คณิตศาสตร์ เล่ม 1

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82 8. œµ¥¤œÉ´ °µ¥» 60ž— že œµ¥» °µ¥» 112®oµ 榤°¸ µ¥¤» µ„„ªµn ¨³¤µ„„ªnµ°¥„¼n ɞ¸ e 9. ‹ŠÁ¦¸¥Š 247810­·­°Š , 247810Á„oµ , 247810­·Á°È— ‹µ„œ°o ¥Åž¤µ„ 10. 4 š°¸É ¥n¼Äœ‹ÎµœªœÄ—˜°n ޜʤ¸ ¸‡µn ¤µ„š­É¸ »— 2438­· ­°Š , 5462 ¨³ 3495­·Á°È— ‹Îµœªœ°³Å¦š¤É¸ µ„„ªµn 500 ¤­¸ µ¤®¨„´ ‡µn …°ŠÁ¨…×—Äœ®¨´„®œªn ¥Áž}œ­µ¤Ášµn …°Š Á¨…×—Äœ®¨„´ ­· ¨³Á¨…×—Äœ®¨´„¦o°¥Áž}œ­°ŠÁšµn …°ŠÁ¨…×—Äœ®¨´„­·

ššÉ¸ 3 „µ¦ž¦³¥„» ˜…r °Š‹ÎµœªœÁ˜¤È ¨³Á¨…¥„„µÎ ¨Š´ 3.1 „µ¦‡·—‡Îµœª– Ĝª¸ ·˜ž¦³‹µÎ ªœ´ Á¦µÄ„o µ¦‡·—‡Îµœª–Á„¥¸É ª„´ ¦µ¥¦´ ¦µ¥‹nµ¥ „µ¦Žº°Ê „µ¦…µ¥ ²¨² ¤ªo nµÄœž‹{ ‹» œ´ ‹³ÄoÁ‡¦°Éº Š‡·—Á¨…Å—„o ˜È µ¤ ĜµŠ­™µœ„µ¦–Ár ¦µ„È¥Š´ ˜°o Š‡—· ‡Îµœª–—ªo ¥˜œÁ°Š Áœn Á¤ºÉ°Á¦µŽºÊ°…°Š Á¦µ°µ‹‡Îµœª–‹µÎ œªœÁŠœ· šÉ˜¸ o°Š‹µn ¥Ã—¥‡·—Ĝċ —Š´ œÊœ´ ‡ªµ¤­µ¤µ¦™Äœ „µ¦‡·—‡µÎ œª–‹¹Š¥´Š¤‡¸ ªµ¤‹µÎ Ážœ} °¥Á¼n ­¤° Ä®œo „´ Á¦¸¥œ¡·‹µ¦–µ˜´ª°¥nµŠ˜n°ÅžœÊ¸ ¡´¦¸ÅžŽº°Ê Ÿ„´ š¸˜É ¨µ—­——´ŠœÊ¸ Ÿ´„‡³œoµ 15 µš ™´Éª {„¥µª 18 µš „³®¨ÉµÎ ž¨¸ 20 µš ¨³¡¦·„…®¸Ê œ¼ 10 µš ™µo Á›°Ä®o›œ˜´ ¦ 100 µšÂ„n¤‡n oµ ¡´¦‹¸ ³Å—oÁŠ·œš°œ„¸Éµš ‹µ„Ëš¥Är œ˜ª´ °¥nµŠœ¡Ê¸ ´ ¦¸°µ‹‡·—Ĝċ—Š´ œ¸Ê …œ´Ê ¦„ ‡·—¦µ‡µŸ„´ šŽ¸É Ê°º š´ÊŠ®¤—Ážœ} 15 + 18 + 20 + 10 = 63 µš …Ê´œš¸É­°Š ‡·—‹µÎ œªœÁŠ·œšÉ¸Å—¦o ´š°œÁž}œ 100 – 63 = 37 µš „µ¦‡·—ÁŠœ· …°Š¡´¦˜¸ µ¤…µo Š˜oœ Á…¥¸ œÁžœ} ž¦³Ã¥‡‡–·˜«µ­˜¦År ——o ´Šœ¸Ê 100 – (15 + 18 + 20 + 10) = 37 ™µo Á¦µ‡—· ªµn ÁŠœ· šÉĸ ®Âo ¤‡n oµ 100 µš ‹nµ¥Ážœ} ‡µn Ÿ„´ ‡³œoµ„°n œ ¨oª‹¹Š‹µn ¥Ážœ} ‡nµ™É´ª „{ ¥µª ‡µn „³®¨ÎµÉ ž¨¸ ¨³‡µn ¡¦·„…ʸ®œ¼ ˜°n ޘµ¤¨Îµ—´ —´Šœ´Êœ„µ¦‡Îµœª–Ëš¥rĜ˜ª´ °¥nµŠœ¸°Ê µ‹Á…¸¥œÁž}œ 100 – 15 – 18 – 20 – 10 ŽÉ¹ŠÁšnµ„´ 100 – (15 + 18 + 20 + 10) ¨³°µ‹Á…¸¥œž¦³Ã¥‡‡–˜· «µ­˜¦r —Š´ „¨nµª…oµŠ˜œo Áž}œ—Š´ œÊ¸ 100 – 15 – 18 – 20 – 10 = 37 Á¦µ°µ‹Â­—Šš¤¸É µ…°Š 100 – 15 – 18 – 20 – 10 ªnµÁšµn „´ 100 – (15 + 18 + 20 + 10) ץč®o ¨„´ Á„–”r…°Š„µ¦¨‹µÎ œªœÁ˜È¤—ªo ¥‹ÎµœªœÁ˜¤È šœÉ¸ „´ Á¦¸¥œÁ‡¥š¦µ¤µÂ¨ªo ªµn ˜´ª˜ŠÊ´ – ˜´ª¨ = ˜ª´ ˜Ê´Š + ‹Îµœªœ˜¦Š…µo ¤…°Š˜´ª¨

