 # Introduction

BASIC ARITHMETIC. Whole numbers are called integers. +3, +5, and +72 are examples of positive integers; −13, −6, and −51 are examples of negative integers. In-between negative and positive numbers are the number 0 it is neither negative nor positive. BASIC ARITHMETIC

The four basic arithmetic operators are, add (+), subtract (−), multiply (×) and divide (÷).

It is expected that adding, subtracting, multiplying, and dividing sensibly small numbers can be attained without a calculator. However, if the revision of this area is needed then some work problems are included in the following sections. BASIC ARITHMETIC

When opposite signs occur together in a calculation, the overall sign will be negative. For example,

3 + (−4) = 3 + −4 = 3 − 4 = −1

and

(+5) × (−2) = −10

The same signs together give an overall positive. For example,

3 − (−4) = 3 − −4 = 3 + 4 = 7

and

(−6) × (−4) = +24

## Revision of addition and subtraction

You can perhaps already add 2 or more numbers together and subtract one number from another. Though, if you need a revision then the following worked problems must be helpful.

### Problem 1.   Determine 735 + 167

1 1

H T U

7  3 5

+ 1  6 7

9  0 2

1. 5 + 7 = 12. Place 2 in units (U) column. Carry 1 (one) in the tens (T) clmn
2. 3 + 6 + 1 (carried) = 10. Place the 0 in the tens column. Carry the 1 (one) in the hundreds (H) clmn
3. 7 + 1 + 1 (carried) = 9. Place the 9 (nine) in the hundreds clmn.

Hence, 735 + 167 = 902

### Problem 2.   Determine 632 − 369

H T U

6  3 2

− 3  6 9

2  6 3

2 − 9 is not possible; therefore ‘borrow’ 1 from the tens column (leaving 2 in the tens column). In the units column, this gives us 12 − 9 = 3.
Place 3 in the units column.
2 − 6 is not possible; therefore ‘borrow’ 1 from the hundreds column  (leaving 5 in the hundreds column). In the tens column, this gives us 12 − 6 = 6.
Place the 6 in the tens column.
5 − 3 = 2.
Place the 2 in the hundreds column.

Hence, 632 − 369 = 263

### Problem 3.   Add 27, −74, 81 and −19

This problem is written as 27 − 74 + 81 − 19. Adding the positive integers: (BASIC ARITHMETIC)

 Adding the positive integers: 27 +81 Sum of positive integers is 108 Adding the negative integers: -74 -19 Sum of negative integers is 93 Taking the sum of the negative numbers from the sum of the positive numbers gives 108 –93  15

Thus, 27 − 74 + 81 − 19 = 15

### Problem 4.   Subtract −74 from 377

This problem is written as 377 − −74.  Like  signs together give an overall positive sign, hence

377 − −74 = 377 + 74

377

+7 4

451

Thus, 377 − −74 = 451

### Problem 5.   Subtract 243 from 126

The problem is 126 − 243. When the second number is larger than the first, take the smaller number from the larger and make the resulting negative. Thus,

126 − 243 = −(243 − 126)

243

−126

117

Thus, 126 − 243 = −117

### Problem 6.   Subtract 318 from −269

The problem is −269 − 318. The sum of the negative integers is

269

+ 318

587

Thus, −269 − 318 = −587

## Now try the following Practice Exercise

Practice Exercise Further problems on addition and subtraction (BASIC ARITHMETIC)

In Problems 1 to 15, determine the values of the expressions given, without using a calculator.

1. 67 kg − 82 kg + 34 kg
2. 73 m − 57 m
3. 851 mm − 372 mm
4. 124 − 273 + 481 − 398
5. £927 − £114 + £182 − £183 − £247
6. 647 − 872
7. 2417 − 487 + 2424 − 1778 − 4712
8. −38419 − 2177 + 2440 − 799 + 2834
9. £2715 − £18250 + £11471 − £1509 +£113274
10. 47 + (−74) − (−23)
11. 813 − (−674)
12. 3151 − (−2763)
13. 4872 g − 4683 g
14. −23148 − 47724
15. \$53774 − \$38441

 1. 19 kg 2.   16 m 3.   479 mm 4.  −66 5.   £565 6.   −225 7.   −2136 8.   −36 121 9.   £107701 10. −4 11.   1487 12.  5914 13. 189 g 14.   −70872 15.  \$15333

BASIC ARITHMETIC

REVISION OF MULTIPLICATION AND DIVISION

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