To determine which context the expression [tex]\(30 \div 6\)[/tex] represents, let's analyze the options provided:
Step-by-step analysis:
1. Expression Explanation:
- The expression [tex]\(30 \div 6\)[/tex] is a division problem where 30 is the dividend (the number to be divided) and 6 is the divisor (the number by which the dividend is divided).
2. Mathematical Interpretation:
- Division can be interpreted as distributing the dividend into a specific number of equal groups.
- In this case, we are distributing 30 into 6 equal groups.
3. Result of the Division:
- When 30 is divided by 6, the result tells us how many items are in each group.
- Performing the calculation, [tex]\(30 \div 6 = 5\)[/tex]. Thus, each group contains 5 items.
4. Contextual Analysis:
- We need to determine which given context appropriately fits this interpretation.
5. Option Analysis:
- A) 30 beads arranged in 30 equal groups: This would be [tex]\(30 \div 30\)[/tex], not [tex]\(30 \div 6\)[/tex].
- B) 6 beads arranged in 30 equal groups: This would be [tex]\(6 \div 30\)[/tex], not [tex]\(30 \div 6\)[/tex].
- C) 30 beads arranged in 6 equal groups: This appropriately matches [tex]\(30 \div 6\)[/tex], representing distributing 30 beads into 6 groups.
- D) 30 beads arranged in 3 equal groups: This would be [tex]\(30 \div 3\)[/tex], not [tex]\(30 \div 6\)[/tex].
Hence, the correct context that [tex]\(30 \div 6\)[/tex] represents is:
30 beads arranged in 6 equal groups.
So, the correct answer is:
(C) 30 beads arranged in 6 equal groups.
