INTEGER OPERATIONS
Addition
When adding numbers together it is important that you place them beneath each other in
the place value columns. For example:
Add together 15, 324, 1596, 2 and 37
1
3
5
1
2
9
3
5
4
6
2
7
Now you can add up each column, starting with the right-hand column. If the total of a
column comes to 9 or more, you need to "carry" the "tens" place value and add it into the
next column.
1
1
3
5
1
2
9
9
3
7
5
4
6
2
7
4
5 + 4 + 6 + 2 + 7 = 24
(Write the 4 in the answer space under that
column and carry the 2 and add it into the
next column)
1 + 2 + 9 + 3 + 2 = 17
(Write the 7 in the answer space under that
column and carry the 1 and add it into the
next column)
3+5+1 = 9
(Write the 9 in the answer space under that
column and there is nothing to carry forward)
Finally there is only the 1 in the last column so write the 1 in the answer space under that
column.
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Updated Feb 2013
Subtraction
When subtracting numbers it is also important that you place them beneath each other in
the place value columns. For example:
Subtract 1635 from 7896.
7 8 9 6
1 6 3 5
Now just as with addition you take one column at a time, working from the right hand side.
7 8 9 6
1 6 3 5
6 2 6 1
7–1=6
8–6=2
9–3 = 6
6–5 = 1
However, sometimes when you subtract, the number on the bottom of a column is larger
then the number above. When this happens, you need to increase the number above by 10,
"borrowing" from the next column on the left.
e.g. Subtract 1973 from 5142
5 1 4 2
1 9 7 3
Taking the column on the right hand side first, we have: 2 - 3
Now you cannot subtract 3 from 2, so we need to increase the 2 to 12, and we do this by
borrowing from the column on the left, decreasing the 4 to 3.
12 - 3 = 9
5 1 3 12
1 9 7 3
9
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Updated Feb 2013
Again we cannot subtract 7 from 3, so we need to increase 3 to 13, by borrowing from the
column on the left, decreasing the 1 to 0.
13 - 7 = 6
5 0 13 12
1 9 7 3
6 9
We cannot subtract 9 from 0, so we need to increase 0 to 10, again "borrowing" from the
column on the left by decreasing 5 to 4.
10 - 9 = 1
4 10 13 12
1 9 7 3
1 6 9
Finally we subtract 1 from 4
4–1 = 3
4 10 13 12
1 9 7 3
3 1 6 9
Multiplication
When multiplying two numbers together place the multiplier beneath the number to be
multiplied, and align them on the right.
 Multiply 341 by 2
3 4 1
2
Start at the right hand side and multiply 1 by 2
12 = 2
3 4 1
2
2
Now move to the left and multiply the next number.
42 = 8
3 4 1
2
8 2
Finally multiply 3 by 2
32 = 6
3 4 1
2
6 8 2
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Updated Feb 2013
More often than not, when you multiply the two numbers together, the product is greater
then 9 and you need to “carry” the digit in the "tens" place into the next column. For
example:
Multiple 976 by 8
Starting at the right hand side we have:
9 7 6
8
6  8 = 48
We place the 8 in the answer space at the right hand side and "carry" the 4 to be added into
the next column.
9 7 6
(4) 8
8
Moving along to the left we next have: 7  8 = 56
However we must add the 4 that we have carried from the previous column. So we have:
56 + 4 = 60
Place the 0 in the answer space and "carry" the 6 to be added into the next column.
9 7 6
(6) (4) 8
0 8
Finally 8  9 = 72 to which we must add the 6 that we have carried.
72 + 6 = 78
9 7 6
(6) (4) 8
7 8 0 8
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Updated Feb 2013
The next step in multiplication is when the multiplier has more than one digit. For example:
Multiply 5146 by 32
5 1 4 6
3 2
Multiply 5146 by 2 as in the previous example
5 1 4 6
2
1 0 2 9 2
Now multiply 5146 by 3, placing the final digit in line underneath the 3 in the multiplier.
5146  3 = 15 438
5 1 4 6
3 2
1 0 2 9 2
15 4 3 8
Finally you add up the two answers
5 1 4 6
3 2
1 0 2 9 2
1 5 4 3 8__
1 6 4 6 7 2
You need to be careful when you come across 0s in the multiplier. For example:
Multiply 1354 by 205
1 3 5 4
2 0 5
Multiply by 5 first, as before.
1 3 5 4
5
6 7 7 0
Now, the next number you have in the multiplier is 0. When you multiply a number by 0 the
answer is 0, so you place 0 in the next answer line under the 0 in the multiplier.
1 3 5 4
0 5
6 7 7 0
0
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Updated Feb 2013
Now multiply by 2 and place the answer with the final number underneath the 2 in the
multiplier as before. You can place it in the second line next to the 0.
