Cindyg Posted October 28, 2010 Share Posted October 28, 2010 I'm really good at homeschool. I even teach Latin!! But math...sigh... Here's the problem: 6/7 of a sandwich weighs 5/8 lb. How much does the whole sandwich weigh? The answer is 35/48 lbs. Can someone please explain it to me? Quote Link to comment Share on other sites More sharing options...

Dana Posted October 28, 2010 Share Posted October 28, 2010 (6/7)(sandwich) = (5/8) direct translation of the problem.... 6/7 of the sandwich (so multiplication) is 5/8 lbs. You've got a linear equation now. You can solve by dividing by 6/7 (which is multiplication by the reciprocal) (7/6)(6/7)(sandwich) = (7/6)(5/8) (sandwich) = 35/48 lbs Quote Link to comment Share on other sites More sharing options...

Suzanne in ABQ Posted October 28, 2010 Share Posted October 28, 2010 I'm really good at homeschool. I even teach Latin!! But math...sigh... Here's the problem: 6/7 of a sandwich weighs 5/8 lb. How much does the whole sandwich weigh? The answer is 35/48 lbs. Can someone please explain it to me? 6/7 OF a sandwich means the same thing as 6/7 TIMES the whole sandwich, which you could call S. Then, 6/7 * S(lb) = 5/8 lbs Solve for S to get the weight of the whole sandwich. Is that all you need, or do you need to know how to solve for S? Quote Link to comment Share on other sites More sharing options...

hsmom3tn Posted October 28, 2010 Share Posted October 28, 2010 Since you gave the answer, I can see how to arrive at the answer (dividing/multiplying the fractions); but if you had not given the answer, I wouldn't have been able to figure it out. I hope someone can explain the "why" behind this, because I don't get it. :blushing: Quote Link to comment Share on other sites More sharing options...

justasque Posted October 28, 2010 Share Posted October 28, 2010 6/7 of a sandwich weighs 5/8 lb. How much does the whole sandwich weigh? The answer is 35/48 lbs. Solve a simpler problem. 1/4 of a sandwich weighs 2 pounds. How much does the whole sandwich weigh? 1/4 of S (the sandwich weight) = 2 1/4 x S = 2 S = 8 lbs. Same process, they're just using awkward fractional numbers instead of 1/4 and 2. Quote Link to comment Share on other sites More sharing options...

Perry Posted October 28, 2010 Share Posted October 28, 2010 (edited) Since you gave the answer, I can see how to arrive at the answer (dividing/multiplying the fractions); but if you had not given the answer, I wouldn't have been able to figure it out. I hope someone can explain the "why" behind this, because I don't get it. :blushing: Substitute easier numbers, just to illustrate the concept. Say one half of a sandwich = 3 pounds. (Big sandwich) Of means times,usually. Let "S" stand for the sandwich. 1/2 of S =3 Or, (1/2)*S = 3 1/2 of 6 is 3, S=6. Edited October 28, 2010 by Perry Quote Link to comment Share on other sites More sharing options...

EKS Posted October 28, 2010 Share Posted October 28, 2010 When I get confused by a problem like this, something that I could do easily if different numbers were used, I just use different numbers and see how I did it. So if 2 sandwiches weigh 6 pounds and I want to know how much 1 sandwich weighs, I know to divide 6 by 2 to get 3. So instead of 2 sandwiches I have 6/7 of a sandwich (it's just another number) and instead of 6 pounds it's 5/8 of a pound. So 5/8 divided by 6/7 is 5/8 x 7/6 which is 35/48. The why is the same as the why for the intuitively obvious problem. Quote Link to comment Share on other sites More sharing options...

AngieW in Texas Posted October 29, 2010 Share Posted October 29, 2010 I looked at the problem in another way. 6/7 of the sandwich weighed 5/8 of a pound so 1/7 of the sandwich must have weighed 1/6 x 5/8 = 5/48 (because 1/7 is 1/6 of 6/7) so take your original 5/8 and add 5/48 5/8 + 5/48 = 30/48 + 5/48 = 35/48 Quote Link to comment Share on other sites More sharing options...

