Презентация на тему Basic arithmetic

of modern day life.
Simplest form of mathematics.
Four

Addition plus sign
Subtraction minus sign
Multiplication multiplication sign
Division division sign

x

Equal or Even Values

equal sign

0,1,2,3,4,5,6,7,8,9
Digits - Name given to place or

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)

Numbers - Symbol or word used to express value or quantity.

Numbers

Digits

Whole Numbers

Fraction

Numbers - Fraction written on one line as whole

Position of period determines power of decimal.

Decimal Numbers

order of value
Adding on the Number Line

Adding with pictures

B. WHOLE NUMBERS

1. Addition

Number Line

Adding on the Number Line

Adding with pictures

- Uses no equal sign
5
+ 5
10

Simple

Complex

Answer is called “sum”.

Table of Digits

Adding in columns

+ 222
318
+ 421
c. 611

d. 1021
+ 1210

2. a. 813
+ 267

924
+ 429

c. 618
+ 861

411
+ 946

3. a. 813
222
+ 318

1021
611
+ 421

c. 611
96
+ 861

d. 1021
1621
+ 6211

444

739

727

2231

1080

1353

1479

1357

1353

2053

1568

8853

Let's check our answers.

show subtraction.
Number Line
Subtraction with pictures
Position larger numbers above

5 3 8
- 3 9 7

1

4

1

4

1

Number Line

- 3
8
- 4
c.

d. 9
- 5

2. a. 11
- 6

b. 12
- 4

c. 28
- 9

d. 33
- 7

3. a. 27
- 19

b. 23
- 14

c. 86
- 57

d. 99
- 33

3

4

3

4

5

8

19

26

8

9

29

66

e. 7
- 3

e. 41
- 8

e. 72
- 65

4

33

7

Let's check our answers.

387
- 241
399

c. 847
- 659

d. 732
- 687

5. a. 3472
- 495

b. 312
- 186

c. 419
- 210

d. 3268
- 3168

6. a. 47
- 38

b. 63
- 8

c. 47
- 32

d. 59
- 48

146

100

188

45

2977

126

209

100

9

55

15

11

7. a. 372
- 192

b. 385
- 246

c. 219
- 191

d. 368
- 29

180

139

28

339

Let's check our answers.

6
+

b. 9
+ 5

c. 18
+ 18

d. 109
+ 236

2. a. 87
- 87

b. 291
- 192

c. 367
- 212

d. 28
- 5

3. a. 34
+ 12

b. 87
13
81
+ 14

d. 21
- 83

13

14

26

335

1

99

55

24

46

195

746

104

4. a. 28
- 16

b. 361
- 361

c. 2793142
- 1361101

22

0

1432141

c. 87
13
81
+ 14

Check these answers using the method discussed.

6
+

b. 9
+ 5
14
- 5
9

c. 18
+ 18
26
- 18
8

d. 109
+ 236
335
- 236
99

2. a. 87
- 87
1
+ 87
88

b. 291
- 192
99
+ 192
291

c. 367
- 212
55
+ 212
267

d. 28
- 5
24
+ 5
29

3. a. 34
+ 12
46
- 12
34

b. 195
87
13
81
+ 14
195

d. 21
+ 83
104
- 83
21

4. a. 28
- 16
22
+ 16
38

b. 361
- 361
0
+ 361
361

c. 2793142
- 1361101
1432141
+ 1361101
2793242

c. 949
103
212
439
+ 195
746

# = Right
# = Wrong

by “times” sign (x).
Learn “Times” Table
6 x 8 =

In Arithmetic

next column.
Complex Multiplication

4. Multiplication (con’t)
Problem: 48 x

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

x 4
81

c. 64
x 5

d. 36
x 3

2. a. 87
x 7

b. 43
x 2

c. 56
x 0

d. 99
x 6

3. a. 24
x 13

b. 53
x 15

c. 49
x 26

d. 55
x 37

84

729

320

108

609

86

0

594

312

795

1274

2035

Let's check our answers.

94
x 73
b.

c. 34
x 32

d. 83
x 69

5. a. 347
x 21

b. 843
x 34

c. 966
x 46

6. a. 360
x 37

b. 884
x 63

c. 111
x 19

6862

2673

1088

5727

7287

28,662

44,436

13,320

55,692

2109

7. a. 493
x 216

b. 568
x 432

c. 987
x 654

106,488

245,376

645,498

Let's check our answers.

divider “goes into” a whole number.

5. Division

15 5 = 3

15 3 = 5

by 48 = 105 w/no remainder.
Or it can be

b.
c.
2.

b.

c.

3. a.

b.

211

62

92

13

310

101

256

687

4. a.

b.

98

67

48

5040

7

434

9

828

9

117

12

3720

10

1010

23

5888

56

38472

98

9604

13

871

5. a.

b.

