Invert and Multiply
Date: 11/08/97 at 14:24:45 From: Anonymous Subject: Fractions! Hi Doc, I am a student teacher, currently taking a methods course in elementary mathematics. I am struggling with how to explain to a class "why" we invert and multiply when dividing fractions. I read your FAQ on this, but still don't understand how I would explain it using concrete materials in a classroom. Please help. Thanks ever so much! Laura
Date: 11/09/97 at 09:56:11 From: Doctor Chita Subject: Re: Fractions! Hi there: Explaining "why" using concrete materials may be difficult. However, this is an opportunity, perhaps, to show students how mathematics relies on proof, rather than pictures or models. Take an "easy" problem such as, 1/2 divided by 3/4. Write this as a compound fraction: (1/2)/(3/4). (Use horizontal fraction bars, not diagonal bars as here. The computer has its handicaps!) Everyone knows that 1 is the multiplicative identity element. Therefore, 1 * (1/2)/(3/4) = (1/2)/(3/4) Substitute 4/4 for 1. Write: 4/4 * (1/2)/(3/4) Think of 4/4 as the compound fraction: (4/1)/(4/1). Then multiply the numerator and deminator of the compound fraction by 4/1: [4/1 * (1/2)]/4/1* (3/4)] The new numerator is 2: the new denominator is 3. The answer is 2/3. Therefore, the rule "invert and multiply" works because what you are really doing is multiplying the numerator and denominator of a compound fraction by the LCD of the fractions in the compound fraction. Try 3/8 divided by 9/5. Write as (3/8)/(9/5) using horizontal bars. Multiply the fraction by 1 = 40/40, in the form of (40/1)/(40/1) where 40 is the LCD of 8 and 5: (40/1)/(40/1) * (3/8)/(9/5) [40/1 * 3/8]/ [40/1 * 9/5] 15/72 = 5/24 After a while, you can drop the 1s in the fraction that represents the LCD. Got it? Put this information together with what's in the archives and write back if you still need more help. Good luck. -Doctor Chita, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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