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MULTIPLICATION FACTS
Knowing your multiple facts quickly makes your life easy!
0 times any number is 0, so no need to study those. 1 times any number is that number, so no need to study those either.
10 times any number: you just add a zero to the number. 11 times any single-digit number is that number twice. Both of those are easy.
When you think about it, there are only 36 facts you really need to know well!
WHEN YOU LOOK AT HOW THE FACTS ARE LISTED BELOW, IT'S NOT SO BAD.
STUDY THESE FACTS!
FIND THE ONES YOU DON'T KNOW WELL AND PRACTICE THOSE.
DO ONE OR TWO FACTS PER DAY.
BE POSITIVE! YOU CAN DO IT!
Twos
2 × 2 = 4
2 × 3 = 6
2 × 4 = 8
2 × 5 = 10
2 × 6 = 12
2 × 7 = 14
2 × 8 = 16
2 × 9 = 18
Threes
3 × 3 = 9
3 × 4 = 12
3 × 5 = 15
3 × 6 = 18
3 × 7 = 21
3 × 8 = 24
3 × 9 = 27
Fours
4 × 4 = 16
4 × 5 = 20
4 × 6 = 24
4 × 7 = 28
4 × 8 = 32
4 × 9 = 36
Fives
5 × 5 = 25
5 × 6 = 30
5 × 7 = 35
5 × 8 = 40
5 × 9 = 45
Sixes
6 × 6 = 36
6 × 7 = 42
6 × 8 = 48
6 × 9 = 54
Sevens
7 × 7 = 49
7 × 8 = 56
7 × 9 = 63
Eights
8 × 8 = 64
8 × 9 = 72
Nines
9 × 9 = 81
DIVISIBILITY RULES
The most useful rules you should memorize to make your life easy for division and when working with fractions:
2: The last digit is an even number (0, 2, 4, 6, or 8).
3: The sum of all the digits is divisible by 3.
4: The number formed by the last two digits is divisible by 4.
5: The last digit is 0 or 5.
6: The number is divisible by both 2 and 3.
9: The sum of all the digits is divisible by 9.
10: The last digit is 0.
More complicated and difficult to remember rules, so refere to them as needed:
7: Double the last digit and subtract it from the remaining truncated number; if the result is divisible by 7 (including 0), the original number is too.
8: The number formed by the last three digits is divisible by 8.
11: The alternating sum of the digits (subtracting and adding alternating digits) is 0 or divisible by 11.
12: The number is divisible by both 3 and 4.