The answer to a multiplication problem is called PRODUCT
The numbers being multiplied together are called FACTORS
I will be going through the facts in the order in which I suggest you learn them.
Once you learn all the tricks, there are really only 23 facts to memorize.
11X11=121
11x12=132
12X9=108
3X12=36
4X12=48
6X12=72
7X12=84
8X12=96
12X12=144
3X3=9
4X4=16
7X7=49
8X8=64
3X4=12
6X7=42
7X8=56
6X4=24
4X7=28
4X8=32
3X6=18
3X7=21
3X8=24
8X6=48
Multiply by zero
The product (answer) is always zero
0X0=0
0X1=0
0X2=0
0X3=0
0X4=0
0X5=0
0X6=0
0X7=0
0X8=0
0X9=0
0X10=0
0X11=0
0X12=0
1X0=0
2X0=0
3X0=0
4X0=0
5X0=0
6X0=0
7X0=0
8X0=0
9X0=0
10X0=0
11X0=0
12X0=0
Multiply by one
The product (answer) is always the factor being multiplied to one
1X0=0
1X1=1
1X2=2
1X3=3
1X4=4
1X5=5
1X6=6
1X7=7
1X8=8
1X9=9
1X10=10
1X11=11
1X12=12
0X1=0
2X1=2
3X1=3
4X1=4
5X1=5
6X1=6
7X1=7
8X1=8
9X1=9
10X1=10
11X1=11
12X1=12
Multiply by ten
The product (answer) is the factor being multiplied to ten with a zero after it.
10X0=0 (zero multiplied by another factor always equals zero)
10X1=10 (write 1 then put a zero after the 1)
also, remember when multiplying 1 and another factor (number) the product (anwser) is the other factor (other number)
10X2=20 (write 2 then put a zero after the 2)
10X3=30 (write 3 then put a zero after the 3)
10X4=40 (write 4 then put a zero after the 4)
10X5=50 (write 5 then put a zero after the 5)
10X6=60 (write 6 then put a zero after the 6)
10X7=70 (write 7 then put a zero after the 7)
10X8=80 (write 8 then put a zero after the 8)
10X9=90 (write 9 then put a zero after the 9)
10X10=100 (write 10 then put a zero after the 10)
10X11=110 (write 11 then put a zero after the 11)
10X12=120 (write 12 then put a zero after the 12)
0X10=0 (zero multiplied by another factor always equals zero)
1X10=10 (write 1 then put a zero after the 1)
also, remember when multiplying 1 and another factor (number) the product (answer) is the other factor (other number)
2X10=20 (write 2 then put a zero after the 2)
3X10=30 (write 3 then put a zero after the 3)
4X10=40 (write 4 then put a zero after the 4)
5X10=50 (write 5 then put a zero after the 5)
6X10=60 (write 6 then put a zero after the 6)
7X10=70 (write 7 then put a zero after the 7)
8X10=80 (write 8 then put a zero after the 8)
9X10=90 (write 9 then put a zero after the 9)
11X10=110 (write 11 then put a zero after the 11)
12X10=120 (write 12 then put a zero after the 12)
When multiplying by 11 if one of the other factors is 1-9 - to write the product, write the other factor twice
11X0=0 (zero multiplied by another factor always equals zero)
11X1=11 (write 1 and then write 1 again)
also, remember when multiplying 1 and another factor (number) the product (answer) is the other factor (other number)
11X2=22 (write 2 and then write 2 again)
11X3=33 (write 3 and then write 3 again)
11X4=44 (write 4 and then write 4 again)
11X5=55 (write 5 and then write 5 again)
11X6=66 (write 6 and then write 6 again)
11X7=77 (write 7 and then write 7 again)
11X8=88 (write 8 and then write 8 again)
11X9=99 (write 9 and then write 9 again)
11X10=110 (multiply by 10 trick - write 11 then put a zero after the 11)
11X11=121 (10X11=110 110+11=121 so 11X11=121)
11X12=132 (memorize OR use rules for multiplying double digit numbers)
0X11=0 (zero multiplied by another factor always equals zero)
1X11=11 (write 1 and then write 1 again)
also, remember when multiplying 1 and another factor (number) the product (answer) is the other factor (other number)
2X11=22 (write 2 and then write 2 again)
3X11=33 (write 3 and then write 3 again)
4X11=44 (write 4 and then write 4 again)
5X11=55 (write 5 and then write 5 again)
6X11=66 (write 6 and then write 6 again)
7X11=77 (write 7 and then write 7 again)
8X11=88 (write 8 and then write 8 again)
9X11=99 (write 9 and then write 9 again)
10X11=110 (multiply by 10 trick - write 11 then put a zero after the 11)
12X11=132 (10X11=110 2X11=22 110+22=132 OR 10X12=120 1X12=12 120+12=132)
Multiply by two
Think of it as an addition doubles problem. Take the factor that is not a two and add it to itself.
