What is the quotient and remainder of 39 divided by 8
The Correct Answer and Explanation is:
To find the quotient and remainder of ( 39 \div 8 ), we can use the division algorithm, which states that for any integers ( a ) and ( b ) (where ( b > 0 )), there exist unique integers ( q ) (the quotient) and ( r ) (the remainder) such that:
[
a = bq + r
]
where ( 0 \leq r < b ).
In this case, we have:
- ( a = 39 )
- ( b = 8 )
To begin, we need to determine how many times ( 8 ) can fit into ( 39 ). We can do this by performing the division:
[
39 \div 8 = 4.875
]
Since we need the integer part of the division, we take ( 4 ) as the quotient (( q )). To find the remainder (( r )), we multiply the quotient by the divisor:
[
8 \times 4 = 32
]
Next, we subtract this product from the original number ( 39 ) to find the remainder:
[
39 – 32 = 7
]
Now, we have identified our values:
- Quotient (( q )): ( 4 )
- Remainder (( r )): ( 7 )
Thus, we can express the division in the form of the division algorithm:
[
39 = 8 \times 4 + 7
]
Finally, we verify the conditions for the remainder:
- The remainder ( 7 ) is indeed less than the divisor ( 8 ).
- The remainder is non-negative.
Therefore, the complete answer is that when ( 39 ) is divided by ( 8 ), the quotient is ( 4 ), and the remainder is ( 7 ).
This process illustrates how division can be interpreted not just as finding a single answer but as a way to break down a number into more manageable parts, confirming the division’s integrity through the relationship defined by the division algorithm.