เล่มที่ 1 2

102
แบบฝกทักษะการแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง
ก ก
5 ( )
4
ก 24
16 = h
72
h = 108
24 × 72 = 108 × 16
1,728 = 1,728
! 16 ! " # $ " % 108
4
2 & ก $' ()*ก
+,ก ! % - , ./
1 & ก $' ()*ก *0 -
- , ./& 1 $' 2%ก3./4(
0 & ก *0 - 5 ()*ก
& 1 -+,ก !

101
ก ก
4 ( )
4
ก 1
200 = 12
f
f = 2,400
1 × 2,400 = 12 × 200
2,400 = 2,400
! ก % 7 + * 2,400 8-. & 1 24 "-
4
2 & ก $' ()*ก
+,ก ! % - , ./
1 & ก $' ()*ก *0 -
- , ./& 1 $' 2%ก3./4(
0 & ก *0 - 5 ()*ก
& 1 -+,ก !
5. ก # $ # %# 24 # ' ( )* ' 72 16 * # ( )*. $ ' ก
1 -": $ ; </
1. (0! *0; </+ - 1 16 ! *=" # > <$
" % ก*0
2. (0! *0; </ก & 1 $ ก ! < !& ?0! 24
! % " # $ " % 72
1 -": $ ; </
2 & -": $ 7@2& +,ก !
1 & ก ": $ ; </ ! -+,ก !
0 & ก ": $ <- ก& 1 -": $ "%<
2 ! 4 ก7@2&
% %! < " % $ ก ! "A(0-:?=
24 ! " # $ " % 72
16 ! " # $ " % h
":*< ! *= 24
16 = h
72
2 ! 4 ก7@2&
2 & ก "%1 ก ()*ก ก7@2& +,ก !
% ":*< +,ก
1 & ก "%1 ก ()*ก ก7@2& 8?0!
7 , *0+,ก <!-* ! 4( ; <
":*< 4(
0 & ก "%1 ก ()*ก ก7@2& -+,ก !
3 " ( ก - 4 *0 !
ก 24
16 = h
72
24 × 72 = h × 16
h = 24 × 72
16
= 108
0 16 # ( )* ' 108
3 " ( ก - 4 *0 !
2 & ก ()*ก ก7@2& 7$'
+,ก ! % -* +,ก !
1 & ก ()*ก ก7@2& ! 7
$' +,ก ! % -* *0+,ก
0 & ก ()*ก ก7@2& *0 -+,ก !
& 1 -* *04( & 1 - 5

100
ก ก
3 ( )
4
ก 1
2 = 175
c c = 350
1 × 350 = 175 × 2
350 = 350
! + A ! 175
A(-A/ ! 350
ก 1
3 = 175
e e = 525
1 × 525 = 175 × 3
525 = 525
! + A ! 175
A ! 525
4
2 & ก $' ()*ก
+,ก ! % - , ./
1 & ก $' ()*ก *0 -
- , ./& 1 $' 2%ก3./4(
0 & ก *0 - 5 ()*ก
& 1 -+,ก !
4. ก 34 ( 1 : 200 *# $ #* ก ' 367(8 * 79 4 8 $ # 3 : :# ก0
12 ; 4
1 -": $ ; </
1. (0! *0; </+ - 1 + < ! *0 $ 4 4!" ก 12
"8 ("- & < ! ก % 7 + * "7F "-
2. (0! *0; </ก & 1 ก & - 1 : 200
1 -": $ ; </
2 & -": $ 7@2& +,ก !
1 & ก ": $ ; </ ! -+,ก !
0 & ก ": $ <- ก& 1 -": $ "%<
2 ! 4 ก7@2&
ก- 1: 200 ":*< 1 : 200
& 1 1
200
+ < !$ 4 4! 12 8-. -- ($& < ! (!
f 8-. ":*< "7F $&- 12 : f & 1 12
f
":*< ! *= 1
200 = 12
f
2 ! 4 ก7@2&
2 & ก "%1 ก ()*ก ก7@2& +,ก !
% ":*< +,ก
1 & ก "%1 ก ()*ก ก7@2& 8?0!
7 , *0+,ก <!-* ! 4( ; <
":*< 4(
0 & ก "%1 ก ()*ก ก7@2& -+,ก !
3 " ( ก - 4 *0 !
ก 1
200 = 12
f
1 × f = 12 × 200
f = 12 × 200
= 2,400 "8 ("-
" 10 ! ก 1 8-. = 100 -.
2,400 8-. = 2,400
100 = 24 "-
0 * ก ' 367(8 * 24 4
3 " ( ก - 4 *0 !
2 & ก ()*ก ก7@2& 7$'
+,ก ! % -* +,ก !
1 & ก ()*ก ก7@2& ! 7
$' +,ก ! % -* *0+,ก
0 & ก ()*ก ก7@2& *0 -+,ก !
& 1 -* *04( & 1 - 5

99
ก ก
3. * # <4< < ' < 63 0 79 2 : 1 : 3 8 < 63 0 * # 175 0 *# <4< '
< 63 0 * #ก0
1 -": $ ; </
1. (0! *0; </+ - 1 + A ! 175 A(-A/
% A !ก*0
2. (0! *0; </ก & 1 ! *0A(-A/ A %
A "7F 2 : 1 : 3
1 -": $ ; </
2 & -": $ 7@2& +,ก !
1 & ก ": $ ; </ ! -+,ก !
0 & ก ": $ <- ก& 1 -": $ "%<
2 ! 4 ก7@2&
! *0A(-A/ A % A "7F 2 : 1 : 3
":*< !: ! A A(-A/ 1: 2 & 1 1
2
+ A ! 175 -- ($&A(-A/ !
c 175 : c & 1 175
c
":*< ! *= 1
2 = 175
c
":*< !: ! A A 1: 3 & 1 1
3
+ A ! 175 -- ($&A(-A/ !
e 175 : e & 1 175
e
":*< ! *= 1
3 = 175
e
2 ! 4 ก7@2&
2 & ก "%1 ก ()*ก ก7@2& +,ก !
% ":*< +,ก
1 & ก "%1 ก ()*ก ก7@2& 8?0!
7 , *0+,ก <!-* ! 4( ; <
":*< 4(
0 & ก "%1 ก ()*ก ก7@2& -+,ก !
3 " ( ก - 4 *0 !
& ! *0A(-A/ ! *=
ก 1
2 = 175
c
1 × c = 175 × 2
c = 175 × 2 = 350
! + A ! 175
A(-A/ ! 350
& ! *0 A ! *=
ก 1
3 = 175
e
1 × e = 175 × 3
e = 175 × 3 = 525
= 1 + A ! 175
A ! 525
0 8 < 63 0 * # 175 0 <4<63 0 * #
350 0 ' < 63 0 * # 525 0
3 " ( ก - 4 *0 !
2 & ก ()*ก ก7@2& 7$'
+,ก ! % -* +,ก !
1 & ก ()*ก ก7@2& ! 7
$' +,ก ! % -* *0+,ก
0 & ก ()*ก ก7@2& *0 -+,ก !
& 1 -* *04( & 1 - 5

