Answer :
To solve this problem, we need to determine the remainder when 181 is divided by 7. We are given two helpful pieces of information involving similar calculations:
- When [tex]86 \div 7[/tex] is performed, the remainder is 2.
- When [tex]95 \div 7[/tex] is performed, the remainder is 4.
Let's verify these calculations first:
For [tex]86 \div 7[/tex]:
- [tex]86 \div 7 = 12[/tex] remainder [tex]2[/tex] because [tex]12 \times 7 = 84[/tex] and [tex]86 - 84 = 2[/tex].
For [tex]95 \div 7[/tex]:
- [tex]95 \div 7 = 13[/tex] remainder [tex]4[/tex] because [tex]13 \times 7 = 91[/tex] and [tex]95 - 91 = 4[/tex].
Now, given that [tex]86 + 95 = 181[/tex], we need to find the remainder when 181 is divided by 7.
Since
[tex]86 \equiv 2 \pmod{7}[/tex]
and
[tex]95 \equiv 4 \pmod{7}[/tex],
when we add these two congruences together,
[tex]86 + 95 \equiv 2 + 4 \pmod{7}[/tex]
which simplifies to:
[tex]181 \equiv 6 \pmod{7}[/tex].
Thus, the remainder when [tex]181[/tex] is divided by [tex]7[/tex] is [tex]6[/tex].
Therefore, the answer is that [tex]181 \div 7[/tex] has a remainder of [tex]6[/tex].
