Question

1. in the lunchroom, 16 $5^{th}$ graders and 24 $6^{th}$ graders are sitting in equal groups. all the students in each group are in the same grade. what is the greatest number of students who could be in each group?

8.
$2\frac{2}{3}\cdot\frac{5}{6} = $

Explanation:

Question 7

Step1: Find GCD of 16 and 24

We need to find the greatest common divisor (GCD) of 16 and 24. The factors of 16 are $1, 2, 4, 8, 16$. The factors of 24 are $1, 2, 3, 4, 6, 8, 12, 24$. The common factors are $1, 2, 4, 8$. The greatest among them is 8.

Step2: Verify the groups

For 5th graders: $16 \div 8 = 2$ groups. For 6th graders: $24 \div 8 = 3$ groups. All students in each group are same grade, and 8 is the largest number that divides both 16 and 24 evenly.

Step1: Convert mixed number to improper fraction

Convert $2\frac{2}{3}$ to improper fraction. $2\frac{2}{3}=\frac{2\times3 + 2}{3}=\frac{8}{3}$.

Step2: Multiply the fractions

Multiply $\frac{8}{3}$ and $\frac{5}{6}$. $\frac{8}{3}\times\frac{5}{6}=\frac{8\times5}{3\times6}=\frac{40}{18}$.

Step3: Simplify the fraction

Simplify $\frac{40}{18}$ by dividing numerator and denominator by 2. $\frac{40\div2}{18\div2}=\frac{20}{9}$ or as a mixed number $2\frac{2}{9}$.

Answer:

8

Question 8