98
ก ก
2. ก 4 ( # $ ' 7= 79 1 : 3 : 2 4' 30 8 > $ 10 8# *# * 63 ก
6
1 -": $ ; </
1. (0! *0; </+ - 1 + $' < 10 +! ก *
"
2. (0! *0; </ก & 1 ก * -* : !&(
< % 7, "7F 1 : 3 : 2 -%
1 -": $ ; </
2 & -": $ 7@2& +,ก !
1 & ก ": $ ; </ ! -+,ก !
0 & ก ": $ <- ก& 1 -": $ "%<
2 ! 4 ก7@2&
":*< : !&( < % 7, "7F 1 : 3 :
2 ก ก * =!&- 1 + 3 + 2 = 6 +!
< ก * "7F 3 : 6 & 1 3
6
+ $' < 10 +! -- ($& ก * d +!
":*< "7F $&- 10 : d & 1 10
d
":*< ! *= 3
6 =
10
d
2 ! 4 ก7@2&
2 & ก "%1 ก ()*ก ก7@2& +,ก !
% ":*< +,ก
1 & ก "%1 ก ()*ก ก7@2& 8?0!
7 , *0+,ก <!-* ! 4( ; <
":*< 4(
0 & ก "%1 ก ()*ก ก7@2& -+,ก !
3 " ( ก - 4 *0 !
ก 3
6 =
10
d
3 × d = 10 × 6
d = 10 × 6
3 = 20 +!
0 8 > $ 10 8# * 63 ก 20 8#
3 " ( ก - 4 *0 !
2 & ก ()*ก ก7@2& 7$'
+,ก ! % -* +,ก !
1 & ก ()*ก ก7@2& ! 7
$' +,ก ! % -* *0+,ก
0 & ก ()*ก ก7@2& *0 -+,ก !
& 1 -* *04( & 1 - 5
4
ก 3
6 =
10
d
d = 20
3 × 20 = 10 × 6
60 = 60
! + $' < 10 +! ก * 20 +!
4
2 & ก $' ()*ก
+,ก ! % - , ./
1 & ก $' ()*ก *0 -
- , ./& 1 $' 2%ก3./4(
0 & ก *0 - 5 ()*ก
& 1 -+,ก !

97
ก 0 8 4 00 3 ก? ก ก@* $7AB C (
>D3 1 ! # ก ก@* $7AB (3( > 4 $4C%ก? 7E 2
ก ก
1. ( $D # * $D #* 79 5 : 3 8 * $D 35 7E *# * 4 $Dก7E
1 -": $ ; </
1. (0! *0; </+ - 1 + " <5 35 7J !& * -* <5ก*07J
2. (0! *0; </ก & 1 <5: !" <5: !
* "7F 5 : 3
1 -": $ ; </
2 & -": $ 7@2& +,ก !
1 & ก ": $ ; </ ! -+,ก !
0 & ก ": $ <- ก& 1 -": $ "%<
2 ! 4 ก7@2&
":*< <5: !" <5: ! *
5 : 3 & 1 5
3
+ " <5 35 7J -- ($& * <5 n 7J
":*< "7F $&- 35 : n & 1 35
n
":*< ! *= 5
3 = 35
n
2 ! 4 ก7@2&
2 & ก "%1 ก ()*ก ก7@2& +,ก !
% ":*< +,ก
1 & ก "%1 ก ()*ก ก7@2& 8?0!
7 , *0+,ก <!-* ! 4( ; <
":*< 4(
0 & ก "%1 ก ()*ก ก7@2& -+,ก !
3 " ( ก - 4 *0 !
ก 5
3 = 35
n
5 × n = 35 × 3
y =
35 × 3
5
= 21 7J
0 8 * $D 35 7E * 4 $D 21 7E
3 " ( ก - 4 *0 !
2 & ก ()*ก ก7@2& 7$'
+,ก ! % -* +,ก !
1 & ก ()*ก ก7@2& ! 7
$' +,ก ! % -* *0+,ก
0 & ก ()*ก ก7@2& *0 -+,ก !
& 1 -* *04( & 1 - 5
4
ก 5
3 = 35
n
n = 21
5 × 21 = 35 × 3
105 = 105
! + " <5 35 7J * -* <5 21 7J
4
2 & ก $' ()*ก
+,ก ! % - , ./
1 & ก $' ()*ก *0 -
- , ./& 1 $' 2%ก3./4(
0 & ก *0 - 5 ()*ก
& 1 -+,ก !

96
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก =
8 × 21 = 12 × h
h = ×
= 14
! !' ! * 14
0 8 #ก (0 ( )*. $ 12 * #* #> # ( 14
4
ก =
h = 14
8 × 21 = 12 × 14
168 = 168
! + !ก $& * " # > <$ 12 ! !' ! * 14

95
4 !' ! * 8 * " # > <$ 21 !& + !ก $& *
" # > <$ 12 ! !' ! *ก*0
1 -": $ ; </
1. (# @* $8 4 + !ก $& * " # > <$ 12 ! !' ! *ก*0
2. (# @* $ก 3 !' ! * 8 * " # > <$ 21
:= *0 2 ! 4 ก7@2&
":*< *0 !ก "7 *< " *< ! *0-* - -A )/ 7$ !
!ก : -ก
"&# + ' ! *"A(0-:?= " % $ ก * % %!
! = ' ! * " % $' * "7F 4ก4
= 1 ' ! * 8 * " # > <$ 21
' ! * h * " # > <$ 12
":*< ! *=
'!*
8
21
12
h
=

94
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก =
60 × 3 = 2 × v
v = ×
= 90 ก@' 4 > @4#
! $' -" # 90 ก(;%"- '0 ;-!
0 8 #ก > ' 3 # 2 > @4#
* # > 4 ) 90 ก@' 4 > @4#
4
ก =
v = 90
60 × 3 = 2 × 90
180 = 180
! + !ก $'" % " ( ! 2 '0 ;-!
!$' -" # 90 ก(;%"- '0 ;-!