2X0=0 (zero multiplied by another factor always equals zero)
2X1=2 (1+1=2)
also, remember when multiplying 1 and another factor (number) the product (answer) is the other factor (other number)
2X2=4 (2+2=4)
2X3=6 (3+3=6)
2X4=8 (4+4=8)
2X5=10 (5+5=10)
2X6=12 (6+6=12)
2X7=14 (7+7=14)
2X8=16 (8+8=16)
2X9=18 (9+9=18)
2X10=20 (10+10=20) also multiply by 10 trick - write 2 then put a zero after the 2
2X11=22 (11+11=22) also multiply by 11 trick - write 2 and then write 2 again
2X12=24 (12+12=24)
0X2=0 (zero multiplied by another factor always equals zero)
1X2=2 (1+1=2)
also, remember when multiplying 1 and another factor (number) the product (answer) is the other factor (other number)
3X2=6 (3+3=6)
4X2=8 (4+4=8)
5X2=10 (5+5=10)
6X2=12 (6+6=12)
7X2=14 (7+7=14)
8X2=16 (8+8=16)
9X2=18 (9+9=18)
10X2=20 (10+10=20) also (multiply by 10 trick - write 2 then put a zero after the 2)
11X2=22 (11+11=22) also multiply by 11 trick - write 2 and then write 2 again
12X2=24 (12+12=24)
This is easy if you know how to tell time on an analog clock.
The products are the numbers when you count by five starting at five
5X0=0 (zero multiplied by another factor always equals zero)
5X1=5 when multiplying 1 and another factor (number) the product (answer) is the other factor (other number)
5X2=10 (Take the factor that is not a two and add it to itself. 5+5=10)
5X3=15
5X4=20
5X5=25
5X6=30
5X7=35
5X8=40
5X9=45
5X10=50 (tens trick - write 5 then put a zero after the 5)
5X11=55 (elevens trick - write 5 and then write 5 again)
5X12=60
0X5=0 (zero multiplied by another factor always equals zero)
1X5=5 when multiplying 1 and another factor (number) the product (answer) is the other factor (other number)
2X5=10 (Take the factor that is not a two and add it to itself. 5+5=10)
3X5=15
4X5=20
6X5=30
7X5=35
8X5=40
9X5=45
10X5=50 (tens trick - write 5 then put a zero after the 5)
11X5=55 (elevens trick - write 5 and then write 5 again)
12X5=60
Multiply by nine
This one has lots of tricks. Use the one that is easiest and fastest for you to find the answer.
