Divide:
$45 \longdiv { 285 }$
Which is true about this division problem? Select all that apply.
A. 45 goes into 285 evenly.
B. 45 does not go into 285 evenly.
C. The quotient contains a repeating decimal.
D. The quotient contains a terminating decimal.
E. The quotient is $6 . \overline{3}$.
F. The quotient is 6.3.
Answer (1)
Divide 285 by 45 and get 6. 3 .
Determine that 45 does not divide 285 evenly since the result is not an integer.
Recognize that the quotient 6. 3 is a repeating decimal.
Conclude that the true statements are: 45 does not go into 285 evenly, the quotient contains a repeating decimal, and the quotient is 6. 3 .
Explanation
Problem Analysis We are asked to divide 285 by 45 and determine which statements about the division problem are true.
Performing the Division First, let's perform the division: $285
div 45$. The result of this division is 6.333333333...
Checking for Even Division Since the result is not an integer, 45 does not go into 285 evenly. When we divide 285 by 45, we get 6 with a remainder of 15.
Identifying the Decimal Type The quotient is 6.333333333... , which can be written as 6. 3 . This is a repeating decimal because the digit 3 repeats infinitely.
Selecting True Statements Now, let's check the given statements:
45 goes into 285 evenly. (False, since there is a remainder)
45 does not go into 285 evenly. (True)
The quotient contains a repeating decimal. (True)
The quotient contains a terminating decimal. (False)
The quotient is 6. 3 . (True)
The quotient is 6.3. (False, since it's 6. 3 )
Therefore, the true statements are:
45 does not go into 285 evenly.
The quotient contains a repeating decimal.
The quotient is 6. 3 .
Final Answer The true statements about the division problem are that 45 does not go into 285 evenly, the quotient contains a repeating decimal, and the quotient is 6. 3 .
Examples
Understanding division and remainders is crucial in everyday situations. For example, if you have 285 apples and want to distribute them equally among 45 people, each person would get 6 apples, and you'd have 15 apples left over. This concept is also used in scheduling, resource allocation, and many other practical applications where fair distribution is important.
