GWOB Posted March 28, 2011 Share Posted March 28, 2011 Can anyone explain to me why we multiply by the reciprocal when dividing fractions? I never learned why, just how. I need to explain this to my 5th grade dd (and to myself really). And links would be appreciated as well. Thanks! Quote Link to comment Share on other sites More sharing options...
Crimson Wife Posted March 28, 2011 Share Posted March 28, 2011 Have you watched Maria Miller's YouTube video on the topic? Quote Link to comment Share on other sites More sharing options...
ELaurie Posted March 28, 2011 Share Posted March 28, 2011 (edited) in my signature line. Click on Sample lessons, then Level 3, then Lesson 5 Multiplying with Fractions for a cogent explanation. :001_smile: ETA: Sorry - I just realized that this reply doesn't answer your question :o Edited March 28, 2011 by ELaurie Quote Link to comment Share on other sites More sharing options...
Storm Bay Posted March 28, 2011 Share Posted March 28, 2011 Have you watched Maria Miller's YouTube video on the topic? This is one of the better explanations I've seen. MUS also has a good teaching on this, but I don't know if it's on YouTube (haven't checked.) Quote Link to comment Share on other sites More sharing options...
regentrude Posted March 28, 2011 Share Posted March 28, 2011 Think of what a fraction means. Lets begin with a simple one: 1/2. Multiplying something by one half is the same as dividing by two. Because the division is the inverse of the multiplication, DIVIDING by 1/2 is the same as multiplying by two, i.e. the reciprocal. You can visualize this by having a pizza and dividing it: division by 1/2 means "how many half pizzas can you fit into one whole"- the answer is 2. For fractions that are 1/3, 1/4 and so on, the same procedure applies: dividing by 1/4 means answering "how many 1/4 are in a whole" - 4. So division by 1/4 is teh same as multiplication by 4. A fraction that has a numerator larger than one is a combination of two actions: a division by the denominator, and a multiplication by a numerator. If I multiply by 3/4, I can first multiply by 3, and then divide by 4 (or vice versa) So, dividing by 3/4 is the same as dividing by 3 and then dividing by 1/4 (or vice versa). Division by 3 is the same as multiplying with 1/3. Division by 1/4 is the same as multiplying with 4. So, division by 3/4 is the same as multiplying with 4/3. hope this helps. Quote Link to comment Share on other sites More sharing options...
GWOB Posted March 28, 2011 Author Share Posted March 28, 2011 Have you watched Maria Miller's YouTube video on the topic? in my signature line. Click on Sample lessons, then Level 3, then Lesson 5 Multiplying with Fractions for a cogent explanation. :001_smile: ETA: Sorry - I just realized that this reply doesn't answer your question :o Think of what a fraction means. Lets begin with a simple one: 1/2.Multiplying something by one half is the same as dividing by two. Because the division is the inverse of the multiplication, DIVIDING by 1/2 is the same as multiplying by two, i.e. the reciprocal. You can visualize this by having a pizza and dividing it: division by 1/2 means "how many half pizzas can you fit into one whole"- the answer is 2. For fractions that are 1/3, 1/4 and so on, the same procedure applies: dividing by 1/4 means answering "how many 1/4 are in a whole" - 4. So division by 1/4 is teh same as multiplication by 4. A fraction that has a numerator larger than one is a combination of two actions: a division by the denominator, and a multiplication by a numerator. If I multiply by 3/4, I can first multiply by 3, and then divide by 4 (or vice versa) So, dividing by 3/4 is the same as dividing by 3 and then dividing by 1/4 (or vice versa). Division by 3 is the same as multiplying with 1/3. Division by 1/4 is the same as multiplying with 4. So, division by 3/4 is the same as multiplying with 4/3. hope this helps. Thank you so, so very much! We watched the youtube video and the Professor B sample. Those were perfect and exactly what she needed. Quote Link to comment Share on other sites More sharing options...
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