93
3 : +< / 7 !& : ก < -" # 60 ก(;%"- '0 ;-! $'" % " ( !
3 '0 ;-! + !ก $'" % " ( ! 2 '0 ;-! !$' -" # "
1 -": $ ; </
1. (# @* $8 4 + !ก $'" % " ( ! 2 '0 ;-! !$' -" # "
2. (# @* $ก 3 : +< / 7 !& : ก < -" # 60 ก(;%"- '0 ;-!
$'" % " ( ! 3 '0 ;-!
:= *0 2 ! 4 ก7@2&
":*< *0 !ก "7 *< " *< ! *0-* - -A )/ 7$ !
!ก : -ก
"&# + -" # +"A(0-:?= " % $ ก " ( ! % %!
! = -" # + " % $ ก " ( ! "7F 4ก4
= 1 -" # 60 ก(;%"- '0 ;-! $'" % " ( ! 3 '0 ;-!
-" # v ก(;%"- '0 ;-! $'" % " ( ! 2 '0 ;-!
":*< ! *=
-"#
"%
60
3
2
v
=

92
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก =
150 × 12 = d × 75
d = ×
= 24
! $'" % ก( : ก *= 24
0 8 4 $= 75 * ก ก ( 0 63 24
4
ก =
d = 24
150 × 12 = 24 × 75
1,800 = 1,800
! + -* <, 75 ก( : ก *= 24

91
2 : & ?0!ก & 150 ก( 12 + -* <, 75
ก( : ก *= ก*0
1 -": $ ; </
1. (# @* $8 4 + -* <, 75 ก( : ก *= ก*0
2. (# @* $ก 3 : & ?0!ก & 150 ก( 12
2 ! 4 ก7@2&
":*< *0 !ก "7 *< " *< ! *0-* - -A )/
7$ ! !ก : -ก
"&# + % %! *0 ก( : ก *="A(0-:?=
! = "7F 4ก4
= 1 150 ก( : & ?0!ก 12
75 ก( : & ?0!ก d
":*< ! *=
150
12
d
75
= % !
=
% !

90
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก =
8 × 30 = m × 25
m = ×
= 9.6
! $'" % 9.6
0 8 4> 25 * > ' ก 9.6
4
ก =
m = 9.6
8 × 30 = 9.6 × 25
240 = 240
! + -*' 25 $'" % $ ก 9.6

89
G'$ 00HIก ก? 1.4
! # ก ก; </7@2& 4ก4
> *# $& ก" *< " (- & 1 : -%!$ ' ! ! *0ก & $&
1 ' 8 $'" % $ ก 30 !& + -*' 25
$'" % $ ก ก*0
1 -": $ ; </
1. (# @* $8 4 + -*' 25 $'" % $ ก ก*0
2. (# @* $ก 3 ' 8 $'" % $ ก 30
2 ! 4 ก7@2&
":*< *0 !ก "7 *< " *< ! *0-* - -A )/ 7$ !
!ก : -ก
"&# + ' "A(0-- ก:?= *0 $& % " # % %!
! = ' *0 $& % " # "7F 4ก4
= 1 ' 8 $'" % $ ก 30
' 25 $'" % $ ก m
":*< ! *=
'
8
30
m
25
= % !
=
% !

88
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก ,
=
1 × f = 11 × 12,000
f = 132,000 "8 ("-
" 10 ! ก 100 "8 ("- = 1 "-
132,000 "8 ("- =
,
= 1,320 "-
" 10 ! ก 1,000 "- = 1 ก(;%"-
1,320 "- =
,
,
= 1.32 ก(;%"-
= 1 < ! ก 7; !" *< 1.32 ก(;%"-
0 $ #* #* ก0 67@ # $ 1.32 ก@' 4
4
ก ,
=
f = 132,000
1 × 132,000 = 11 × 12,000
132,000 = 132,000
! < ! ก 7; !" *< 132,000 "8 ("-
& 1 1.32 ก(;%"-

87
4 + 4 4!$'- 1 : 12,000 < ! ก 7; !" *< 11
"8 ("- !& < ! (! ก 7; !" *< "7F < !7 - .ก*0ก(;%"-
1 -": $ ; </
1. (# @* $8 4 & < ! (! ก 7; !" *< "7F < !7 - .ก*0ก(;%"-
2. (# @* $ก 3 + 4 4!$'- 1 : 12,000 < ! ก 7; !" *< 11
"8 ("-
:= *0 2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
ก- 1 : 12,000 &- < -
+ < !$ 4 4!< .....1......& < < ! (!< .....12,000.......& <
":*< ...........1 : 12,000..........& 1 .......... ,
.........
< !$ 4 4! ....11...."8 ("- -- ($& < ! (!....f..."8 ("-
":*< $&- ...........11 : f..........& 1 ......... ...........
":*< ! *= =
< !$ 4 4!
< ! (!
1
12,000
11
f

86
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก ,
=
1 × e = 9 × 2,000
e = 18,000 ก(;%"-
= 1 < ! (! 18,000 ก(;%"-
0 $ #* # 18,000 ก@' 4
4
ก ,
=
e = 18,000
1 × 18,000 = 9 × 2,000
18,000 = 18,000
! < ! (! 18,000 ก(;%"-

85
3 ก & - 1 8-. : 2,000 ก-. !& < ! (!"7F ก(;%"-
+ < ! *0 $ 4 4!" ก 9 "8 ("-
1 -": $ ; </
1. (# @* $8 4 & < ! (!"7F ก(;%"- + < ! *0 $ 4 4!" ก 9 "8 ("-
2. (# @* $ก 3 ก & - 1 8-. : 2,000 ก-.
:= *0 2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
ก- 1 8-. : 2,000 ก-. &- < -
+ < !$ 4 4!< .....1......"8 ("- < ! (!< .....2,000.......ก(;%"-
":*< ...........1 : 2,000..........& 1 .......... ,
.........
< !$ 4 4! ....9...."8 ("- -- ($& < ! (!....e...ก(;%"-
":*< $&- ...........9 : e..........& 1 ......... ...........
":*< ! *= =
< !$ 4 4!
< ! (!
1
2,000
9
e

84
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก , ,
=
.
1 × m = 27.5 × 2,500,000
m = 68,750,000 "8 ("-
" 10 ! ก 100 "8 ("- = 1 "-
68,750,000 "8 ("- =
, ,
= 687,500 "-
" 10 ! ก 1,000 "- = 1 ก(;%"-
687,500 "- =
,
,
= 687.5 ก(;%"-
= 1 < ! ก: ก +?! -5 687.5 ก(;%"-
0 $ #* #* ก ก 8%#(4D ( 687.5 ก@' 4
4
ก , ,
=
.
m = 68,750,000
1 × 68,750,000 = 27.5 × 2,500,000
68,750,000 = 68,750,000
! < ! ก: ก +?! -5 68,750,000 "8 ("-
& 1 687.5 ก(;%"-

