BASIC ARITHMETIC

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1

A.

BASIC ARITHMETIC
•
•

Foundation of modern day life.
Simplest form of mathematics.

Four Basic Operations :
•
•
•
•

Addition
Subtraction
Multiplication
Division

plus sign
minus sign
x multiplication sign
division sign

Equal or Even Values

equal sign

2

1.

Beginning Terminology
•

Numbers
Numbers - Symbol or word used to express value or quantity.
Arabic number system - 0,1,2,3,4,5,6,7,8,9

•

Digits
Digits - Name given to place or position of each numeral.
Number Sequence

2.

Kinds of numbers
•

Whole Numbers
Numbers - Complete units , no fractional parts. (43)
Whole
May be written in form of words. (forty-three)

•

Fraction - Part of a whole unit or quantity. (1/2)

3

2.

Kinds of numbers (con’t)
•

Decimal
Decimal Numbers
Numbers - Fraction written on one line as whole no.
Position of period determines power of decimal.

4

B.

WHOLE NUMBERS
1.

Addition
•

Number Line
Line - Shows numerals in order of value
Number

•

Adding on
on the
the Number
Number Line
Line (2 + 3 = 5)
Adding

•

Adding with
with pictures
pictures
Adding

5

1.

Addition (con’t)
•

Adding in columns - Uses no equal sign
5
+5
10
Simple

897
+ 368
1265

Answer is called “sum”.

Complex

Table of Digits

6

ADDITION PRACTICE EXERCISES

1. a. 222
+ 222

c.

444

b. 318
+ 421
739

2. a. 813
+ 267
1080

b. 924
+ 429
1353

c.

3. a. 813
222
+ 318
1353

b. 1021
d. 1021
c. 611
611
1621
96
+ 421
+ 6211
+ 861
2053
1568
8853

611
+ 116

d. 1021
+ 1210
727

2231

d. 411
618
+ 946
+ 861
1357
1479

7

2.

Subtraction
•

Number Line - Can show subtraction.
Subtraction with pictures

Number Line

Position larger numbers above smaller numbers.
If subtracting larger digits from smaller digits, borrow from
next column.

4 1
53

8

-397
141
8

SUBTRACTION PRACTICE EXERCISES
1.

a.

6
- 3

b.

8
- 4

3

2.

3.

a. 11
-6

a. 27
- 19

4

b.
5

8

c.

12
- 4

8

b. 23
- 14

c. 28
- 9

c.
9

5
- 2

86
- 57

d. 9

- 5

3

d.
19

d.
29

33
- 7

4

e. 7
- 3

e.

41
- 8

26

99
- 33

e.
66

4

33

72
- 65

7

9

SUBTRACTION PRACTICE EXERCISES (con’t)
4.

a.

5.

6.

7.

387
- 241

146

a. 3472

- 495
2977

a. 47
- 38

a.

b.

372
- 192

b.

b.
9
b.
180

399
- 299

c.
100

312
- 186

63

- 8

385
- 246

c.
126
c.

55
c.
139

847
- 659

419
- 210

47
- 32

219
- 191

188

d. 732
- 687

d.
209
d.

3268
- 3168

59
- 48

15
d.
28

45

368
- 29

100

11

339

10

Checking Addition and Subtraction
•

Check
Check Addition
Addition - Subtract one of added numbers from sum.
Result should produce other added number.

5
+3
8
-3
5

2
+8
10
-8
2

•

Check Three or more #s - Add from bottom to top.
To Add

•

73
+ 48
121
- 48
73

927
318
426
183
927

To Check

3.

Check
Check Subtraction
Subtraction - Add subtracted number back.
5
-4
1
+4
5

62
- 37
25
+ 37
62

103
- 87
16
+ 87

103

11

CHECKING ADDITION & SUBTRACTION PRACTICE EXERCISES
1.

a.

6
+8

b.

9
+5

c.
14

13

2.

3.

a. 87
- 87
1

b.

a. 34
+ 12

a.

c.

b.

28
- 16

87
13
81
+ 14
195

b.
22

26

361
- 361

28

- 5

55

24
d.

c. 87
13
81
+ 14

21
- 83
104

746

c.
0

335

d.

367
- 212

99

46

4.

291
- 192

d. 109
+ 236

18
+ 18

2793142
- 1361101
1432141

Check these answers using the method discussed.

12

CHECKING ADDITION & SUBTRACTION PRACTICE EXERCISES
1.

a.

6
+8
13

- 8

b.

5
2.

a. 87
- 87
1
+ 87

b.

291
- 192
99
+ 192

a. 34
+ 12
46
- 12

a.

28
- 16
22
+ 16

38

c.

291
b.

b.

361
- 361
0
+ 361

361

18
+ 18
26
- 18

d. 109
+ 236
335
- 236

8

99

367
- 212
55
+ 212

267
195

c.

