Question

1. today a student completed \\(\frac{13}{24}\\) more homework than yesterday. if this student completed \\(\frac{1}{3}\\) of their homework yesterday, how much of their homework was completed today?

options: \\(\frac{7}{8}\\), \\(\frac{14}{27}\\), \\(\frac{5}{6}\\), \\(\frac{1}{3}\\)

Explanation:

Step1: Identify yesterday's homework

Yesterday's homework completion is $\frac{1}{3}$.

Step2: Calculate today's additional homework

Today, the student completed $\frac{13}{24}$ more than yesterday. So we need to add $\frac{1}{3}$ and $\frac{13}{24}$. First, find a common denominator for $\frac{1}{3}$ and $\frac{13}{24}$. The common denominator of 3 and 24 is 24. Convert $\frac{1}{3}$ to a fraction with denominator 24: $\frac{1}{3} = \frac{1\times8}{3\times8} = \frac{8}{24}$.

Step3: Add the fractions

Now add $\frac{8}{24}$ and $\frac{13}{24}$: $\frac{8}{24} + \frac{13}{24} = \frac{8 + 13}{24} = \frac{21}{24}$. Simplify $\frac{21}{24}$ by dividing numerator and denominator by 3: $\frac{21\div3}{24\div3} = \frac{7}{8}$.

Answer:

$\frac{7}{8}$ (corresponding to the first option, likely labeled as A. $\frac{7}{8}$ if following the option labels, but based on the calculation, the answer is $\frac{7}{8}$)