Trick 1 - use your hands
look at your hands palms down
start with your left hand
9X1 put one finger down (pinky) 9 fingers are left the answer is 9
9X2 count two fingers: pinky and ring finger; put ring finger down; 1 finger up, space, 8 fingers up and the answer is 18
9X3 count three fingers: pinky, ring finger and middle finger; put the middle finger down; 2 fingers up, space, 7 fingers up and the answer is 27
9X4 count four fingers: pinky, ring finger, middle finger, and pointer finger; put the pointer finger down; 3 fingers up, space, 6 fingers and the answer is 36
9X5 count five fingers: pinky, ring finger, middle finger, pointer finger, and thumb; put the thumb down; 4 fingers up, space, 5 fingers up and the answer is 45
9X6 count six fingers: pinky, ring finger, middle finger, pointer finger, thumb, and thumb; put the second thumb down; 5 fingers up, space, 4 fingers up and the answer is 54
9X7 count seven fingers: pinky, ring finger, middle finger, pointer finger, thumb, thumb and pointer finger; put the pointer finger down; 6 fingers up, space, 3 fingers up and the answer is 63
9X8 count eight fingers: pinky, ring finger, middle finger, pointer finger, thumb, thumb, pointer finger and middle finger; put the middle finger down; 7 fingers up, space, 2 fingers up and the answer is 72
9X9 count nine fingers: pinky, ring finger, middle finger, pointer finger, thumb, thumb, pointer finger, middle finger, and ring finger; put the ring finger down; 8 fingers up, space, 1 fingers up and the answer is 81
9x10 count nine fingers: pinky, ring finger, middle finger, pointer finger, thumb, thumb, pointer finger, middle finger, ring finger, and pinky; put the pinky down; 9 fingers up, space, no fingers up and the answer is 90
Trick 2 - look at the products
look at the tens place, it goes down 0 to 9
look at the ones place, it goes down 9 to 0 the opposite of the tens place
9X1= 9
9X2= 18
9X3= 27
9X4= 36
9X5= 45
9X6= 54
9X7= 63
9X8= 72
9X9= 81
9X10=90
Trick 3 - look at the products
this builds off of trick 2
Notice the digits in the products each add up to 9
9X1= 9 (0+9=9)
9X2= 18 (1+8=9)
9X3= 27 (2+7=9)
9X4= 36 (3+6=9)
9X5= 45 (4+5=9)
9X6= 54 (5+4=9)
9X7= 63 (6+3=9)
9X8= 72 (7+2=9)
9X9= 81 (8+1=9)
9X10=90 (9+0=9)
Now here is the trick - take 1 away from the factor that is not nine, write down that number in the tens place then take the number you put in the tens place and subtract it from 9 and that is what you put in the ones place
9X1= 9 (1-1=0 so 0 or nothing is in the tens place 9-0=9 so 9 is in the ones place)
9X2= 18 (2-1=1 so 1 is in the tens place 9-1=8 so 8 is in the ones place)
9X3= 27 (3-1=2 so 2 is in the tens place 9-2=7 so 7 is in the ones place)
9X4= 36 (4-1=3 so 3 is in the tens place 9-3=6 so 6 is in the ones place)
9X5= 45 (5-1=4 so 4 is in the tens place 9-4=5 so 5 is in the ones place)
9X6= 54 (6-1=5 so 5 is in the tens place 9-5=4 so 4 is in the ones place)
9X7= 63 (7-1=6 so 6 is in the tens place 9-6=3 so 3 is in the ones place)
9X8= 72 (8-1=7 so 7 is in the tens place 9-7=2 so 2 is in the ones place)
9X9= 81 (9-1=8 so 8 is in the tens place 9-8=1 so 1 is in the ones place)
9X10=90 (10-1=9 so 9 is in the tens place 9-9=0 so 0 is in the ones place)
All the nine facts and tricks
9X0=0 (use a nine trick or zero trick)
9X1=9 (use a nine trick or the one trick)
9X2=18 (use a nine trick or the two trick)
9X3=27
9X4=36
9X5=45 (use a nine trick or the five trick (counting by five or memorizing telling time on an analog) clock)
9X6=54 (9X5=45 switch the digits (numbers) in the product (answer) and 9X6=54)
9X7=63
9X8=72
9X9=81
9X10=90 (use a nine trick or the ten trick)
9X11=99 (use a nine trick or the eleven trick)
9X12=108 (11X9=99 99+9=108 notice the digits all add up to 9)
0X9=9 (use a nine trick or zero trick)
1X9=9 (use a nine trick or the one trick)
2X9=18 (use a nine trick or the two trick)
3X9=27
4X9=36
5X9=45 (use a nine trick or the five trick (counting by five or memorizing telling time on an analog clock)
6X9=54
7X9=63
8X9=72
10X9=90 (use a nine trick or the ten trick)
11X9=99 (use a nine trick or the eleven trick)
12X9=108 (11X9=99 99+9=108 notice the digits all add up to 9)
Multiply by twelve
Use the eleven fact and add the other factor to the product of the eleven fact.