87
13
81
+ 14
195

34
4.

c.

9

88
3.

9
+5
14

-5

949
103
212
439
+ 195
746

c.

2793142
- 1361101
1432141
+ 1361101

2793242

d.

28
- 5
24
+5

29
d. 21
+ 83
104
- 83

21

# = Right
# = Wrong

13

4.

Multiplication
•

In Arithmetic - Indicated by “times” sign (x).

Learn “Times” Table
6 x 8 = 48

14

4.

Multiplication (con’t)
•

Complex Multiplication - Carry result to next column.

Problem: 48 x 23

+2

48

X 23
4

+2

48

X 23
144

+1

48

X 23
144
6

+1

48

X 23
144
960
1104

Same process is used when multiplying
three or four-digit problems.
15

MULTIPLICATION PRACTICE EXERCISES
1.

a.

21
x 4

b.

81
x 9

84

2.

3.

a.

87
x7

a. 24
x 13

b.
609

312

43
x 2

c.
729

86

b. 53
x 15

c. 56
x 0

c.
795

64
x 5

320

d. 36
x 3

d.
0

108

99
x 6
594

d. 55
49
x 26
x 37
2035
1274

16

MULTIPLICATION PRACTICE EXERCISES (con’t)
4.

a.

5.

94

x 73
6862
a.

347
x 21
7287

b.

99
x 27
2673

c.

34
x 32
1088

b.

843
c. 966
x 34
x 46
28,662
44,436

6.

a. 360
x 37
13,320

b.

884
c. 111
x 63
x 19
55,692
2109

7.

a.

b.

568
c. 987
x 432
x 654
245,376
645,498

493
x 216
106,488

d. 83
x 69
5727

17

5.

Division
•

15

Finding out how many times a divider “goes into” a
whole number.

5=3

15

3=5

18

5.

Division (con’t)

Shown by
by using
using aa straight
straight bar
bar ““
• Shown

10 5
48 5040
48
2 40
240
0

““ or
or ““

““ sign.
sign.

48 “goes into” 50 one time.

1 times 48 = 48
50 minus 48 = 2 & bring down the 4
48 goes into 24 zero times.
Bring down other 0.
48 goes into 240, five times
5 times 48 = 240
240 minus 240 = 0 remainder

So, 5040 divided by 48 = 105 w/no remainder.
Or it can be stated:

48 “goes into” 5040, “105 times”
19

DIVISION PRACTICE EXERCISES

3.

4.

5.

1.

211
a. 48 5040

2.

13
a. 9 117

a.

256
23 5888

a.

98
98 9604

a.

50
50 2500

b.

62
7 434

b.

310
12 3720

b.

687
56 38472

b.

67
13 871

b.

123
789 97047

c.

92
9 828

c.

101
10 1010

20

DIVISION PRACTICE EXERCISES (con’t)

8.

9.

6.

7
a. 21 147

7.

61
a. 32 1952

b.

9000
3 27000

b.

101
88 8888

b.

858 r 13
15 12883

a.

67 r 19
87 5848

a.

12 r 955
b.
994 12883

22 r 329
352 8073

21

C.

FRACTIONS - A smaller part of a whole number.
Written with one number over the other, divided by a
line.
3
11
11
3

8

16

or

8

16

Any number smaller than 1, must be a fraction.
Try thinking of the fraction as “so many of a specified number of parts”.
For example: Think of 3/8 as “three of eight parts” or...
Think of 11/16 as “eleven of sixteen parts”.

1.

Changing whole numbers to fractions.
Multiply the whole number times the number of parts being
considered.

Changing the whole number 4 to “sixths”:

4 = 4 x 6 = 24 or
6
6

24
6
22

CHANGING WHOLE NUMBERS TO FRACTIONS EXERCISES
1. 49 to sevenths

= 49 x 7
7

=

343
7

or

343
7

2. 40 to eighths

= 40 x 8
8

=

320
8

or

320
8

3. 54 to ninths

= 54 x 9
9

=

486
9

or

486
9

4. 27 to thirds

= 27 x 3
3

=

81
3

or

81

5. 12 to fourths

= 12 x 4
4

=

48
4

or

48

6. 130 to fifths

= 130 x 5 =
5

650
5

or

650
5

3
4

23

2.

Proper and improper fractions.
Proper Fraction - Numerator is smaller number than denominator.
3/4
Improper Fraction - Numerator is greater than or equal to denominator.
15/9

3.

Mixed numbers.
Combination of a whole number and a proper fraction.

4.

Changing mixed numbers to fractions.
Change 3 7/8 into an improper fraction.
•

Change whole number (3) to match fraction (eighths).

3
•

=

3x8
8

24
8

=

or

24

8