Peter says $$ \frac{3}{4} $$ of a pizza is always the same as $$ \frac{6}{8} $$ of a pizza. Nadia says while $$ \frac{3}{4} $$ and $$ \frac{6}{8} $$ are equivalent fractions, $$ \frac{3}{4} $$ and $$ \frac{6}{8} $$ of a pizza could represent different amounts.

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UpStudy AI · Accepted Answer

1. We start by verifying that the fractions are equivalent. To do this, we can simplify $$ \frac{6}{8} $$ by dividing the numerator and the denominator by their greatest common divisor, which is 2:

$$
\frac{6 \div 2}{8 \div 2} = \frac{3}{4}.
$$

Thus, mathematically, $$ \frac{3}{4} $$ and $$ \frac{6}{8} $$ are equivalent.

2. Peter’s assertion focuses on the fact that when the fractions are considered in a pure mathematical sense (without any further context), they represent exactly the same portion of a given whole.

3. Nadia, on the other hand, is considering the real-life scenario where the size of the whole (in this case, a pizza) may vary. While the fractions themselves are equivalent, if one pizza is larger than another, then:

- $$ \frac{3}{4} $$ of a large pizza may be a larger amount of pizza by area than $$ \frac{6}{8} $$ of a smaller pizza.
   - Similarly, $$ \frac{6}{8} $$ of a pizza in one situation might not match $$ \frac{3}{4} $$ of another if the pizzas differ in size.

4. Therefore, both points of view are valid:

- Peter is correct in stating that the fractions are equivalent.
   - Nadia is correct in noting that the actual amount (the physical area or volume of pizza) represented by the fraction depends on the size of the pizza.

5. The key idea is distinguishing between a fraction as a representation of a relative portion of a whole, and the absolute value of that portion when the size of the whole varies.
Peter and Nadia are both correct. Mathematically, $$ \frac{3}{4} $$ and $$ \frac{6}{8} $$ are equivalent fractions. However, in real-life situations, the actual amount they represent can differ based on the size of the pizza.

Peter says of a pizza is always the same
as of a pizza. Nadia says while and are
equivalent fractions, and of a pizza could
represent different amounts.

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Peter says of a pizza is always the same as of a pizza. Nadia says while and are equivalent fractions, and of a pizza could represent different amounts.