Question

1. critique reasoning laurie says summer is \\(\frac{1}{4}\\) of the year. maria says summer is \\(\frac{3}{12}\\) of the year. who is correct? explain.

Explanation:

Step1: Recall the number of months in summer

Summer typically has 3 months, and a year has 12 months. So the fraction of the year that is summer is $\frac{3}{12}$.

Step2: Simplify $\frac{3}{12}$

To simplify $\frac{3}{12}$, we divide both the numerator and the denominator by their greatest common divisor, which is 3. So $\frac{3\div3}{12\div3}=\frac{1}{4}$.

Step3: Compare the fractions

Laurie says summer is $\frac{1}{4}$ of the year, and Maria says it is $\frac{3}{12}$ of the year. Since $\frac{1}{4}=\frac{3}{12}$ (because we just showed that simplifying $\frac{3}{12}$ gives $\frac{1}{4}$), both are correct.

Answer:

Both Laurie and Maria are correct because $\frac{1}{4}$ and $\frac{3}{12}$ are equivalent fractions (since $\frac{3}{12}$ simplifies to $\frac{1}{4}$ by dividing numerator and denominator by 3), and summer is 3 months out of 12, which can be represented as either $\frac{3}{12}$ or $\frac{1}{4}$ of the year.