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Gain confidence and improve speed by practicing new multiplication methods.
Tips and tricks for calculations involving multiplication.
- General tips to get the ball rolling.
Since every multiplication has a twin, it may help to switch the numbers in order to arrange a more familiar mathematical expression. Six times five for example, may be simpler than five times six.
If the second number is quite large, multiply by the closest number that has units digit equal to zero. Then add or subtract the difference.
Example: 14×38
Worked answer:
14×40=560
560-14-14=532
Ignore the zeros, and add them back at the end.
Example: 110×80
Worked answer:
11×8=88
Give or take a few decimals.
Ignore the decimals, and add them back at the end.
Example: 1.5×2.5
Worked answer:
15×25=375
A ballpark estimate is usually required.
1.5×2.5 is definitely less than ten, which means there is no tens digit in the answer.
Adding back the decimal gives 3.75.
Create more groups and work with smaller numbers.
Example: 68×6
Worked answer:
Break up the larger number, 68, into two numbers, 60 and 8.
(60×6)+(8×6)
360+48=408.
- Case by case.
Any number multiplied by zero is zero.
Any number multiplied by one is the same number.
Add the number to itself.
Double the number twice.
Example: 4×16
Worked answer:
2×16=32
2×32=64
Method 1
An easy way to multiply by five is to first multiply by ten, and then divide the product by two, or vice versa.
With odd numbers, start with multiplication; this makes the number even and easier to divide by two.
Example 1: 535
First multiply by ten and then divide by two.
Worked answer:
10×535=5,350
5,350÷2=2,675
Example 2: 482
First divide by two and then multiply by ten.
Worked answer:
482÷2=241
241×10=2,410
Method 2
Count by fives.
Example: 5×6
To multiply six by five, count by five six times.
Worked answer:
5,10,15,20,25,30
Method 3
Even numbers - halve the number and add a zero.
Example: 5×44
Worked answer:
44÷2=22
Adding a zero makes 220.
Method 4
Odd numbers - subtract 1, halve the result and then make 5 the units digit.
Example: 5×43
Worked answer:
43-1=42
42÷2=21
Adding 5 makes 215.
Note: When multiplying by five, the last digit is always five or zero.
An easier way to multiply by six, is to multiply by three, and then by two.
Example: 6×133
Worked answer:
3×133=399
2×399=798
Note: Multiplying any even number by six will end in the same digit (6×8=48, 6×12=72, 6×14=84).
Method 1
Calculate the product of the previous multiple. Then add ten and subtract two.
Example: 8×13
Worked answer:
8×12=96
96+10=106
106-2=104
Method 2
Multiply by more convenient multiples of two.
Example: 8×17
Worked answer:
2×17=34
4×34=136
Method 1
First multiply by ten, and then subtract the original number.
Example: 9×442
Worked answer:
10×442=4,420
4,420-442=3,978
Method 2
Bring out both hands and extend all fingers. Fold the finger which is being multiplied by nine.
Example: 9×4
Fold the fourth finger
There are 3 fingers to the left and 6 to the right, therefore the answer is 36.
This method works for numbers up until 9×10.
Note: The sum of the digits of a two-digit number, where 9 is one of its factors, will always equal 9.
Example 1: 54
54=9×6
5+4=9
Example 2: 63
63=9×7
6+3=9
99 (9x11), is an exception, since 9+9=18
Method 1
For numbers up until nine simply repeat the number.
Example:
11×8=88
Method 2 - for two digit numbers.
First add the number's digits.
In case of a single digit place it between the first and last digits of the number.
Example: 11×52
5+2=7
5 7 2
If the result is a double digit:
Step 1: Place the units digit between the first and last digits of the number.
Step 2: Add the tens digit to the leftmost digit.
Example: 11×98
9+8=17
978
9+1 7 8
1,078
Method 3
Add two digits at a time and proceed from right to left.
Example: 11×938,421
1=1; 1
1+2=3; 31
2+4=6; 631
4+8=12; 2631
8+3=11 (+1 carried over); 22631
9+3=12 (+1 carried over); 322631
9=9 (+1 carried over); 10322631
10,322,631
Note: The order is from right to left, because if the sum is greater than nine, the remainder gets carried over to the number on its left.
Method 4
Similar to method 3, this time however, include a zero to the left of the number.
Start from the right. For each digit, add the digit to its right, and place it underneath the same number.
Carry over the tens digit of any double digit.
Example: 11×158,749
The rightmost 9 remains 9 because there is no number to its right. The second number becomes 13 (4+9=13); write down 3 and carry over one.
0158749
1746239
First multiply by 10, and then add the original number twice.
Example: 12×156
10×156=1,560
1,560+156+156=1,872
Method 1
First multiply by ten, then by three, and add the two together.
Example: 13×14
10×14=140
3×14=42
140+42=182
Method 2
First space out the number and place the sum of the digits in the middle. If the sum of the digits have double digits, then leave the unit digit in the middle and add the tens digit to the leftmost number. Then add double the original number to get the answer.