50

123

50

2500

789

97047

Let's check our answers.

b.
7.

b.

8. a.

b.

7

9000

61

101

67 r 19

858 r 13

9. a.

b.

12 r 955

22 r 329

21

147

3

27000

32

1952

88

8888

87

5848

15

12883

994

12883

352

8073

Let's check our answers.

whole number times the number of parts being considered.
Changing

4 =

4 x 6
6

=

24
6

or

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”.

to sevenths
2. 40 to eighths
3. 54 to

4. 27 to thirds

5. 12 to fourths

6. 130 to fifths

49 x 7
7

=

343
7

or

343

7

=

40 x 8
8

=

320
8

or

320

8

=

54 x 9
9

=

486
9

or

486

9

=

27 x 3
3

=

81
3

or

81

3

=

12 x 4
4

=

48
4

or

48

4

=

130 x 5
5

=

650
5

or

650

5

=

Let's check our answers.

1/2
3. 19 7/16
5. 6 9/14
2. 8

4. 7 11/12

6. 5 1/64

Let's check our answers.

19/3 into whole/mixed number..
CHANGING IMPROPER FRACTIONS TO WHOLE/MIXED NUMBERS

Let's check our answers.

following fractions to LOWER terms:
15
20
=
a.
to 4ths
Divide the

36

40

=

b.

to 10ths

24

36

=

c.

to 6ths

12

36

=

d.

to 9ths

16

76

=

f.

to 19ths

30

45

=

e.

to 15ths

Let's check our answers.

the following fractions to LOWEST terms:
6
10
a.
3
9
=
b.
6

=

c.

13

32

=

d.

16

76

=

f.

32

48

=

e.

=

Cannot be reduced.

Let's check our answers.

the same denominator.
When denominators are not the same, a

6 x 8 x 9 x 12 x 18 x 24 x 36 = 80,621,568

80,621,568 is only one possible common denominator ...
but certainly not the best, or easiest to work with.

10. Least Common Denominator (LCD)

Smallest number into which denominators of a group of two or more fractions will divide evenly.

appears in a set is multiplied by the most

10. Least Common Denominator (LCD) con’t.

To find the LCD, find the “lowest prime factors” of each denominator.

2 x 3

2 x 2 x 2

3 x 3

2 x 3 x 2

2 x 3 x 3

3 x 2 x 2 x 2

2 x 2 x 3 x 3

(2 x 2 x 2) x (3 x 3) = 72

Remember: If a denominator is a “prime number”, it can’t be factored except by itself and 1.

LCD Exercises (Find the LCD’s)

2 x 2 x 2 x 3 = 24

2 x 2 x 2 x 2 x 3 = 48

2 x 2 x 3 x 5 = 60

Let's check our answers.

denominators, then multiply both the numerator and denominator of

11. Reducing to LCD

Reducing to LCD can only be done after the LCD itself is known.

Remaining fractions are handled in same way.

to their LCD.
Let's check our answers.

Then determine LCD for fractions.
Reduce fractions

fractions and mixed numbers, reducing answers to lowest terms.
Let's

that a common denominator must be found first.
Then subtract

fractions and mixed numbers, reducing answers to lowest terms.
4.
=

2

5

-

1

3

33

15

2.

=

3

12

-

5

8

3.

=

1

3

-

2

5

47

28

5.

=

15

16

-

1

4

101

57

6.

=

5

12

-

3

4

14

10

Let's check our answers.

required for multiplication.
1. First, multiply the numerators.
2.

3. Reduce answer to its lowest terms.

Change to an improper fraction before multiplication.
1. First,

2. Then, multiply the numerators and denominators.

3. Reduce answer to its lowest terms.

easier.

If numerator of one of fractions and denominator

Cancellation can be done on both parts of a fraction.

Reduce to lowest terms.
Multiplying Fractions and Mixed Numbers Exercises
1.
2.
3.
4.
5.
6.
7.
8.
9.
1
26
X
=
4
5
X
=
2
3
9
5
X
=
4
16
3
4
X
=
4
35
35
4
X
=
7
12
1
6
X
=
3
5
9
10
X
=
5
11
2
3
X
=
77
15
X
=
26
3
5
1
1
Let's

Reduce to lowest terms.
Dividing Fractions,Whole/Mixed Numbers Exercises
1.
2.
3.
4.
5.
3
8
=
=
=
3
6
5
8
=
7
4
14
3
=
18
144
51
16
1
8
15
7
12

on ten (10).
Decimal fraction has a denominator of

Written on one line as a whole number, with a period (decimal point) in front.

3 digits

.999 is the same as

1. Decimal System

are read to the right of the decimal point.
.63

.136 is read as “one hundred thirty-six thousandths.”