1354  2 = 2708
1 3 5 4
2 0 5
6 7 7 0
2 7 0 8 0
Finally add up the two answers.
1 3
2
6 7
2 7 0 8
2 7 7 5
5 4
0 5
7 0
0__
7 0
Division
Division is different from the other three operations, in that you start working from the left
hand side. You write a division as follows:
Divide 7659 by 3
3 7 6 5 9
Take the first digit on the left hand side of the number to be divided into and divide it by 3.
7  3 = 2 with 1 left over
Write the 2 in the answer line above the 7.
Now write the 6 under the 7, and subtract it from 7, leaving 1.
2
3 7 6 5 9
6
1
Bring the next digit in the number being divided into (6) down beside the 1.
2
3 7 6 5 9
6
1 6
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Updated Feb 2013
Now divide 16 by 3.
16  3 = 5 remainder 1
Write the 5 in the next place in the answer
Write the 15 under the 16 and subtract it leaving 1.
2 5
3 7 6 5 9
6
1 6
15
1
Bring down the next digit in the number being divided into (5)
2
3 7
6
1
1
5
6 5 9
6
5
1 5
Divide 15 by 3. 15  3 = 5 no remainder
Write the 5 in the next place
in the answer and write the 15
under the 15, subtract to get 0.
2
3 7
6
1
1
Bring down the 9 and divide it by 3.
6
5
15
15
0
2 5 5 3
3 7 6 5 9
6
1 6
1 5
1 5
1 5
0 9
9
9  3 = 3 no remainder
Write the 3 in the next answer space.
Subtract the 9 from the 9,
leaving no remainder
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Updated Feb 2013
5 5
6 5 9
It is not much different when dividing by a larger number. For example:
Divide 7968 by 32
3 2 7 9 6 8
32 obviously does not divide into 7, but it will divide into 79.
You need to estimate how many times it will divide into it.
79  32  80  30
and 30 will divide into 80 twice.
32  2 = 64 Write the 64 under the 79 and subtract.
Place the 2 in the answer line above the 9.
2
3 2 7 9 6 8
6 4
1 5
Bring down the 6
2
3 2 7 9 6 8
6 4
1 5 6
Estimate how many times 32 will divide into 156.
150  30  5, but 5  30 = 160, which is too big, so try 4
32  4 = 128 which is less than 156
Put 4 into the next place in the answer and subtract 128 from 156
3 2 7
6
1
1
2 4
9 6 8
4
5 6
2 8
2 8
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Updated Feb 2013
Bring down the 8
3 2 7
6
1
1
2
9
4
5
2
2
4
6 8
6
8
8 8
Estimate how many times 32 will divide into 288
300  30 = 10, but 32  10 = 320 which is too big, try 9
32  9 = 288 which is exact.
Place 9 in the last answer position.
2 4 9
3 2 7 9 6 8
6 4
1 5 6
1 2 8
2 8 8
2 8 8
You need to be careful when you bring down a number and find that the next number still
cannot be divided into. For example:
Divide 5565 by 53
5 3 5 5 6 5
53 will divide into 55
1
5 3 5 5 6 5
5 3
2
Bring down the 6
1
5 3 5 5 6 5
5 3
2 6
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Updated Feb 2013
53 will not divide into 26, so you must place a 0 in the next answer place and bring down the
next number.
1 0
5 3 5 5 6 5
5 3
2 6 5
Estimate: 250  50 = 5
53  5 = 265
The final number in the answer is therefore 5.
1 0 5
5 3 5 5 6 5
5 3
2 6 5
2 6 5
Multiplication and division by multiples of 10
When multiplying a number by a multiple of ten, multiply the non-zero digit(s) together and
add the number of 0s at the end, on the right of the number to get your answer.
23  200
23  2 = 46
There are two 0s, so add two 0s to your answer: 4600
1030  400
103  4 = 412
There are three 0s altogether at the end on the right hand sides of the numbers, so the
answer is: 412 000
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Updated Feb 2013
It doesn't matter how many numbers there are, multiply the numbers together and add on
the number of 0s at the end. For example:
20  30  40
2  3  4 = 24
There are 3 0s, so the answer is 24 000
When dividing by a multiple of ten, you count the number of 0s in the divisor, delete the 0s
in the divisor and delete the same number of 0s from the number to be divided into. Now
perform the division. For example:
 Divide 2600 by 20
There is one 0 in 20, so delete one 0 from 2600, giving:
260  2 = 130
 Divide 306 000 by 3000
There are three 0s in the divisor, so delete 3 from both numbers, giving:
306  3 = 102
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Updated Feb 2013
Integer operations exercises
1. Add these numbers together. Estimate the answer first.
a)
7 + 11 + 506 + 20 400
b)
493 + 21 + 1056 + 77 + 11 900
c)
400 + 50 900 + 4999
d)
96 + 213 + 14306 + 9 + 8878
e)
212 + 31 600 + 1205 + 32 + 9
f)
43 + 70 000 + 222 + 99
g)
999 + 1056 + 293 + 44 + 10 459 + 378
2. Subtract these numbers. Estimate the answer first.
“Back check” your computation.
