Find the remainder when 11
7
+9 is divided by 10.
- A1
- B0
- C3
- D2
Solution & Step-by-step Explanation
To find the remainder when an expression is divided by 10, we evaluate the expression modulo 10.
Let's simplify 11(mod10):
11≡1(mod10)
Therefore:
11
7
≡1
7
≡1(mod10)
Now substitute this back into our expression:
11
7
+9≡1+9(mod10)
11
7
+9≡10(mod10)
Since 10 is perfectly divisible by 10, the remainder is 0:
10≡0(mod10)
Let's simplify 11(mod10):
11≡1(mod10)
Therefore:
11
7
≡1
7
≡1(mod10)
Now substitute this back into our expression:
11
7
+9≡1+9(mod10)
11
7
+9≡10(mod10)
Since 10 is perfectly divisible by 10, the remainder is 0:
10≡0(mod10)