.5625 is read as “five thousand six hundred twenty-five
ten-thousandths.”

3.5 is read “three and five tenths.”

Whole numbers and decimals are abbreviated.

6.625 is spoken as “six, point six two five.”

is same as addition of whole numbers except for

Add .865 + 1.3 + 375.006 + 71.1357 + 735

Align numbers so all decimal points are in a vertical column.
Add each column same as regular addition of whole numbers.
Place decimal point in same column as it appears with each number.

.865
1.3
375.006
71.1357
+ 735.

“Add zeros to help eliminate errors.”

000

0000

0

0

“Then, add each column.”

1183.3067

is same as subtraction of whole numbers except for

Solve: 62.1251 - 24.102

Write the numbers so the decimal points are under each other.
Subtract each column same as regular subtraction of whole numbers.
Place decimal point in same column as it appears with each number.

62.1251
- 24.102

“Add zeros to help eliminate errors.”

0

“Then, subtract each column.”

38.0231

as whole numbers.
Count the number of decimal places to

Solve: 38.639 X 2.08

3 8 .6 3 9
x 2.0 8

“Add zeros to help eliminate errors.”

0

“Then, add the numbers.”

3 0 6 9 5 2

Rules For Multiplying Decimals

7 7 2 7 8

0

8 0 3 4 7 5 2

.

Place decimal point 5 places over from right.

be divided (dividend) inside the division box.
Place divisor

Rules For Dividing Decimals

5 7 3

.
.

.

.
.
8
1 0 9 9 2
1 3 6

3

9

1 2 3 6 6

1 2 8 7

0

0

9

1 2 3 6 6

5 0 4

0

0

4 1 2 2

3

9 1 8

remainder

decimals.
.6 + 1.3 + 2.8 =

72.8 + 164.02 +

2. Subtract the following decimals.

2.0666 - 1.3981 =

18.16 - 9.104 =

1.0224 - .9428 =

1.22 - 1.01 =

0.6 - .124 =

18.4 - 18.1 =

1347.008 - 108.134 =

111.010 - 12.163 =

64.7 - 24.0 =

4.7

410.83

277.733

3318.08606

0.6685

9.056

0.0796

0.21

0.467

0.3

1238.874

98.847

40.7

“WORK ALL 4 SECTIONS (+, , X, )

Let's check our answers.

decimals.
3.01
x 6.20
b. 21.3
x

c. 1.6
x 1.6

d. 83.061
x 2.4

e. 1.64
x 1.2

f. 44.02
x 6.01

g. 63.12
x 1.12

h. 183.1
x .23

i. 68.14
x 23.6

18.662

25.56

2.56

199.3464

1.968

264.5602

70.6944

42.113

1608.104

Let's check our answers.

decimals.
3 0.5
a. 1.4 4 2.7 0
b.

c. 1.2 6 2 0.4

d. 6 6.6 7 8 6

e. 1.1 110.0

5.7875

5 1 7

1.1 1 3 1

10 0

Let's check our answers.

be changed to a decimal by dividing the numerator

Change to a decimal.

4 3.0

.75

.6

.6

.8

.2

.5

.4

.35

.75

.28

.48

.85

.98

1.9

1.04

6.6

Let's check our answers.

many parts of a total are taken out.
Short

or

To change a decimal to a %, move decimal point two places to right and write percent sign.

.15 = 15%
.55 = 55%
.853 = 85.3%
1.02 = 102%

“Zeros may be needed to hold place”.

.8 = 80%

= _________

58.5% = _________

17.45% = __________

5% = _________

Write as

.35

.14

.585

.1745

.05

75

40

40

40

Let's check our answers.

its decimal equivalent, multiply by 0.01
Change 6 1/4% to

Change the mixed number to an improper fraction, then divide the
numerator by the denominator.

6 1/4 = 25/4 = 6.25

Now multiply the answer (6.25) times 0.01

6 .25 x 0.01 = 0.0625

Rules For Finding Any Percent of Any Number

Convert the percent into its decimal equivalent.
Multiply the given number by this equivalent.
Point off the same number of spaces in answer as in both numbers multiplied.
Label answer with appropriate unit measure if applicable.

Find 16% of 1028 square inches.

16 x .01 = .16

1028 x 0.16 = 164.48

Label answer: 164.48 square inches

of a given number.
First number is called “base”.

Rule: The product of the base, times the rate, equals the percentage.

Percentage = Base x Rate or P=BxR

NOTE: Rate must always be in decimal form.

To find the formula for a desired quantity, cover it and the remaining factors indicate the correct operation.

Only three types of percent problems exist.

1. Find the amount or rate. R=PxB

each problem A through E for the

The labor and material for renovating a building totaled $25,475. Of this amount,
70% went for labor and the balance for materials. Determine: (a) the labor cost,
and (b) the material cost.

