resulting fraction. This can also be explained using the concept of multiplying by a reciprocal, where the second fraction is flipped and then multiplied.
Yes, the division of fractions can be proved by multiplying the first fraction by the reciprocal of the second fraction. This can also be explained by flipping the second fraction and then using the same method as proving multiplication of fractions.
Two fractions are equivalent if they represent the same value. To prove this, find the simplest form of both fractions and compare them. If they are the same, then the fractions are equivalent. Another method is to cross-multiply and see if the resulting equations are equal.