12X0=0 (0X11=0 0+0=0 so 12X0=0 OR use the times zero trick)
12X1=12 (1X11=11 11+1=12 so 12X1=12 OR use the times one trick)
12X2=24 (2X11=22 22+2=24 so 12X2=24 OR use the times two trick 12+12=24)
12X3=36 (3X11=33 33+3=36 so 12X3=36)
12X4=48 (4X11=44 44+4=48 so 12X4=48)
12X5=60 (5X11=55 55+5=60 so 12X5=60 or use the times five trick)
12X6=72 (6X11=66 66+6=72 so 12X6=72)
12X7=84 (7X11=77 77+7=84 so 12X7=84)
12X8=96 (8X11=88 88+8=96 so 12X8=96)
12X9=108 (9X11=99 99+9=108 so 12X9=108 or use a times nine trick)
12X10=120 (10X11=110 110+10=120 so 12X10=120 or use the times ten trick)
12X11=132 (11X11=121 121+11=132 so 12X11=132 OR 12X10=120 1X12=12 120+12=132)
12X12=144 (12X11=132 132+12=144 so 12X12=144 OR 10x12=120 2X12=24 120+24=144 so 12X12=144)
0X12=0 (0X11=0 0+0=0 so 12X0=0 OR use the times zero trick)
1X12=12 (1X11=11 11+1=12 so 12X1=12 OR use the times one trick)
2X12=24 (2X11=22 22+2=24 so 12X2=24 OR use the times two trick 12+12=24)
3X12=36 (3X11=33 33+3=36 so 12X3=36)
4X12=48 (4X11=44 44+4=48 so 12X4=48)
5X12=60 (5X11=55 55+5=60 so 12X5=60 or use the times five trick)
6X12=72 (6X11=66 66+6=72 so 12X6=72)
7X12=84 (7X11=77 77+7=84 so 12X7=84)
8X12=96 (8X11=88 88+8=96 so 12X8=96)
9X12=108 (9X11=99 99+9=108 so 12X9=108 or use a times nine trick)
10X12=120 (10X11=110 110+10=120 so 12X10=120 or use the times ten trick)
11X12=132 (11X11=121 121+11=132 so 12X11=132 OR 12X10=120 1X12=12 120+12=132)
0X0=0 (use the times zero trick)
1X1=1 (use the times one trick)
2X2=4 (use the times two trick)
3X3=9 (1X3=3 2X3=6 6+3=9 so 3X3=9)
4X4=16 (4X2=8 8+8=16 so 4X4=16)
5X5=25 (use the times five trick)
6X6=36 (5X6=30 30+6=36 so 6X6=36)
7X7=49 (4X7 + 3X7) (14+14=28 14+7=21 28+21=49)
8X8=64 (5X8=40 40+8=48 2X8=16 48+16=64 so 8X8=64)
9X9=81 (use the times nine trick)
10X10=100 (use the times ten trick)
11X11=121 (10X11=110 110+11=121 so 11X11=121)
12X12=144 (12X11=132 132+12=144 so 12X12=144 OR 10x12=120 2X12=24 120+24=144 so 12X12=144)
Multiply by double plus one factors
0X1=0 (use the times zero trick)
1X2=2 (use the times one trick)
2X3=6 (use the times two trick)
3X4=12 (2X3=6 6+6=12 so 4X3=12)
4X5=20 (use the times five trick)
5X6=30 (use the times five trick)
6X7=42 (5X7=35 35+7=42 so 6X7=42)
7X8=56 (5X7=35 35+7=42 2X7=14 42+14=56 so 8X7=56)
8X9=72 (use the times nine trick)
9X10=90 (use the times ten trick)
10X11=110 (use the times ten trick)
11X12=132 (11X11=121 121+11=132 so 12X11=132 OR 12X10=120 1X12=12 120+12=132)
1X0=0 (use the times zero trick)
2X1=2 (use the times one trick)
3X2=6 (use the times two trick)
4X3=12 (2X3=6 6+6=12 so 4X3=12)
5X4=20 (use the times five trick)
6X5=30 (use the times five trick)
7X6=42 (5X7=35 35+7=42 so 6X7=42)
8X7=56 (5X7=35 35+7=42 2X7=14 42+14=56 so 8X7=56)
9X8=72 (use the times nine trick)
10X9=90 (use the times ten trick)
11X10=110 (use the times ten trick)
12X11=132 (11X11=121 121+11=132 so 12X11=132 OR 12X10=120 1X12=12 120+12=132)
Multiply by four
Use the times two trick product twice.
