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Answer :
To divide [tex]$679$[/tex] by [tex]$4$[/tex], we want to find how many whole times [tex]$4$[/tex] can fit into [tex]$679$[/tex] and what is left over. This is equivalent to writing
[tex]$$679 = 4 \times (\text{quotient}) + \text{remainder},$$[/tex]
where the remainder is less than [tex]$4$[/tex].
Step 1: Determine the quotient.
We look for a number [tex]$q$[/tex] such that
[tex]$$4 \times q \le 679.$$[/tex]
If we try [tex]$q = 169$[/tex], we compute
[tex]$$4 \times 169 = 676.$$[/tex]
Since [tex]$676$[/tex] is less than or equal to [tex]$679$[/tex], [tex]$169$[/tex] is a good candidate for the quotient.
Step 2: Compute the remainder.
Subtract the product from [tex]$679$[/tex] to find the remainder:
[tex]$$\text{remainder} = 679 - 676 = 3.$$[/tex]
Since [tex]$3$[/tex] is less than [tex]$4$[/tex], this is the valid remainder.
Verification:
We can check our work:
[tex]$$679 = 4 \times 169 + 3 = 676 + 3 = 679.$$[/tex]
The calculation is correct.
Thus, the result of dividing [tex]$679$[/tex] by [tex]$4$[/tex] is a quotient of [tex]$169$[/tex] with a remainder of [tex]$3$[/tex].
[tex]$$679 = 4 \times (\text{quotient}) + \text{remainder},$$[/tex]
where the remainder is less than [tex]$4$[/tex].
Step 1: Determine the quotient.
We look for a number [tex]$q$[/tex] such that
[tex]$$4 \times q \le 679.$$[/tex]
If we try [tex]$q = 169$[/tex], we compute
[tex]$$4 \times 169 = 676.$$[/tex]
Since [tex]$676$[/tex] is less than or equal to [tex]$679$[/tex], [tex]$169$[/tex] is a good candidate for the quotient.
Step 2: Compute the remainder.
Subtract the product from [tex]$679$[/tex] to find the remainder:
[tex]$$\text{remainder} = 679 - 676 = 3.$$[/tex]
Since [tex]$3$[/tex] is less than [tex]$4$[/tex], this is the valid remainder.
Verification:
We can check our work:
[tex]$$679 = 4 \times 169 + 3 = 676 + 3 = 679.$$[/tex]
The calculation is correct.
Thus, the result of dividing [tex]$679$[/tex] by [tex]$4$[/tex] is a quotient of [tex]$169$[/tex] with a remainder of [tex]$3$[/tex].
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