123_BASIC MATH _ (123)

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1

A.

BASIC ARITHMETIC
•
•

Foundation of modern day life.
Simplest form of mathematics.

Four Basic Operations :
• Addition
plus sign
• Subtraction
minus sign
• Multiplication x multiplication sign
• Division
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 - Complete units , no fractional parts. (43)
➤

•

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
444

b. 318
+ 421
739

c.

2. a. 813
+ 267
1080

b. 924
+ 429
1353

c.

3. a. 813
222
+ 318
1353

b. 1021
611
+ 421
2053

c. 611
96
+ 861
1568

611
+ 116
727

d. 1021
+ 1210
2231

618
+ 861
1479

d. 411
+ 946

1357
d. 1021
1621
+ 6211
8853

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
3

b.

8
- 4
4

2.

a. 11
-6
5

b.

3.

a. 27
- 19
8

b. 23
- 14
9

12
- 4
8

d. 9
- 5
4

e. 7
- 3
4

c. 28
- 9
19

d.

33
- 7
26

e.

41

- 8
33

c.

d.

99
- 33
66

e.

72
- 65
7

c.

5
- 2
3

86
- 57
29

9

SUBTRACTION PRACTICE EXERCISES (con’t)
4.

a.

387
- 241
146

b.

399
- 299
100

c.

847
- 659
188

d. 732
- 687
45

5.

a. 3472
- 495
2977

b.

312
- 186
126

c.

419
- 210
209

d.

3268
- 3168
100

6.

a. 47
- 38
9

b.

63
- 8
55

c.

47
- 32
15

d.

59
- 48
11

7.

a.

b.

385
- 246
139

c.

219
- 191
28

d.

372
- 192
180

368
- 29
339

10

Checking Addition and Subtraction
•

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

•

73
+ 48
121
- 48
73

927
318
426
183
927

To Check

3.

Check 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
13

b.

9
+5
14

c.

18
+ 18
26

d. 109
+ 236
335

2.

a. 87
- 87
1

b.

291
- 192
99

c.

367

- 212
55

d.

28
- 5
24

3.

a. 34
+ 12
46

b.

d.

21
- 83
104

4.

a.

b.

28

- 16
22

87
13
81
+ 14
195

361
- 361
0

c. 87
13
81
+ 14
746

c.

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

a. 34
+ 12
46
- 12

b.

a.

28

- 16
22
+ 16

38

291
- 192
99
+ 192

c.

291
b.

195

b.

361
- 361
0
+ 361

361

18
+ 18
26

- 18

d. 109
+ 236
335
- 236

8

99

367
- 212
55
+ 212

267
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
84

b.

81
x 9
729

c.

2.

a.

87
x7
609

b.

43
x 2
86

c. 56
x 0
0

d.

99
x 6
594

3.

a. 24
x 13
312

c.

d.

55
x 37
2035

b. 53
x 15
795

64
x 5
320

49
x 26
1274

d. 36
x 3
108

16

MULTIPLICATION PRACTICE EXERCISES (con’t)
4.

a.

94
x 73
6862

b.

5.

a.

347
x 21
7287

b.

6.

a. 360
x 37
13,320

7.

a.

493

x 216
106,488

99
x 27
2673

c.

843
x 34
28,662

c.

b.

884
x 63
55,692

c. 111
x 19
2109

b.

c.

568

x 432
245,376

34
x 32
1088

d. 83
x 69
5727

966
x 46
44,436

987
x 654
645,498

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

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
62
7 434

1.

211
a. 48 5040

b.

2.

13
a. 9 117

310
b. 12 3720

3.

256
a. 23 5888

687
b. 56 38472

4.

98
a. 98 9604

67
b. 13 871

5.

50
a. 50 2500

123
b. 789 97047

c.

92
9 828

101
c. 10 1010

20

DIVISION PRACTICE EXERCISES (con’t)
9000
3 27000

6.

7
a. 21 147

b.

7.

61
a. 32 1952

101
b. 88 8888

8.

67 r 19
a. 87 5848

858 r 13
b. 15 12883

9.

12 r 955
a. 994 12883

22 r 329
b. 352 8073

21

C.

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

3
8

11
16

or

3

8

11
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