Basic arithmetic презентация

Four Basic Operations :

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

x

Equal or Even Values

equal sign

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

Position of period determines power of decimal.

Decimal Numbers

Adding with pictures

B. WHOLE NUMBERS

1. Addition

Number Line

Adding on the Number Line

Adding with pictures

5
+ 5
10

897
+ 368
1265

Simple

Complex

Answer is called “sum”.

Table of Digits

Adding in columns

318
+ 421

c. 611
+ 116

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.

Subtraction with pictures

Position larger numbers above smaller numbers.

If subtracting larger digits from smaller digits, borrow from next column.

5 3 8
- 3 9 7

1

4

1

4

1

Number Line

8
- 4

c. 5
- 2

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.

399
- 299

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.

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.

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

Learn “Times” Table

6 x 8 = 48

In Arithmetic

Problem: 48 x 23

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

81
x 9

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.

b. 99
x 27

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.

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

5. Division

15 5 = 3

15 3 = 5

b.

c.

2. a.

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. a.

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.

Changing the whole number 4 to “sixths”:

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”.

3. 54 to ninths

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.

5. 6 9/14

2. 8 3/4

4. 7 11/12

6. 5 1/64

Let's check our answers.

CHANGING IMPROPER FRACTIONS TO WHOLE/MIXED NUMBERS EXERCISES

Let's check our answers.

15

20

=

a.

to 4ths

Divide the original denominator (20) by the desired denominator (4) = 5..
Then divide both parts of original fraction by that number (5).

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.

6

10

a.

3

9

=

b.

6

64

=

c.

13

32

=

d.

16

76

=

f.

32

48

=

e.

=

Cannot be reduced.

Let's check our answers.

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.

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.

11. Reducing to LCD

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

Remaining fractions are handled in same way.

Let's check our answers.

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.

2. Then, multiply the denominators.

3. Reduce answer to its lowest terms.

1. First, the whole number (4) is changed to improper fraction.

2. Then, multiply the numerators and denominators.

3. Reduce answer to its lowest terms.

Cancellation can be done on both parts of a fraction.

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 check our answers.

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

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

.63 is read as “sixty-three hundredths.”

.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.”

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

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

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.

Rules For Dividing Decimals

1 3 6 5

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

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.

b. 21.3
x 1.2

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.

b. .8 4.6 3000

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.

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.

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%

.35

.14

.585

.1745

.05

75

40

40

40

Let's check our answers.

Change 6 1/4% to its decimal equivalent.

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

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

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.

Let's check our answers.

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)

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

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”

Metric Abbreviations:

mm = millimeter = one-thousandth of a meter

cm = centimeter = one-hundredth of a meter

Km = Kilometer = one thousand meters

Metric Scales

Both scales graduated the same... Numbering is different.
Always look for the abbreviation when using metric scales.
Always place “0” at the starting point and read to end point.

8.35cm or 83.5mm

110mm or 11.0cm

_______ mm
_______ mm
_______ cm
_______ mm
_______ cm
_______ mm
_______ cm
_______ 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.

Compare the following:

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.

1 liter

Equivalent Units:

Kilo Thousands
Hecto Hundreds
Deka Tens
base unit Ones
deci Tenths
centi Hundredths
milli Thousandths

Place Value

Prefix

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

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

Comparison and Conversion Practice Exercises

Let's check our answers.

millimeter
centimeter
square feet
cm

2. Milli - is the prefix for which one of the following?

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.

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.

2. 154758
3906
4123
5434
+ 76

3. 12.54 + 932.67 + 13.4

2.21931

168297

= 958.61

Let's check our answers.

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

Let's check our answers.

Let's check our answers.