83
2 4 *07 " P < 5- 1 : 2,500,000 + < ! ก: ก +?!
-5 $ 4 *0 7 - . 27.5 "8 ("- !& : ก <,& ! ก
-5 7 - .ก*0ก(;%"-
1 -": $ ; </
1. (# @* $8 4 : ก <,& ! ก -5 7 - .ก*0ก(;%"-
2. (# @* $ก 3 4 *07 " P < 5- 1 : 2,500,000 + < ! ก
: ก +?! -5 $ 4 *0 7 - . 27.5 "8 ("-
2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
ก- 1 : 2,500,000 &- < -
+ < !$ 4 *0< .....1......& < < ! (!< .....2,500,000.......& <
":*< ...........1 : 2,500,000..........& 1 .......... , ,
.........
< !$ 4 *0 ....27.5...."8 ("- -- ($& < ! (!....m..."8 ("- ":*<
$&- ...........27.5 : m..........& 1 .........
.
...........
":*< ! *= =
< !$ 4 *0
< ! (!
1
2,500,000
27.5
m

82
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก =
.
1 × d = 3.6 × 250
d = 900 ก(;%"-
= 1 < ! & !"-1 ! =! ! 900 ก(;%"-
0 $ #* # # 4! # #( # 900 ก@' 4
4
ก =
.
d = 900
1 × 900 = 3.6 × 250
900 = 900
! < ! & !"-1 ! =! ! 900 ก(;%"-

81
G'$ 00HIก ก? 1.3
! # ก ก; </7@2& ($ ,7: !- )
> *# $& ก" *< " (- & 1 : -%!$ ' ! ! *0ก & $&
1 - *0$'":*< 4 *0 4 & ?0!"7F 1 8-. : 250 ก-. + < & !
"-1 ! !"-1 !$ 4 *0"7F 3.6 "8 ("- !& < ! & !"-1 ! =! !
1 -": $ ; </
1. (# @* $8 4 & < ! & !"-1 ! =! !
2. (# @* $ก 3 - *0$'":*< 4 *0 4 & ?0!"7F 1 8-. : 250 ก-. + < & !
"-1 ! !"-1 !$ 4 *0"7F 3.6 "8 ("-
2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
ก- 1 8-. : 250 ก-. &- < -
+ < !$ 4 *0< .....1......"8 ("- < ! (!< .....250.......ก(;%"-
":*< ...........1 : 250..........& 1 .......... .........
< !$ 4 *0 .....3.6...."8 ("- -- ($& < ! (!......d......ก(;%"-
":*< $&- ...........3.6 : d..........& 1 .........
.
...........
":*< ! *= =
< !$ 4 *0
< ! (!
1
250
3.6
d

80
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก =
8 × d = 30 × 20
d =
×
d = 75
= 1 = - 7@S 75 ก -
0 63 4 7AK 75 ก 4
4
ก =
d = 75
8 × 75 = 30 × 20
600 = 600
! = - 7@S 75 ก -

79
4 = - 7@S -* 4 -: ! = - "ก%1 % = "'10 -"7F 7 : 5 : 8 ก -
+ $' = "'10 - 30 ก - = - 7@S ก*0ก -
1 -": $ ; </
1. (# @* $8 4 + $' = "'10 - 30 ก - = - 7@S ก*0ก -
2. (# @* $ก 3 = - 7@S -* 4 -: ! = - "ก%1 % = "'10 -
"7F 7 : 5 : 8 ก -
:= *0 2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
4 -: ! = - "ก%1 % = "'10 - "7F 7 : 5 : 8
ก = - 7@S =!&- 7 + 5 + 8 = 20 ก -
= "'10 - = - 7@S "7F 8 : 20
+ = "'10 - 30 ก - -- ($& = - 7@S d ก -
":*< $&-: ! = "'10 - = - 7@S
30 : d & 1
":*< ! *= =
= "'10 -
= - 7@S
8 30
20 d

78
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
& *0 % *0& ?0! ! *=
ก =
6 × y = 75 × 7
y =
×
y = 87.5
= 1 *0 % *0& ?0! 87.5
0 ( 063' 30 %#( 063 87.5
& *0 % *0 - ! *=
ก =
6 × z = 75 × 5
z =
×
z = 62.5
! *0 % *0 - 62.5
0 ( 063' 30 ( 4( 063 62.5
4
ก =
y = 87.5
6 × 87.5 = 75 × 7
525 = 525
! : ! *0 % *0& ?0! 87.5
ก =
z = 62.5
6 × 62.5 = 75 × 5
375 = 375
! : ! *0 % *0 - 62.5

77
3 4,": 3 "7F 6 : 7 : 5 *0 %
*0 ! 75 !& : ! *0 % *0& ?0!
% : ! *0 % *0 -
1 -": $ ; </
1. (# @* $8 4 : ! *0 % *0& ?0! % *0 %
*0 -
2. (# @* $ก 3 4,": 3 "7F 6 : 7 : 5 *0
% *0 ! 75
:= *0 2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ % "7F
% " *< ก
: !4,": 3 "7F 6 : 7 : 5
":*< *0 % *0 ! *0 % *0& ?0!
6 : 7 & 1
+ *0 % *0 ! 75 -- ($& *0 % *0& ?0!
y ":*< ! *= =
":*< *0 % *0 ! *0 % *0 -
6 : 5 & 1
+ *0 % *0 ! 75 --5 ($& *0 % *0 -
z ":*< ! *= =

76
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก =
6 × 60 = n × 12
n =
×
n = 30
= 1 -< : ! *0< *0 5 30 "8 ("-
0 3 $ (D34 4$ 30 ; 4
4
ก =
n = 30
6 × 60 = 30 × 12
360 = 360
! *0< *0 5 -* -< 30 "8 ("-

75
2 -"&%*0<- ,7& ?0!-* -< : ! "7F 2 : 4 : 6 + -"&%*0<- ,7 *=
-* -< ,7" ก 60 "8 ("- !& -< : ! *0< *0 5
1 -": $ ; </
1. (# @* $8 4 + -"&%*0<- ,7 *=-* -< ,7" ก 60 "8 ("- !& -<
: ! *0< *0 5
2. (# @* $ก 3 -"&%*0<- ,7& ?0!-* -< : ! "7F 2 : 4 : 6
2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
$& -< : ! *0< *0 5 "7F n
-< : ! ,7 -"&%*0<- "7F 2 : 4 : 6
U = *0< *0 5 < 6
-< ,7 -"&%*0<-" ก 2 + 4 + 6 = 12
":*< *0< *0 5 -< ,7
6 : 12 & 1
+ -< ,7< 60 "8 ("- -- ($& < *0 5 < n "8 ("-
":*< $&-: ! *0< *0 5 -< ,7
n : 60 & 1
":*< ! *= =
*0< *0 5
-< ,7
6 n
12 60

