Task 1
What time is 5 hours after 10 o'clock?
15 ≡ 3 mod 12
What time is 9 hours after 4 o'clock?
13 ≡ 1 mod 12
What time is 13 hours after 6 o'clock?
19 ≡ 7 mod 12
What time is 20 hours after 5 o'clock?
25 ≡ 1 mod 12
What time is 36 hours after 2 o'clock?
38 ≡ 2 mod 12
Task 2
2+3≡ 5 mod 7
5+2≡ 0 mod 7
6+6≡ 5 mod 7
4×2≡ 1 mod 7
3×3≡ 2 mod 7
Task 3
2−5≡ 4 mod 7
1−2≡ 6 mod 7
Task 4
What additions could be used instead of these subtractions when working modulo 7?
−1 ≡6
−3 ≡4
−5 ≡ 2
−6 ≡1
Task 5
20≡ 6 mod 7
32≡ 4 mod 7
50≡ 1 mod 7
91≡ 0 mod 7
If I know that x≡3 mod 7 then what values could x be?
10,13,16,19,22...
Can you find a general expression for x?
x=3y+7
If I know that x≡a mod 7 then can you find a general expression for x?
x=ay+7
https://nrich.maths.org/14856
Task 6
Thursday 31≡ 3 mod 7 Monday-Tuesday-Wednesday-Thursday
Saturday 268 ≡ 2 mod 7 Thursday-Friday-Saturday
Sunday 366≡ 2 mod 7 Friday-Saturday-Sunday
Professor Pat’s BirthDay:
Today is friday 21/5/2021
My Birthday is on 25/1/2022
Tuesday 249 ≡ 4 mod 7 Friday-Saturday-Sunday-Monday-Tuesday
Professor Andrew’s BirthDay:
Today is friday 21/5/2021
My Birthday is on 28/1/2022
Friday 252 ≡ 0 mod 7 Friday