1968-09-10 — Page 15

*EXAGA

日八十月七閏年申

有效僑華 育

英価

ROD LET

EXAMPLE

LESSON HURTY-FIVE

ALGEBRY

SCHAFTER D

Write in svmbols the following

{{1}^ofis greater than 8,

(2) Yas no less than 91

(3) 4 and are identically equal.

Three imos X quals fifteen,

(4)

(5)

therefore, X equals five, Y plus five equals eleven, therefore Y equals SING

(6) 2 minus tan equals fifteen,

therefore 2 equals.

(7) Because I equals twenty-fi

therefore X plus fave equajs (8) One-third of A equals five,

therefore A equals fifteeti.. (9) Türke B equals twenty,

therefore 8 equals ten, (EO) CAMS thirteen equals mune,

thereturë & equals twentye buu

UTION:

(8):

(9)

(10)

EXERCISE

(A) State in words the following:

(19)

(2) B 7:

(3).08

(10) "abcd=" (11)

5.9

(4)-D 4.9

(12) a + b

(5) E = F

(13) ab-

(6) GH

(14) fgh

(7) X-L

(15) +

(B) write in symbols, the following:

1) a is greater than 15

(2), b is not greater Than-ag

(3)

e 15, not less than 20

(5) m and tare, identically squal, (6) -Four times. A equals twenty-four

therefore equals six

(7) 9 manus, aventy equals twenty-three,

therefore B equals. forty-three..

(8) Because (equals six, therefore C plus.

10) Five times I equals forty,

Thereture F. equals sight.

(3) FACTOR

CHAPTER 2

Each of the quantities multiplisa together to form a product is valled Taylor, of the producti

arī trimeta ོ་

15

product 15.

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中學自然科

道英文書院主編

Short Out in Calculating

Seems to me most of the Leenages or Hong Kong

useful

nowadays are afraid of math, and science subjects, Ine numbers, symbols and calculations are a real headache to them. This article provides you:2 method in calculation, or simply say, it is a short cuL in calculating besides saving time, you should find it enjoyable to amaze your friend, with your quick. calculating powers.

Many short cuts are specified to be used only under certain conditions. However, the more we know about short-cuts, the more useful they become.

Multiplying by 5.

If a number N is to be multiplied by 5, tre snort-cut should be

"Divide M by 2, and then multiply by Example:-

Usual method.

5794

28,970

his

Multipitestion with the units digits connected by Sum of 10 and identical ten's dizita

The units digit of these pa are connected by a sum of and identical in tents di

12 x 18

15 x 15

45 x 45

23 x 27.

73 x 79

Usually reth

79

639.

·497

5609

5794

2897 x 10 =281970

sport-cut has a great advantage over the ordinary method of multiplication. It is quick and easy to divide 3 number mentally by 2 and then multiply by 10%

Bagis crinciple

tiply by 25

It is also possible to provide multiplication of N x 25.

"Divide N by 4 and mul

Example:

Usual Method

5376

25

26880

·∙10752·

134400

Principle

100

25N

)(N)

(100)

short cut in the

ply by 100.

Short-out method

415376

1344 100 × 334,400;

Short cut

63 x 67:

6x(6+1

7x(7-1)

518

hen the

C10N

| 7 × 10 - 1 | | 7 × 10 • (10 -

the ten's digit

the units digit equation is

[1ON (10 - M)]

adly two numbers that differ by two

(1)19 x 21.

(2)

51 X 49

(3) 85 x 84

(4) 91 x 89

All the products in the above are made up or factors that differ by 2, The quick calculation is aone as foLLOWS :-

"Square the mean of the two factors and subtract one from it, "1eJ

Multiplication

(mean)

Subtract

product

M. x N

(1) 19 x 21 (2)

(20)(20)

399

(50)(50)

2499

86 x 84

(25)(85)

7224

91 x 89

(90) (90)

8099

Gare the fact

the pre

COEFFICIENT,(a)If one of the Factors of a product

is a numerical quantity it is called the COEFFICIENT or the NUMERICAL COEFFICIENT the remaining factors.

fig. Jia, is the coefficient or ca.

(6)

A coefficient in ren involves lecter is called a literal coefficient.

(C) POWER? 12 Z

Olim ok is the coefficient of

SECOND POWER::Cur

(b) THIRD POWER (or

Um The Joefficient

Divide by 5

Dividing any number by 5 is the same as doubling the number and then dividing it by 10.

2N

Example:-

308

308 x 2

10

·61,6

Divide by 25

Dividing any number by 25 is as mul and then dividing by 100,

100

AN

100

Multiply by

lying it

Principle

(x + 1) (x - 1).

is a proof for the short two factors.

Multiplying two numbers just under 100

the man

This short cut can save you a lot of tims multiplying two numbers between 80 and 100. Example:-

If 92 x 97.

Usual method

92

97

644

828

3924

Short cut

100

97

1,00

97

89 x 100 8924

8x3

c) FOURTH POWER

5.5 5.

(0) ALGEBRAIC EXPRESSION

452

4972

Any expression with numbers and symbols connected by the signs

an algebraic expression. NOTE)

Parts of an expression separated.

Signsor are called · TERMS, Signs » and + do not separate.

(a) SIMPLE (MONÓMIAL) EXPRESSION

86, 94

(b) BINOMIAL EXPRESSION (Two: teros)

called

The short out here helps you to multiply any number by 11 mentally and quickly.

lis ual me thod

452

Short cut

More examples for consolidation:-) (1), 94 x 97

91 x 100, 181

- 9118

(2)94 x 961

9000 120 9024

(3)198 x 9

965

9100

11

9114

965

aud 1 darry

carry

TRINOMIAL EXPRESSION (Three tergs)

項式

.52

965 20525

30 in multiplying by 11, we simply write down

the last digit of the number and proceed in adding

up the neighbouring digits, carry 1 as in usual additon, mentally,

With a practice on a few of these multiplication, you can sure to mester any other difficult problets.

There are many suprises, puzzles tricks and interesting ideas in Mathematics. Please explore and share your exploration with us.

(4) ▼ 95 x 95

9025)

(5)

91 x 57

·8000+

8099

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日八十月七閏年申歷實