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9514 1404 393

Answer:

  1. 2/8
  2. 3/5

Step-by-step explanation:

1. The denominator of a fraction indicates how many (equal) pieces a quantity is divided into. When that quantity is 1 cake, and it is divided into 8 equal pieces, each piece is 1/8 of the cake, and there are 8 pieces, or 8/8 of the cake altogether. 8/8 = 1 entire.

When 2/8 of the cake is eaten, there are 8-2 = 6 pieces left, or 6/8 of the cake remains.

When an additional 4/8 of the cake is eaten, there are 6-4 = 2 pieces left, or 2/8 of the cake remains.

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The fraction 2/8 can be written as the product of fractions ...

  [tex]\dfrac{2}{8}=\dfrac{1\cdot2}{4\cdot2}=\dfrac{1}{4}\cdot\dfrac{2}{2}[/tex]

We know that 2/2 = 1, and anything times 1 is that same thing, so the fraction 2/8 can be "reduced" to its equivalent, 1/4.

  [tex]\dfrac{2}{8}=\dfrac{1}{4}\cdot1=\dfrac{1}{4}[/tex]

As far as we can tell, this question does not ask you to reduce the fraction. Since we're counting 1/8 cake slices, and there are 2 remaining, it is reasonable to leave the fraction as 2/8.

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2. The given fractions are 1/5 pound, so it is reasonable to think of the whole weight of the 1-pound box as 5/5 pound. Two parts are 1/5 pound each, so the part remaining after considering those is ...

  5/5 - 1/5 - 1/5 = (5 -1 -1)/5 = 3/5

The third item in the box is 3/5 pound.