Cindyg Posted October 29, 2010 Author Share Posted October 29, 2010 (edited) Thank you so much everyone. I think we understand. I just hope we can remember what we understand. ETA: I don't want to post at the bottom and bump this, but I really appreciate everyone's responses. My ds gets very frustrated with my inability to explain math, and he knows from experience that we can post the question on the WTM and get a good explanation. So you helped us through the day. :) Edited October 29, 2010 by Cindyg Quote Link to comment Share on other sites More sharing options...

Abigail4476 Posted October 29, 2010 Share Posted October 29, 2010 This is how I would solve it: 6/7 OF the sandwich (s) = 5/8 (lbs.) Equation 6/7s = 5/8 Divide both sides by 6/7 to isolate S. 6/7s divided by 6/7 = 5/8 divided by 6/7 Then invert and multiply to divide. (technically, to divide you multiply by the reciprocal) 6/7 * 7/6 cancels leaving... s = 5/8 * 7/6 s = 35/48 lbs. Quote Link to comment Share on other sites More sharing options...

zaichiki Posted October 29, 2010 Share Posted October 29, 2010 The Singapore Math way has the child draw a bar and label it 5/8 lb. Then, draw lines in the bar to divide it into 6 equal pieces. Add the seventh piece. The 6 pieces equal 5/8 lb, so what would 1 of the pieces be worth? 5/8 divided by 6 tells us what one piece is worth. Then, if you want to find out the whole (seven pieces), you'd multiply that one box by 7. Does that help? Wish I could draw the bar and show you. Quote Link to comment Share on other sites More sharing options...

Jenny Piaaree Posted October 29, 2010 Share Posted October 29, 2010 (edited) Or, after getting your correct equation 6/7 x s = 5/8 you can cross-multiply (easier for me) (6 x s)/7 = 5/8, 6s x 8 = 7 x 5 48s = 35 s = 35/48 Edited October 29, 2010 by Jenny Piaaree formatting error Quote Link to comment Share on other sites More sharing options...

silliness7 Posted October 29, 2010 Share Posted October 29, 2010 6/7 of a sandwich weighs 5/8 lb. How much does the whole sandwich weigh? The answer is 35/48 lbs. Solve a simpler problem. 1/4 of a sandwich weighs 2 pounds. How much does the whole sandwich weigh? 1/4 of S (the sandwich weight) = 2 1/4 x S = 2 S = 8 lbs. Same process, they're just using awkward fractional numbers instead of 1/4 and 2. That's what I did only I made the numbers super simple. 1/2 of a sandwich is 10 lbs. How much does one sandwich weigh. So intuitively I know it weighs 20 lbs. Then I figure out the equation that got 20 lbs. and then I plugged the 6/7 and 5/8 into it. So it's not how geniuses figure it out but I think my brain has a math handicap. :001_smile: Quote Link to comment Share on other sites More sharing options...

JeneralMom Posted October 29, 2010 Share Posted October 29, 2010 This is how I would solve it: 6/7 OF the sandwich (s) = 5/8 (lbs.) Equation 6/7s = 5/8 Divide both sides by 6/7 to isolate S. 6/7s divided by 6/7 = 5/8 divided by 6/7 Then invert and multiply to divide. (technically, to divide you multiply by the reciprocal) 6/7 * 7/6 cancels leaving... s = 5/8 * 7/6 s = 35/48 lbs. This is exactly what I would have done. Quote Link to comment Share on other sites More sharing options...

nmoira Posted October 29, 2010 Share Posted October 29, 2010 I looked at the problem in another way. 6/7 of the sandwich weighed 5/8 of a pound so 1/7 of the sandwich must have weighed 1/6 x 5/8 = 5/48 (because 1/7 is 1/6 of 6/7) so take your original 5/8 and add 5/48 5/8 + 5/48 = 30/48 + 5/48 = 35/48 The bolded part is how I'd start to explain it, but I'd finish by multiplying the weight of 1/7 of the sandwich by 7 to get the weight of a single, whole sandwich. After doing a few examples like this, you can see that you are in essence multiplying by the inverse of the quantity (flip the fraction) of the thing you want converted to a unit, in this case sandwiches (6/7 * 7/6 = 1). It works for whole numbers as well: e.g. for 3 sandwiches, you would have multiplied by 1/3 (the inverse of 3/1). Quote Link to comment Share on other sites More sharing options...

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