4X0=0 (use the times zero trick)
4X1=4 (use the times one trick)
4X2=8 (use the times two trick)
4X3=12 (2X3=6 6+6=12 so 4X3=12)
4X4=16 (4X2=8 8+8=16 so 4X4=16)
4X5=20 (use the times five trick)
4X6=24 (2X6=12 12+12=24 so 4X6=24)
4X7=28 (2X7=14 14+14=28 so 4X7=28)
4X8=32 (2X8=16 16+16=32 so 4X8=32)
4X9=36 (use the times nine trick)
4X10=40 (use the times ten trick)
4X11=44 (use the times eleven trick)
4X12=48 (use the times twelve trick)
0X4=0 (use the times zero trick)
1X4=4 (use the times one trick)
2X4=8 (use the times two trick)
3X4=12 (2X3=6 6+6=12 so 4X3=12)
5X4=20 (use the times five trick)
6X4=24 (2X6=12 12+12=24 so 4X6=24)
7X4=28 (2X7=14 14+14=28 so 4X7=28)
8X4=32 (2X8=16 16+16=32 so 4X8=32)
9X4=36 (use the times nine trick)
10X4=40 (use the times ten trick)
11X4=44 (use the times eleven trick)
12X4=48 (use the times twelve trick)
Multiply by three
Use the times one and times two products together.
3X0=0 (use the times zero trick)
3X1=3 (use the times one trick)
3X2=6 (use the times two trick)
3X3=9 (1X3=3 2X3=6 6+3=9 so 3X3=9)
3X4=12 (1X4=4 2X4=8 4+8=12 so 3X4=12 OR use the times four trick: 4X2=8 8+8=16 so 4X4=16)
3X5=15 (1X3=5 2X5=10 5+10=15 so 3X5=15 OR use the times five trick)
3X6=18 (1X6=6 2X6=12 6+12=18)
3X7=21 (1X7=7 2X7=14 7+14=21)
3X8=24 (1X8=8 2X8=16 8+16=24)
3X9=27 (1X9=9 2X9=18 9+18=27 OR use a times nine trick)
3X10=30 (use the times ten trick)
3X11=33 (use the times eleven trick)
3X12=36 (1X12=12 2X12=24 12+24=36 OR use the times twelve trick)
0X3=0 (use the times zero trick)
1X3=3 (use the times one trick)
2X3=6 (use the times two trick)
4X312 (1X4=4 2X4=8 4+8=12 so 3X4=12 OR use the times four trick: 4X2=8 8+8=16 so 4X4=16)
5X3=15 (1X3=5 2X5=10 5+10=15 so 3X5=15 OR use the times five trick)
6X3=18 (1X6=6 2X6=12 6+12=18)
7X3=21 (1X7=7 2X7=14 7+14=21)
8X3=24 (1X8=8 2X8=16 8+16=24)
9X3=27 (1X9=9 2X9=18 9+18=27 OR use a times nine trick)
10X3=30 (use the times ten trick)
11X3=33 (use the times eleven trick)
12X3=36 (1X12=12 2X12=24 12+24=36 OR use the times twelve trick)
Multiply by six
Use the times five trick and then add 6
6X0=0 (use the times zero trick)
6X1=6 (use the times one trick)
6X2=12 (use the times two trick)
6X3=18 (use the times three trick: 1X6=6 2X6=12 6+12=18)
6X4=24 (use the times four trick: 2X6=12 12+12=24 so 4X6=24)
6X5=30 (use the times five trick)
6X6=36 (5X6=30 30+6=36 so 6X6=36)
6X7=42 (5X7=35 35+7=42 so 6X7=42)
6X8=48 (5X8=40 40+8=48 so 6X8=48)
6X9=54 OR use a times nine trick)
6X10=60 (use the times ten trick)
6X11=66 (use the times eleven trick)
6X12=72 ( OR use the times twelve trick)
0X6=0 (use the times zero trick)
1X6=6 (use the times one trick)
2X6=12 (use the times two trick)
3X6=18 (use the times three trick: 1X6=6 2X6=12 6+12=18)
4X6=24 (use the times four trick: 2X6=12 12+12=24 so 4X6=24)
5X6=30 (use the times five trick)
7X6=42 (5X7=35 35+7=42 so 6X7=42)
8X6=48 (5X8=40 40+8=48 so 6X8=48)
9X6=54 OR use a times nine trick)
10X6=60 (use the times ten trick)
11X6=66 (use the times eleven trick)
12X6=72 ( OR use the times twelve trick)
Multiply by eight
Add the products of the times 2 trick and the times 6 trick.