Example 1: 13×26
2__6
2+6=8
2 8 6
26×2=52
286+52=338
Example 2: 13×48
4__8
4+8=12 (the sum of the digits has double digits.)
4 12 8
5 2 8 (the +1 in 12 was carried over to the left)
48×2=96
528+96=624
Multiply by two and then by seven, or vice versa.
Example 1: 14×7
7×7=49
2×49=98
Example 2: 14×15
2×15=30
7×30=210
First multiply by ten, divide that number by two, then add it back to the first result.
Example: 15×13
10×13=130
130÷2=65
130+65=195
Method 1
Multiply the number four times by two.
Example: 16×14
2×14=28
2×28=56
2×56=112
2×112=224
Method 2
For the first part, multiply the number by ten. For the second part, halve the number, and then multiply by ten. Add all three results together.
Example: 16×18
10×18=180
18÷2=9
10×9=90
180+90+18=288
Multiply the number separately by ten and then by seven. Add both results together.
Example: 17×15
10×15=150
7×15=105
150+105=255
Multiply the number separately by twenty and then by two. Subtract the second number from the first.
Example: 18×17
20×17=340
2×17=34
340-34=306
First multiply by twenty and then subtract the original number.
Example: 19×13
20×13=260
260×13=247
First multiply by eight, and then multiply that result by three.
Example: 24×8
8×8=64
64×3=192
Add two zeros to the multicand, then divide twice by two.
Example: 25×135
13,500
13,500÷2=6,750
6,750÷2=3,375
Multiply by thirty and subtract three times the original number.
Example: 27×9
30×9=270
270−27=243
Multiply by 50 and subtract 5 times the original number.
Example: 45×15
50×15=750
750−75=675
Multiply by nine, and affix a zero on right (units position).
Example: 90×14
9×14=126
1,260
First multiply by one hundred, and then subrtact twice the original number.
Example: 98×14
100×14=1,400
14×2=28
1,400-28=1,372
Method 1
First multiply by one hundred, and then subtract the original number.
Example: 99×15
100×15=1,500
1,500-15=1,485
Method 2
Applies to one and two digit numbers.
Step 1: Subtract one from the number.
Step 2: Subtract the number from 100.
Step 2: Place step 2 to the right of step 1.
Example: 99×15
15-1=14
100-15=85
1,485
Method for one digit numbers:
Write the same number twice, with zero in the middle
Example: 101×5
505
Method for two digit numbers:
Write the same number twice.
Example: 101×51
5,151
First add three zeros and divide by eight.
Make the division in steps; halve both the numerator and the denominator, step by step.
Example 1: 125×18
18,000÷8
9,000÷4
4,500÷2=2,250
Example 2: 125×124
124,000÷8
62,000÷4
31,000÷2=15,500
Step 1: For each digit find the difference between that digit and five.
Step 2: Add both numbers together.
Step 3: For each previous difference, find the difference with five.
Step 4: Multiply both numbers together.
Step 5: Place the first result before the second result.
Example: 8×6
8−5=3
6−5=1
3+1=4
5−3=2
5−1=4
2×4=8
48
Step 1: Place the higher number over the lower number.
Step 2: Add top and bottom numbers, ignoring the bottom tens digit.
Step 3: Add zero in the position of the units digit.
Step 4: Multiply the units digits of the top and bottom numbers in step 1.
Step 5: Add the results of step 3 and 4.
Example 1: 14×13
14
13
14+3=17
170
3×4=12
170+12=182
Example 2: 18×17
18
17
18+7=25
250
8×7=56
250+56=306
Step 1: Multiply the units digits with each other.
Step 2: Cross multiply and add the two products.
Step 3: Multiply the tens digits with each other
Note: Whenever a number is greater than nine, carry over the leftmost digit.
Example 1: 15×18
15
18
5×8=40; carry over 4
(1×8)+(1×5)+4=17; carry over the 1
(1×1)=1 +1=2
270
Example 2: 13×67
13
67
3×7=21; carry over 2
(1×7)+(3×6)+2=277; carry over the 2
(1×6)=6 +2=8
871
Calculate the square root of the in-between number and then subtract one.
Example 1: 19×21
202=400
400−1=399
Example 2: 29×31
302=900
900−1=899
Step 1: For each factor calculate digit sum.
Step 2: Multiply the two digit sums and calculate a new digit sum from the product.
Step 3: Calculate the digit sum of the answer being verified.
If step 2 and step 3 are equal then the answer is probably correct. However if they are not equal, then the answer is definitely wrong.
Note: For all steps, in calculating digit sums, continue adding until a one-digit digit sum is made.
Example: 44×62=2,728
44; digit sum is 4+4=8
62; digit sum is 6+2=8
8×8=64; digit sum is 6+4=10, 1+0=1
2,728; digit sum is 2+7+2+8=19, 1+9=10, 1+0=1
The last two results are equal, therefore 44×62=2,728 is probably correct.
When one number is a decimal, halve the whole number, and double the decimal.
Example: 4×3.5
2×7=14