$17,832.50 (labor) b. $ 7642.50 (materials)

35% of 82 = 4. 14% of 28 =

Sales tax is 9%. Your purchase is $4.50. How much do you owe?

You have 165 seconds to finish your task. At what point are you 70% finished?

You make $14.00 per hour. You receive a 5% cost of living raise. How much raise per hour did you get? How much per hour are you making now?

28.7

4.32

$4.91

115.5 seconds

$.70 /hr raise

Making $14.70 /hr

Let's check our answers.

x 12 = 216

240 x 8 = 30

3.5 +

Let's check our answers.

changing from English weights and measures
to

Metric Prefixes:

Most commonly used prefixes are Kilo, centi, and milli.

Kilo = 1000 units
Hecto = 100 units
Deka = 10 units
deci = 0.1 unit (one-tenth of the unit)
centi = 0.01 (one-hundredth of the unit)
milli = 0.001 (one thousandth of the unit)

decimal system.
No fractions or mixed numbers
Easier to

Example 1:

Using three pieces of masking tape of the following English measurement lengths:
4 1/8 inches, 7 6/16 inches, and 2 3/4 inches, determine the total length of the tape.

Step 1: Find the least common
denominator (16). This
is done because unequal
fractions can’t be added.

Step 2: Convert all fractions to the
least common denominator.

Step 3: Add to find the sum.

Step 4: Change sum to nearest
whole number.

14 7/16

“Now, compare with Example 2 using Metrics”.

13 23/16

of masking tape of the following lengths: 85 mm,

Step 1: Millimeters and centimeters
cannot be added, so convert
to all mm or cm.

85mm = 85mm
19.4cm = 194mm
57mm = 57mm

Step 2: Add to find the sum.

336 mm

or

85mm = 8.5cm
19.4cm = 19.4cm
57mm = 5.7cm

33.6 cm

“MUCH EASIER”

like “inches, feet, millimeters, & centimeters take too much

Metric Abbreviations:

mm = millimeter = one-thousandth of a meter

cm = centimeter = one-hundredth of a meter

Km = Kilometer = one thousand meters

Easy to read.
Graduated in millimeters and centimeters.
Metric Scales

8.35cm or 83.5mm

110mm or 11.0cm

the lines and record their length.
_______ mm
_______ mm
_______ cm
_______

109

81.5

3.1

103

6.3

80.5

10.85

23

91.5

4.25

Let's check our answers.

Metrics are everywhere.
Useful to be able to convert.
Compare

One Yard: About the length between your nose and the end
of your right hand with your arm extended.

One Meter: About the length between your left ear and the
end of your right hand with your arm extended.

One Centimeter: About the width of the fingernail on your pinky
finger.

One Inch: About the length between the knuckle and the
end of your index finger.

quart are approximately the same.
1 liter
Equivalent Units:
Kilo Thousands
Hecto Hundreds
Deka

Place Value

Prefix

To change to a smaller unit,
move decimal to right.

To change to a larger unit,
move decimal to left.

liters
3. 10 cm = _______ mm
4. 500 cm = _______ m
5. 4

Comparison and Conversion Practice Exercises

Let's check our answers.

after initial calculation.

following is not a metric measurement?
millimeter
centimeter
square feet
cm
2. Milli -

100 ones
0.001 unit
0.0001 unit
0.00001 unit

3. How long are lines A and B in this figure?

A

B

4. How long is the line below? (Express in metric units).

5. Convert the following:

1 meter = __________millimeters
5 cm = ____________millimeters
12 mm = ___________centimeters
7m = _____________centimeters

A = 53 mm, or 5.3 cm
B = 38 mm, or 3.8 cm

69 mm

Let's check our answers.

manufacturer to the next.
Most have same basic functions.

if given the wrong information or command.
Decimals must

Step 1: Press “3” key - number 3 appears on screen..
Step 2: Press “+” key - number 3 remains on screen.
Step 3: Press “8” key - number 8 appears on screen.
Step 4: Press “+” key - running total of “11” appears on screen.
Step 5: Press the “9” key - number 9 appears on screen.
Step 6: Press “+” key - running total of “20” appears on screen.
Step 7: Press “1 & 4” keys - number 14 appears on screen.
Step 8: Press the = key - number 34 appears. This is the answer.

In step 8, pressing the + key would have displayed the total. Pressing the = key stops the running total function and ends the overall calculation.

following.
.06783
.49160

2. 154758
3906
4123
5434
+ 76

3. 12.54 + 932.67 + 13.4

2.21931

168297

= 958.61

Let's check our answers.

- number 187 appears on screen..
Step 2: Press “-” key

In step 4, pressing the - key would have displayed the total.

Let's check our answers.

and 2 keys - number 342 appears on screen..
Step

Let's check our answers.