Back to Basics
Basic Arithmetic
Operations
Table of contents
Long Addition
3
Long Subtraction
4
Long Multiplication
5
Long Division
7
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2
Long Addition
237+80+125=?
1. Write the numbers in the exercise vertically.
237
+ 80
+ 125
2. Summarize each column separately- starting with the units digits. In case that the sum
of any column is larger than nine pass the tens digit to the next column to the left and
so forth.
2.1. Begin with the units' column. 5+0+7=12. The digit 2 is written below, and the
digit 1 is moving to the tens column.
1
237
+ 80
+ 125
2
2.2. Continue with the tens' column: 1+3+8+2=14. The 4 is written below and the
digit 1 is moving to the hundreds. Do the same with the hundreds column:
1+2+1=4.
11
+ 237
+ 80
125
442
3. Another technique for long addition is separating each number to small numbers
which are easier to calculate: Thus, 237= (200+30+7), 125= (100+20+5), and
rearranging the numbers according to their numerical attribution:
(200+100) + (80+20+30) + (7+5) = 300+130+12=442
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3
Long Subtraction
4252 - 823 = ?
1. Write the numbers in the exercise vertically.
4252
- 823
2. Subtract each column separately- starting with the units digits.
2.1. In case the figure of the first number is smaller than the second one we
will "borrow" 1 ten from the tens and add it to the units.
3. Continue to subtract the tens, the hundreds etc the same way.
We will begin with the units' column. Since 2 is smaller than 3 we need to "lend" 1 from
the tens. So we will get 12-3=9. We will write the 9 below. Now we are left with 4 at the
tens, 4-2=2. The hundreds are left the same (2-0=2).
(5-1)
4252
- 823
9
→
424x
- 82x
29
→
→
3xxx
- xxx
3429
→
(4-1)
42xx
- 8xx
429
In conclusion:
4252
- 823
3429
Another technique for long subtraction is separating each number to small numbers
which are easier to calculate:
For example:
2252-823=?
2252=2200 + 40 + 12; 823 = 800 + 20 + 3
→ (2200-800) + (40-20) + (12-3) = 1400 + 20 + 9 = 1429.
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4
Long Multiplication
141x 73 = ?
1. Write the numbers in the exercise vertically.
141
x 73
2. Multiply each of the digits of the first (upper) number by the units' digit of the second
(lower) number. Write the product below.
2.1. For any product larger than 9, write the units digit, and carry other digits
to the next multiplication.
3. Multiply each of the digits of the first (upper) number by the tens digit of the second
(lower) number. Write a zero digit under the units' column, and begin writing the
product under the tens column, and so forth.
First step – multiplication with the units' digit of the lower number.
141
x 73
3
carry 1
141
x 73
23
1
141
x 73
(3+1)23
After multiplying with the lower number's units' digit:
141
x 73
423
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Second step – multiplication with the tens' digit of the lower number. Mark it by writing
zero beneath the units' digits column. Don't forget, In case the product of one column is
double digit number, write the units digit below, and the tens digit above the next column
(one column to the left). After multiplying the next digit, add the tens digit to the product
from the last multiplication.
141
x 73
423
0
→
carry 2
141
x 73
423
870
141
x 73
423
70
2
→
141
x 73
423
(7+2)870
After multiplying with the lower number's tens' digit:
141
x 73
423
9870
4. When all multiplications are over, add the results by long addition.
141
x 73
423
+ 9870
10293
Another technique for long multiplication is separating one of the numbers to small
numbers which are easier to calculate by creating "small" multiplication exercises:
For example:
16×12 =?
16×12 = 16 ×(10 + 2) = 16×10 + 16×2 = 160 + 32 = 192
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6
Long Division
1980:15 = ?
1. Write the numbers in long division form.
15 1980 =
2. We will start by checking whether the left digit of the dividend number is bigger or
equal to the one of the divisor.
2.1. If the answer is "yes"- divide the digits and write the quotient above
(ignore the remainder if there is one).
2.2. If the answer is "no" - write 0 above the number and combine the next
digit to get a two digit number.
01
15 1980
3. Multiply the result above the line by the divisor. Write the product under the left
digits and then subtract it from the left initial number accordingly.
01
15 1980
-15
480
4. Add the digit right of the dividend number to the result from the last stages (the 8 to
the 4) so that you'll get a two digit number. Continue to divide this number the
same way as steps 2 and 3:
013
15 1980
-15
480
- 45
30
48:15 = 3 (rem 3)
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5. The exercise is done when the result of the subtraction in zero.
0132
15 1980
-15
480
- 45
30
- 30
0
30:15 = 2
The solution is the number received above the line: 132.
Another technique for long division, especially when the divisor is relatively small, is by
dividing the dividend number to small numbers which are easier to calculate.
For instance: 192:3 =?
192:3= (180:3 + 12:3) = (60+4) = 64
Tip
It is worth knowing, that in the case of a multiple choice test you can transfer any long
division exercise to a multiplication one. We can do so by multiplying the divisor by
each one of the answer choices, and examine whether it leads to the divided number
that appears in the original question or not, e.g:
11 242 = ?
A. 10
B. 20
C. 12
D. 22
E. 24
You can always eliminate by performing multiplications:
11x10 = 110 ☒
11x20 = 220 ☒
11x12 = 132 ☒
11x22 = 242 ☑
division.
D is the correct answer, and we managed not to practice long
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