a)
405 – 308
b)
6007 - 2016
c)
10 001 - 9009
d)
8500 – 601
e)
5010 - 3999
f)
40 000 - 20 908
g)
4050 - 1090
3. Perform these multiplications. Estimate the answer first.
a)
8  245
b)
681  41
c)
230  320
d)
869  36
e)
508  409
f)
140  36
g)
1414  25
c)
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Updated Feb 2013
4. Perform these divisions. Estimate the answer first.
“Back check” your computation.
a)
4242  6
b)
2688  48
c)
798  42
d)
4646  23
e)
539  11
f)
1683  17
g)
24 575  25
5. Multiply the following
a)
18  100
b)
34  200
c)
17  400
d)
140  2000
e)
100  845
f)
10 500  500
g)
350  240
h)
2800  3300
i)
30 600  7100
j)
30  40  50
k)
800  40  700
l)
30  30  30  30  30
6. Perform the following divisions:
a)
150  10
b)
800  100
c)
17 000  100
d)
2 300 000  10 000
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Updated Feb 2013
e)
4500  90
f)
34 000  200
g)
84 000  12 00
h)
40800  120
i)
1 740 000  6000
7. a)
Five thousand six hundred multiplied by three hundred.
b)
Seven million multiplied by forty.
c)
Four hundred thousand multiplied by eight hundred.
d)
Fourteen million divided by seven thousand.
e)
Six hundred and twenty million divided by thirty-one thousand.
8. a)
Tom earns $10 an hour as a bar attendant. How much would he earn in 30
hours?
b)
Fiona has an 8000 word essay to type. Typing at a rate of 50 words per minute,
how long would she take to type the essay?
c)
A ream of paper contains 500 sheets. If an office photocopier uses 20 reams
per week, how many sheets of paper would be used in a year if the office is open
for 50 weeks in a year?
d)
The labour costs of Tom's car repairs came to $390. If labour is charged at $30
per hour, how many hours work was done?
e)
In a fund raising campaign $450 000 was collected from an estimated 50 000
donors. On average how much did each donor give?
f)
If a car uses 7 litres of petrol every 100 kilometres travelled, how much would a
2000 kilometre journey cost if petrol costs 90 cents per litre?
g)
A chain of supermarkets in New Zealand has 90 stores throughout the country.
They employ a total of 1980 people. On average how many people work in each
store.
h)
The insurance premium for replacing or repairing a damaged house is about $2
for every $1000 of value of the house. What would be the premium on a $240
000 house?
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Updated Feb 2013
i)
Bill owns has own plumbing business. He charges $30 per hour. How much would he
charge for a five day week, working eight hours per day?
j)
A disco machine costs $500 to hire. If the cost is shared between 20 people, how much
would each pay?
Test
1.
Write the number two million, forty three thousand and two.
2.
Write in words 401 023.
3.
What figure is in the hundred thousand place in 907 138 245?
4.
How many hundreds in ten thousand?
5.
Add together 46, 294, 1199, 6 and 46 007.
6.
From eighty four thousand and two, subtract twenty five thousand three hundred and
nine.
7.
43  251 =
8.
3941  7 =
9.
5805  45 =
10.
If a car uses 6 litres of petrol every 100 kilometres travelled, how much would a 3000
kilometre journey cost if petrol costs 110 cents per litre?
15
Updated Feb 2013
Integer Solutions
1 a) 20 924
e) 33 058
b) 13 547
f) 70 364
c)
g)
56 299
13 229
d) 23 502
2 a)
d)
97
1011
b) 3991
e) 19 092
c)
f)
992
2960
d) 7899
3. a)
e)
1960
207 772
b) 27 921
f) 5040
c) 73 600
g) 35 350
d) 31 284
4. a)
e)
707
49
b) 56
f) 99
c)
g)
19
983
d) 202
5. a) 1800
e) 84 500
i) 217 260 000
b) 6800
f) 5 250 000
j) 60 000
c)
g)
k)
6800
84 000
22 400 000
d) 280 000
h) 9 240 000
l) 24 300 000
6. a) 15
e) 50
i) 290
b) 8
f) 170
c)
g)
170
70
d) 230
h) 340
7. a) 1 680 000
d) 2000
b) 280 000 000
e) 20 000
8. a) $300
d) 13 hours
h) $480
b) 160 minutes
e) $9
i) $1200
c)
c)
f)
j)
320 000 000
500 000 sheets
$126
g) 22
$25
Test solutions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
2 043 002
Four hundred and one thousand and twenty three
1
100
47 552
58 693
10 793
563
129
$198
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Updated Feb 2013