74
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก =
!
,
3 × 30,000 = a × 5
a =
× ,
a = 18,000
= 1 !: !ก(Wก 18,000
0 กLก* 63 0( 0# 18,000 0
4
ก =
!
,
a = 18,000
3 × 30,000 = 18,000 × 5
90,000 = 90,000
= 1 ก(Wก ! 18,000

73
G'$ 00HIก ก? 1.2
! # ก ก; </7@2& ($ ,7 " 10 !)
> *# $& ก" *< " (- & 1 : -%!$ ' ! ! *0ก & $&
1 ก(Wก :%5< % *- ! กก %! 5 < 3 : 5 : 2 + :%5<
!"7F "!( 30,000 ก(Wก !ก*0
1 -": $ ; </
1. (# @* $8 4 + :%5< !"7F "!( 30,000 ก(Wก !ก*0
2. (# @* $ก 3 ก(Wก :%5< % *- ! กก %! 5 < 3 : 5 : 2
2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
$&ก(Wก !"7F "!( a
ก %! 5 : !ก(Wก :%5< % *- "7F 3 : 5 : 2 -%
ก %! 5 : !ก(Wก :%5< "7F 3 : 5 & 1
+ :%5< ! 30,000 -- ($&ก(Wก ! a
":*< $&-: ! !: !ก(Wก !: !:%5<
a : 30,000 & 1
!
,
":*< ! *= =
!: !ก(Wก
!: !:%5<
3 a
5 30,000

72
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก =
10 × d = 15 × 25
d =
×
d = 37.5
= 1 " ( < ! 37.5 "-
0 B# 3 63 $ # 37.5 4
4
ก =
d = 37.5
10 × 37.5 = 15 × 25
375 = 375
! " ( < ! 37.5 "-

71
4 &2(! & ?0!$'" % " ( 10 * " ( < ! 25 "- + &2(! *=$'" %
" ( 15 * " ( < !ก*0"-
1 -": $ ; </
1. (# @* $8 4 + &2(! *=$'" % " ( 15 * " ( < !ก*0"-
2. (# @* $ก 3 &2(! & ?0!$'" % " ( 10 * " ( < ! 25 "-
:= *0 2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
$&" ( < ! d "-
&2(! & ?0!$'" % " ( 10 * " ( < ! 25 "-
":*< " % " ( "7F * < !"7F "-
10 : 25 & 1
+ &2(! *=$'" % " ( 15 * -- ($& < ! d "-
":*< $&-: !" % " ( "7F * < !"7F "-
15 : d & 1
":*< ! *= =
" %
< !
10 15
25 d

70
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก =
"
#
7 × B = 84 × 8
B =
" ×
B = 96
= 1 & < 96
0 $( 063 96
4
ก =
"
#
B = 96
7 × 96 = 84 × 8
672 = 672
! : !& < 96

69
3 (' .( P /: ! ( : !& <
"7F 7 : 8 + ( 84 !& : !& <
1 -": $ ; </
1. (# @* $8 4 + ( 84 !& : !& <
2. (# @* $ก 3 (' .( P /: ! ( : !& <
"7F 7 : 8
:= *0 2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ % "7F
% " *< ก
$& : !& <"7F B
":*< : ! ( : !& <
7 : 8 & 1
+ ( 84 -- ($&& < B
":*< $&-: ! ( & <
84 : B & 1
"
#
":*< ! *= =
(
& <
7 84
8 B

68
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก =
2 × y = 160 × 3
y =
×
y = 240
= 1 = -* < 240 "-
0 ( 43 $ 240 4
4
ก =
y = 240
2 × 240 = 160 × 3
480 = 480
! ! <"!( - - ! 240

67
2 = ,7 *0"&%*0<-41 4 ก ! 160 "- + : ! ก ! <
"7F 2 : 3 = &! *= < "
1 -": $ ; </
1. (# @* $8 4 + : ! <ก ! < "7F 2 : 3 = &! *= < "
2. (# @* $ก 3 = ,7 *0"&%*0<-41 4 ก ! 160 "-
2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ % "7F %
" *< ก
$& -< = "7F y "-
":*< ก ! <
2 : 3 & 1
+ = -* ก ! 160 "- -- ($& < y "-
":*< $&-: ! ก ! <
160 : y & 1
":*< ! *= =
ก !
<
2 160
3 y

66
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก = $
12 × A = 60 × 21
A =
×
A = 105
= 1 ! <"!( - - ! 105
0 * $ # 4 4 # 79 # 105 0
4
ก = $
A = 105
12 × 105 = 60 × 21
1260 = 1260
! ! <"!( - - ! 105

65
G'$ 00HIก ก? 1.1
! # ก ก; </7@2&
> *# $& ก" *< " (- & 1 : -%!$ ' ! ! *0ก & $&
1 - - ! 12 4% 21 + 81= - - ! 60 4% ! <"!( "
1 -": $ ; </
1. (# @* $8 4 + 81= - - ! 60 4% ! <"!( "
2. (# @* $ก 3 - - ! 12 4% 21
2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
$& <"!( "7F .........A.........
- - ! 12 4% 21
":*< - - !"7F 4% "7F
12 : 21 & 1
+ 81= - - ! 60 4% -- ( ! <"!( A
":*< $&-: ! - - !"7F 4% "7F
60 : A & 1 $
":*< ! *= =
- - !
12 60
21 A

แบบฝกทักษะการแกโจทยปญหาคณิตศาสตร
เล#มที่
'10 ..........................................................
#0 %ก 00HIก ก?
00HIก ก? C (
Z[ก ก3 1.1
Z[ก ก3 1.2
Z[ก ก3 1.3
Z[ก ก3 1.4
4 00HIก ก?
ก3 $ ก ก; </7@2&
แบบฝกทักษะการแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิ
ึ
เล#มที่ 1 การแกโจทยปญหาสัดส#วน
.........................................................."%: *0...................'= -)<-P?ก3 7J *0
00HIก ก? ' 00 3 ก? ก ก@* $7AB
00HIก ก? C ( )4 63
32
32
32
32
128
ก3 $ ก ก; </7@2& >D3 1 40
64
โดย เพลินพิศ ปฏิเตนัง
'= -)<-P?ก3 7J *0 2
' 00 3 ก? ก ก@* $7AB C (
$'

