# I need help with a prealgebra word problem.

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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?

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(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

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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?

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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:

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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.

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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 by Perry
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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.

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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)

5/8 + 5/48 = 30/48 + 5/48 = 35/48

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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 by Cindyg
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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.

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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.

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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 by Jenny Piaaree
formatting error
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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:

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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.

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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)

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).

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