8X0=0 (use the times zero trick)
8X1=8 (use the times one trick)
8X2=16 (use the times two trick)
8X3=24 (use the times three trick: 1X8=8 2X8=16 8+16=24)
8X4=32 (use the times four trick: 2X8=16 16+16=32 so 4X8=32)
8X5=40 (use the times five trick)
8X6=48 (use the times six trick: 5X8=40 40+8=48 so 6X8=48)
8X7=56 (5X7=35 35+7=42 2X7=14 42+14=56 so 8X7=56)
8X8=64 (5X8=40 40+8=48 2X8=16 48+16=64 so 8X8=64)
8X9=72 (5x9=45 45+9=54 2x9=18 54+18=72 OR use a times nine trick)
8X10=80 (use the times ten trick)
8X11=88 (use the times eleven trick)
8X12=96 (5X12=60 60+12=72 2X12=24 72+24=96 so 8X12=96 OR use the times twelve trick)
0X8=0 (use the times zero trick)
1X8=8 (use the times one trick)
2X8=16 (use the times two trick)
3X8=24 (use the times three trick: 1X8=8 2X8=16 8+16=24)
4X8=32 (use the times four trick: 2X8=16 16+16=32 so 4X8=32)
5X8=40 (use the times five trick)
6X8=48 (use the times six trick: 5X8=40 40+8=48 so 6X8=48)
7X8=56 (5X7=35 35+7=42 2X7=14 42+14=56 so 8X7=56)
9X8=72 (5x9=45 45+9=54 2x9=18 54+18=72 OR use a times nine trick)
10X8=80 (use the times ten trick)
11X8=88 (use the times eleven trick)
12X8=96 (5X12=60 60+12=72 2X12=24 72+24=96 so 8X12=96 OR use the times twelve trick)
Multiply by seven
7X0=0 (use the times zero trick)
7X1=7 (use the times one trick)
7X2=14 (use the times two trick)
7X3=21 (use the times three trick 1X7=7 2X7=14 7+14=21)
7X4=28 (use the times four trick: 2X7=14 14+14=28 so 4X7=28)
7X5=35 (use the times five trick)
7X6=42 (use the times six trick: 5X7=35 35+7=42 so 6X7=42)
7X7=49 (4X7 + 3X7) (14+14=28 14+7=21 28+21=49)
7X8=56 (use the times eight trick: 5X7=35 35+7=42 2X7=14 42+14=56 so 8X7=56)
7X9=63 OR use a times nine trick)
7X10=70 (use the times ten trick)
7X11=77 (use the times eleven trick)
7X12 =84 ( OR use the times twelve trick)
0X7=0 (use the times zero trick)
1X7=7 (use the times one trick)
2X7=14 (use the times two trick)
3X7=21 (use the times three trick 1X7=7 2X7=14 7+14=21)
4X7=28 (use the times four trick: 2X7=14 14+14=28 so 4X7=28)
5X7=35 (use the times five trick)
6X7=42 (use the times six trick: 5X7=35 35+7=42 so 6X7=42)
8X7=56 (use the times eight trick: 5X7=35 35+7=42 2X7=14 42+14=56 so 8X7=56)
9X7=63 (use a times nine trick)
10X7=70 (use the times ten trick)
11X7=77 (use the times eleven trick)
12X7=84 (use the times twelve trick)
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