63
ภาคผนวก

62
0 Dก 4
ก ก %* 53.ก ก5% % . . (2554). #(! $ $ > <! M C ( ก'D4( ก $ =
C ( 4.2 '4 1. (A(-A/ =! *0 3). ก 5!" A-& : ก3 " (2 P /.
ก !P?ก3 )(ก . (2554). #(! $ $ > <! M C ( '4 1 > 4 $4C%ก? 7E 2.
(A(-A/ =! *0 2). ก 5!" A-& : ; !A(-A/ ก % A .
U * . "P - %</ % . . (2546). ก*ก 4 C ( > 4 $4C%ก? 7E 2 '4 1.
ก 5!" A-& : 7 -( .
! ( </ 5 .) . (2553). #(! $ ( 4 C ( <4 4 4.2 . $ 1.
ก 5!" A-& : กA(-A/ -# .
. (2553). #(! $ ( 4 C ( <4 4 4.1 . $ 2.
ก 5!" A-& : กA(-A/ -# .
AA &<- ! % - %( / ( )( . (2547). #(! ( ก $ =<! M C (
ก'D4( ก $ = C ( > 4 $4C%ก? 7E 2. ก 5!" A-& : (3 A
5.> A (' ก (A .).
A ( A( (] - '< % . . (2548). 00HIก( ก $ =<! M C ( <! M 4.2
. $ 1. ก 5!" A-& : กA(-A/ -# .
"%(P "ก . (2547). =( # C ( > 4 $4C%ก? 7E 2 '4 1. (A(-A/ =! *0 1).
ก 5!" A-& : ก3 " (2 P /.
!" (-ก ( < P / % " ; ;%<*, + . (2554). =4! =( ก $ =<! M
C ( '4 1 > 4 $4C%ก? 7E 2 4 'ก(= ก C%ก? <! M <D Cก > 2551.
ก 5!" A-& : ; !A(-A/ ก . % A .
!" (-ก ( < P / % " ; ;%<*, + . (2554). #(! $ ( ก $ =<! M
C ( '4 1 > 4 $4C%ก? 7E 2 4 'ก(= ก C%ก? <! M <D Cก > 2551.
(A(-A/ =! *0 1). ก 5!" A-& : ; !A(-A/ ก .% A .
2 -* ! % ! / -.*"%#ก. (2547). C ( 4. 2 '4 (40= 00. ก 5!" A-& :
A ('.

61
5. ก # $ # %# 24 # ' ( )* ' 72 16 * #
( )*. $ ' ก
1 4 *@* $ (2 )
1) (0! *0; </+ - (1 )....................................................................................................
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2) (0! *0; </ก & (1 )................................................................................................
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2 # : ก7AB (2 )
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3 3 ก 4 : #6 ; < ! ()*ก ก7@2& - 4 *0 ! (2 )
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4 *( 0 0 (2 )
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60
4. ก 34 ( 1 : 200 *# $ #* ก ' 367(8 * 79 4 8 $ #
3 : :# ก0 12 ; 4
1 4 *@* $ (2 )
1) (0! *0; </+ - (1 )....................................................................................................
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2) (0! *0; </ก & (1 )................................................................................................
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2 # : ก7AB (2 )
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3 3 ก 4 : #6 ; < ! ()*ก ก7@2& - 4 *0 ! (2 )
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59
3. * # <4< < ' < 63 0 79 2 : 1 : 3 8 < 63 0 * # 175 0 *#
<4< ' < 63 0 * #ก0
1 4 *@* $ (2 )
1) (0! *0; </+ - (1 )....................................................................................................
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3 3 ก 4 : #6 ; < ! ()*ก ก7@2& - 4 *0 ! (2 )
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58
2. ก 4 ( # $ ' 7= 79 1 : 3 : 2 4' 30 8 > $ 10 8# *#
* 63 ก 6
1 4 *@* $ (2 )
1) (0! *0; </+ - (1 )....................................................................................................
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57
1. ( $D # * $D #* 79 5 : 3 8 * $D 35 7E *# * 4 $Dก7E
1 4 *@* $ (2 )
1) (0! *0; </+ - (1 )....................................................................................................
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56
00 3 ก? ก ก@* $7AB C (
>D3 1 ! # ก ก@* $7AB (3(
> *#
1. *=7 ก <7@2& ! .( P / 5 : " % 1 '0 ;-!
2. 7@2& % : -*:= < < <, 4 :=
3. $& ก" *< ":*< %!$ A1= *0 *0ก & $&
4. $& ก" *< P?ก3 ()*ก % := ก %!-1
5. ก $& $& % := < < ; <-* := % 2
'10 ................................................................."%: *0.............'= -)<-P?ก3 7J *0 2

55
3 " ( ก - 4 *0 !
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4
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54
4
!' ! * 8 * " # > <$ 21 !& + !ก $& *
" # > <$ 12 ! !' ! *ก*0
1 -": $ ; </
1. (# @* $8 4 ! ...............................................................................................................
2. (# @* $ก 3 ! ..........................................................................................................
2 ! 4 ก7@2&
":*< *0 !ก "7 *< " *< ! *0-* - -A )/
7$ ! !ก : -ก
.........................................................................................................................................
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53
3 " ( ก - 4 *0 !
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4
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52
3
: +< / 7 !& : ก < -" # 60 ก(;%"- '0 ;-! $'" % " ( !
3 '0 ;-! + !ก $'" % " ( ! 2 '0 ;-! !$' -" # "
1 -": $ ; </
1. (# @* $8 4 ! ............................................................................................................
2. (# @* $ก 3 ! .......................................................................................................
............................................................................................................................................
2 ! 4 ก7@2&
":*< *0 !ก "7 *< " *< ! *0-* - -A )/
7$ ! !ก : -ก
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51
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก ..................... = ......................
..................... = ......................
..................... = ......................
= ......................
! ................................................................................................................
0 ................................................................................................................
4
ก ..................... = ......................
..................... = ......................
..................... = ......................
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! ........................................................................................................

50
2
: & ?0!ก & 150 ก( 12 + -* <, 75
ก( : ก *= ก*0
1 -": $ ; </
1. (# @* $8 4 ! ............................................................................................................
2. (# @* $ก 3 ! ......................................................................................................
2 ! 4 ก7@2&
":*< *0 !ก "7 *< " *< ! *0-* - -A )/
7$ ! !ก : -ก
$&ก( : ....................
"&# + % %! *0 ก( : ก *="A(0-:?=
3# "7F 4ก4
! ................ ก( : & ?0!ก .................
................ ก( : & ?0!ก .................
":*< ! *=
......................
....................
= % !
=
% !

49
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก ..................... = ......................
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= ....................
! $'" % ...............................
0 ................................................................................................................
4
ก ..................... = ......................
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! ................................................................................................................

