Question

What if Viki took three pieces of the tart home and Elena to three pieces of the tart home how could you combine the pieces to a fraction that represents the part each friend took home explain

Answer 1

Answer:

one-third of tart is taken by each friend, and the remaining part is also one third, so

$\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=1$ (the whole tart)

Step-by-step explanation:

Let, 'x' be the tart present initially which is,

$x = 1$

since, both of them took 3 pieces of tart to their home out of the whole tart, then there must be some piece of it remaining:

$\frac{x}{3} + \frac{x}{3} + y = 1$

∵ $x = 1$

$\frac{1}{3} + \frac{1}{3} + y = 1\\y = 1 -\frac{1}{3} -\frac{1}{3}$

∴ $y = \frac{1}{3}$

This fraction explains the part each friend took, i.e. one third of the tart, and the part that remains is also one third of the whole tart.

Answer 2

This question is incomplete. Below is the complete question:

Vicki made a fruit tart and cut it into 6 equal piei, Vicki, Silvia and Elena took 2 pieces of the tart home. Vicki says she and each of her friends took 1/3 of the tart home.

a. Is Vicki correct?

b. What if Vicki took 3 pieces of the tart home and Elena took three pieces of the tart home. How could you combine the pieces to a fraction that represents the part each friend took home? Explain.

Answer:

a. Vicki is very correct

b. The pieces the two friends took home are: 3/6 + 3/6 or 1/2 + 1/2

Step-by-step explanation:

a. If the fruit tart was cut into 6 equal pieces and later, Vicki, Silvia and Elena each took home 2 pieces of the tart; then the fraction or portion of the fruit that each friend took home is:-

2/6 + 2/6 + 2/6 = 6/6 = 1

If we reduce each of these fractions to its lowest term (using the numerator to divide the denominator), we will have:-

1/3 + 1/3 + 1/3 = 3/3 = 1

The 6 parts can be seen as 3 parts while the 2 parts that the friends took each can also be seen as 1 part. So we can now see that Vicki is correct since two out of six parts (2/6) is the same as one part of three parts (1/3).

b. If on the other hand, it is assumed that Vicki took home 3 pieces out of the total pieces that it was cut into; and Elena took home the remaining pieces of the total pieces that the fruit tart was cut into, we can represent the fraction that the two friends took:-

Firstly, since the fruit was cut into six pieces and Vicki took home 3 pieces, the portion or fraction that Vicki took home is 3 out of six (3/6).

Again Elena took the remaining pieces that Vicki left behind. Since the total pieces were 6 and Vicki took three pieces, the remaining pieces that Elena took = (6-3) = 3 pieces. If Elena took three pieces, the fraction that she took was 3/6 also.

If I combine the fractions of the fruits that the two friends took home, it will be:

3/6 + 3/6 = 6/6 = 1

We can also reduce each of these fractions to their lowest terms by dividing 6 by 3. If we do this, we will have:

1/2 + 1/2 = 1

This means that three portions or three pieces out of the six pieces can also be seen as one portion and the total of six pieces can also be see as two portions.