Depth · one concept from first principles · step 2 of 4
A box holding 5 identical bottles of juice weighs . After taking 1 bottle of juice out of the box, the box weighs . How many pounds does the empty box weigh?
Removing exactly one bottle made the weight fall from 1.96 lb to 1.66 lb. That drop is one bottle: 1.96 - 1.66 = 0.30 lb.
The weight that disappeared equals what you took out - one bottle.
5.NBT.B.7Analyze The UnitsThe 0.30 lb the scale lost when one bottle came out, 1.96 - 1.66, is exactly the weight of one bottle.
A weighing reads the weight of everything on the scale, and that reading is just the box and the bottles inside it added together.
The box and each bottle are separate pieces with no gaps and no overlaps, so their weights add back to the single number the scale shows.
Both weighings hold the same box and the same four other bottles, so the only thing missing from the second reading is the one bottle that was taken out.
Removing that bottle takes away exactly the weight it had added to the pile, because subtracting is the move that undoes adding.
After removing one bottle, 4 bottles remain in the box. Four bottles weigh 4 x 0.30 = 1.20 lb.
Four equal bottles is just the one-bottle weight added four times.
5.NBT.B.7Work BackwardsThe 1.66 lb weighing is the box plus those 4 bottles. Take the bottles away: 1.66 - 1.20 = 0.46 lb is the empty box.
Removing the bottle weight from the total leaves only the box.
4.MD.A.2Work BackwardsThe weight that vanished when you removed one bottle IS one bottle - then just subtract the bottles away!
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