'10 .............................................................
> *# $& ก" *< " (- & 1 : -%!$ ' ! ! *0ก & $&
' 8 $'" % $ ก
1. (# @* $8 4 ! ......
2. (# @* $ก 3 !
":*< *0 !ก "7 *< " *< ! *0-* - -A )/ 7$ !
!ก : -ก
$&$'" % $ ก
"&# +
3#
! ' ..............
' ..............
":*< ! *=
......................
แบบฝกทักษะ 1.4
! # ก ก; </7@2& 4ก4
............................................................."%: *0..............'= -)<-P?ก3 7J *0
$& ก" *< " (- & 1 : -%!$ ' ! ! *0ก & $&
1
$'" % $ ก 30 !& + -*' 25 $'" % $ ก
1 -": $ ; </
......^^^^^^^^^^^^^^^^^^^^^^^^^^.
! ..^^^^^^^^^^^^^^^^^^^^^^^^^^.
2 ! 4 ก7@2&
*0 !ก "7 *< " *< ! *0-* - -A )/ 7$ !
$&$'" % $ ก ....................
"&# + ' "A(0-- ก:?= *0 $& % " # % %!
' *0 $& % " # "7F 4ก4
.............. $'" % $ ก ...............
.............. $'" % $ ก ...............
....................
% !
==
48
'= -)<-P?ก3 7J *0 2
$& ก" *< " (- & 1 : -%!$ ' ! ! *0ก & $&
$'" % $ ก ก*0
^^^^^^^^^^^^^^^^^^^^^^^^^^.
^^^^^^^^^^^^^^^^^^^^^^^^^^.
*0 !ก "7 *< " *< ! *0-* - -A )/ 7$ !
$& % " # % %!
$& % " # "7F 4ก4
=
% !

47
3 " ( ก - 4 *0 !
ก 12
b = 3
5
12 × 5 = 3 × b
b = 12 × 5
3
= 20
! ! ! ! 20
0 8 #ก # ' ( )*. $ ' 3 * #* # # 20
4
ก 12
b = 3
5
b = 20
12 × 5 = 3 × 20
60 = 60
! + !ก $&! % " # > <$ " % 3 ! ! ! 20

46
ตัวอยางที่ 2
! ! 12 * 0 $& % " # > <$ 5 + !ก $&! % " #
$ 3 ! ! ! ก*0
1 -": $ ; </7@2&
1. (# @* $8 4 1 + !ก $&! % " # $ 3 ! ! ! ก*0
2. (# @* $ก 3 1 ! ! 12 * 0 $& % " # > <$ 5
2 ! 4 ก7@2&
; <":*< *0 !ก "7 *< " *< ! *0-* - -A )/ 7
$ ! !ก : -ก
$& ! ! b
"&# + ! "A(0-- ก:?= *0 ! $& % " # % %!
3# ! *0 ! $& % " # "7F 4ก4
! ! 12 * 0 $& % " # > <$ 5
! b * 0 $& % " # > <$ 3
":*< ! *=
!
12
5
3
b
= % !
=
% !

45
3 " ( ก - 4 *0 !
ก 60
p = 10
30
60 × 30 = 10 × p
p = 60 × 30
10
= 180
! !"%*=<!"7F 180
0 8 #ก 43. $ ' 10 * # '$# 793 180
4
ก 60
p = 10
30
p = 180
60 × 30 = 10 × 180
1,800 = 1,800
! + !ก $& & *=&- > <$ " % 10 !"%*=<!"7F 180

44
บัตรตัวอยาง 1.4
เรื่อง การแกโจทยปญหาสัดสวนผกผัน
"7F 60 ก( & & ?0!&- > <$ " % 30 + !ก $& & *=
&- > <$ " % 10 !"%*=<!"7F ก*0
1 -": $ ; </7@2&
1. (# @* $8 4 1 + !ก $& & *=&- > <$ " % 10 !"%*=<!"7F ก*0
2. (# @* $ก 3 1 "7F 60 ก( & & ?0!&- > <$ " % 30
2 ! 4 ก7@2&
; <":*< *0 !ก "7 *< " *< ! *0-* - -A )/
7$ ! !ก : -ก
$&"%*=<!"7F p
"&# + "7F "A(0-- ก:?= *0ก( & % %!
3# "7F *0ก( & "7F 4ก4
! "7F 60 ก( & &- > <$ " % 30
"7F p ก( & &- > <$ " % 10
":*< ! *=
"7F
60
30
10
p
= % !
=
% !

43
3 " ( ก - 4 *0 !
........................................................................................................................................
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4
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42
4
+ 4 4!$'- 1 : 12,000 < ! ก 7; !" *< 11
"8 ("- !& < ! (! ก 7; !" *< "7F < !7 - .ก*0ก(;%"-
1 -": $ ; </
1. (# @* $8 4 1 .............................................................................................................
2. (# @* $ก 3 1 .......................................................................................................
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^.
2 ! 4 ก7@2&
.........................................................................................................................................
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.........................................................................................................................................
.........................................................................................................................................

41
3 " ( ก - 4 *0 !
...........................................................................................................................................
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4
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...........................................................................................................................................
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...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................

40
3
ก & - 1 8-. : 2,000 ก-. !& < ! (!"7F ก(;%"-
+ < ! *0 $ 4 4!" ก 9 "8 ("-
1 -": $ ; </
1. (# @* $8 4 ! ..............................................................................................................
2. (# @* $ก 3 ! ..........................................................................................................
^^^^^^^^^^^^^^^^^^^^^^^^^^^^..^^^^^^.
2 ! 4 ก7@2&
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
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...........................................................................................................................................
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..........................................................................................................................................

39
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก ......................... = .......................................
......................... = .......................................
......................... = .......................................
" 10 ! ก........................"8 ("- = ...................................."-
.........................."8 ("- = ........................
= ...................... "-
" 10 ! ก..........................."- = ............................ก(;%"-
..........................."- = ...................
= ................... ก(;%"-
! < ! ก: ก +?! -5 ....................... ก(;%"-
0 .............................................................................................
4
ก ......................... = .......................................
......................... = .......................................
......................... = .......................................
......................... = .......................................
! < ! ก: ก +?! -5 ............................"8 ("-
& 1 .............................ก(;%"-

38
2
4 *07 " P < 5- 1 : 2,500,000 + < ! ก: ก +?!
-5 $ 4 *0 7 - . 27.5 "8 ("- !& : ก <,& ! ก
-5 7 - .ก*0ก(;%"-
1 -": $ ; </
1. (# @* $8 4 ! ..............................................................................................................
2. (# @* $ก 3 1 .........................................................................................................
^^^^^...........................................................................................................................
2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
$&: ก & ! ก -5 ..................ก(;%"-
ก- 1 : 2,500,000 &- < -
+ < !$ 4 *0< ................& < < ! (!< ..............................& <
":*< ..............................& 1 .......................................
< !$ 4 *0 ............."8 ("- -- ($& < ! (!............."8 ("-
":*< $&- ..............................& 1 ...............................
":*< ! *= =
................................
...........................

37
3 " ( ก - 4 *0 !
& 7 $ ; <$' ()*ก ,. :
ก ....................... = ...................................
....................... = ...................................
....................... = ...................................
....................... = ...................................
! < ! & !"-1 ! =! !...........................ก(;%"-
0 ............................................................................................
4
ก ....................... = ...................................
....................... = ...................................
....................... = ...................................
....................... = ...................................
....................... = ...................................
! < ! & !"-1 ! =! !...........................ก(;%"-

! # ก ก; </7@2&
'10 ...............................................................
> *# $& ก" *< " (- & 1 : -%!$ ' ! ! *0ก & $&
- *0$'":*< 4 *0 4 & ?0!"7F
"-1 ! !"-1 !$ 4 *0"7F
1. (# @* $8 4 1 ...............................................................................................................
2. (# @* $ก 3 1
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ % "7F %
" *< ก
$& < ! & !"-1 ! =! !"7F
+ < !$ 4 *0<
":*<
< !$ 4 *0
":*< $&-
":*< ! *=
แบบฝกทักษะ 1.3
ก ก; </7@2& ($ ,7: !- )
..............................................................."%: *0.............'= -)<-P?ก3 7J *0
$& ก" *< " (- & 1 : -%!$ ' ! ! *0ก & $&
1
- *0$'":*< 4 *0 4 & ?0!"7F 1 8-. : 250 ก-. + < & !
"-1 ! !"-1 !$ 4 *0"7F 3.6 "8 ("- !& < ! & !"-1 ! =! !
1 -": $ ; </
...............................................................................................................
1 ...........................................................................................................
2 ! 4 ก7@2&
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ % "7F %
$& < ! & !"-1 ! =! !"7F ............ก(;%"- ก- 1 8-
+ < !$ 4 *0< ................."8 ("- < ! (!< ...................
...................................& 1 .....................................
< !$ 4 *0 .............."8 ("- -- ($& < ! (!............
$&- ...................................& 1 .....................................
=
^^^^^^^^^
^^^^^^^.
36
'= -)<-P?ก3 7J *0 2
$& ก" *< " (- & 1 : -%!$ ' ! ! *0ก & $&
+ < & !
"8 ("- !& < ! & !"-1 ! =! !
...............................................................................................................
...........................................................................................................
":*< ! ; <$&% : ! (0! *0"7 *< " *< $ % "7F %
8-. : 250 ก-.
.......ก(;%"-
.....................................
ก(;%"-
.....................................

35
3 " ( ก - 4 *0 !
ก 1
150 = 2.4
k
1 × k = 2.4 × 150
k = 2.4 × 150
1
= 360 ก@' 4
! < !$ >,-(7 " P 360 ก(;%"-
0 $ #* # .=47 C 360 ก@' 4
4
ก 1
150 = 2.4
k
k = 360
1 × 360 = 2.4 × 150
360 = 360
! < ! (!$ >,-(7 " P 360 ก(;%"-

34
- $ 4 *0"7F 1 8-. : 150 ก-. + < !$ 4 4! 2.4
"8 ("- < ! (!$ >,-(7 " P"7F ก*0ก(;%"-
1 -": $ ; </7@2&
1. (# @* $8 4 1 + < !$ 4 4! 2.4 "8 ("- < ! (!
$ >,-(7 " P"7F ก*0ก(;%"-
2. (# @* $ก 3 1 - $ 4 *0"7F 1 8-. : 150 ก-.
2 ! 4 ก7@2&
; <":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
$& < ! (!$ >,-(7 " P"7F k ก(;%"-
ก- 1 8-. : 150 ก-. &- < -
+ < !$ 4 *0< 1 "8 ("- < ! (!< 150 ก(;%"-
":*< "7F 1 : 150 & 1 1
150
< !$ 4 *0 2.4 8-. -- ($& < ! (! k ก-.
":*< $&- 2.4 : k & 1 2.4
k
":*< ! *= =
1
150
2.4
k
< !$ 4 4!
< ! (!

33
3 " ( ก - 4 *0 !
ก 1
50,000 = 7.5
x
1 × x = 7.5 × 50,000
x = 7.5 × 50,000
1
= 375,000 ; 4
" 10 ! ก 100 "8 ("- = 1 "-
375,000 "8 ("- = 375,000
100 = 3,750 4
" 10 ! ก 1,000 "- = 1 ก(;%"-
3,750 "- = 3,750
1,000 = 3.75 ก@' 4
! < ! ก; !A< % 7 3.75 ก(;%"-
0 $ #* #* ก@ #<$ 0 '67 3 3.75 ก@' 4
4
ก 1
50,000 = 7.5
x
x = 375,000
1 × 375,000 = 7.5 × 50,000
375,000 = 375,000
! < ! (! ก; !A< % 7 3.75 ก(;%"-

32
บัตรตัวอยาง 1.3
เรื่อง การแกโจทยปญหาสัดสวน (ในรูปมาตราสวน)
< ! ก; !A< % 7 4 4!- 1 : 50,000 7.5 "8 ("-
!& < ! (!7 - .ก*0ก(;%"-
1 -": $ ; </7@2&
1. (# @* $8 4 1 & < ! (! ก; !A< % 7 7 - .ก*0ก(;%"-
2. (# @* $ก 3 1 < ! ก; !A< % 7 4 4!-
1 : 50,000 7.5 "8 ("-
2 ! 4 ก7@2&
; <":*< ! ; <$&% : ! (0! *0"7 *< " *< $ %
"7F % " *< ก
$& < ! (!"7F x "8 ("-
ก- 1 : 50,000 &- < - + < !$ 4 *0< 1 & <
< ! (!< 50,000 & < ":*< "7F 1 : 50,000 & 1 1
50,000
< !$ 4 4! 7.5 8-. -- ($& < ! (! x 8-.
":*< $&- 7.5 : x & 1 7.5
x
":*< ! *= =
1
50,000
7.5
x
< !$ 4 4!
< ! (!

31
3 " ( ก - 4 *0 !
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4
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30
4
= - 7@S -* 4 -: ! = - "ก%1 % = "'10 -"7F 7 : 5 : 8 ก -
+ $' = "'10 - 30 ก - = - 7@S ก*0ก -
1 -": $ ; </
1. (# @* $8 4 ! ..............................................................................................................
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^..
2. (# @* $ก 3 ! .........................................................................................................
^^^^^.^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^.
2 ! 4 ก7@2&
..............................................................................................................................................
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