84 ŽŠ¹É ­—ŠÅ——o Š´ œÊ¸ 100 – 15– 18 – 20 – 10 = 100 + (-15) + (-18) + (-20) + (-10) = 100 + {(-15) + (-18) + (-20) + (-10)} = 100 + (-63) = 100 – 63 = 100 – (15 + 18 + 20 + 10) Œ³œ´ÊœÁ¤ºÉ°¤Ã¸ ‹š¥šr ɤ¸ ¸„µ¦—µÎ Áœœ· „µ¦ÁŒ¡µ³„µ¦ª„¨³„µ¦¨…°Š‹µÎ œªœÁ˜¤È ®¨µ¥ Ç ‹µÎ œªœ Áœn 5 + 11 – 12 + 8 – 9 °µ‹‡Îµœª–Å—­o °Šª›· —¸ Š´ œÊ¸ 1. ‡Îµœª–‹µ„Žµo ¥Åž…ªµš¨¸ ³­°Š‹µÎ œªœ 5 + 11 = 16 5 + 11 – 12 + 8 – 9 = 16 – 12 + 8 – 9 16 – 12 = 4 = 4+8–9 4 + 8 = 12 = 12 – 9 =3 ®¦°º 2. Á…¥¸ œÃ‹š¥Är ®¤Än ®o°¥nļ œ¦ž¼ „µ¦ª„šÊŠ´ ®¤—¨ªo Šn ‹µÎ œªœ°°„Ážœ} ­°Š„¨¤»n ‡º°„¨n»¤…°Š‹µÎ œªœÁ˜È¤ª„¨³„¨n»¤…°Š‹µÎ œªœÁ˜¤È ¨ ×¥ č­o ¤´˜·„µ¦­¨´ š¸É¨³­¤´˜·„µ¦Áž¨¥¸É œ®¤­¼n 宦´„µ¦ª„‹µÎ œªœÁ˜¤È 5 + 11 – 12 + 8 – 9 = 5 + 11 + (-12) + 8 + (-9) = (5 + 11 + 8) – (12 + 9) = 24 – 21 =3 ‹³­Š´ Á„˜Å—oªµn „µ¦‡µÎ œª–×¥ª›· œ¸ ʤ¸ „¸ µ¦‹—´ „¨¤n» ‹µÎ œªœÁ˜¤È ª„¨³„¨¤»n ‹ÎµœªœÁ˜È¤¨ ץčªo ŠÁ¨È ¨³­¤´˜·„µ¦ª„¨³„µ¦¨‹µÎ œªœÁ˜È¤ „µ¦ÄoªŠÁ¨È Á¡É°º ‹—´ „¨¤n» ‹µÎ œªœšµÎ ŗo —Š´ œ¸Ê 1. ™oµ˜o°Š„µ¦Ä­ªn ŠÁ¨È ‡¨¤» „¨n¤» ‹µÎ œªœÄ—¨³¤Á¸ ‡¦ºÉ°Š®¤µ¥ª„°¥®¼n œoµªŠÁ¨È Á¤°ºÉ Ä­ªn ŠÁ¨È ¨ªo Ä®‡o ŠÁ‡¦É°º Š®¤µ¥Á—¤· —´Š˜ª´ °¥nµŠ

85 12 + 3 + 5 = 12 + (3 + 5) 12 + 3 – 5 = 12 + (3 – 5) Ĝ„¦–¸š¸¤É ¸Á‡¦º°É Š®¤µ¥¨°¥®¼n œoµªŠÁ¨È Ä®Áo ž¨É¸¥œÁ‡¦É°º Š®¤µ¥š¸‹É ³°¥Än¼ œªŠÁ¨ÈÁžœ} ˜¦Š„´œ…µo ¤ —Š´ ˜ª´ °¥µn Š 12 – 3 + 5 = 12 – (3 – 5) 12 – 3 – 5 = 12 – (3 + 5) 2. ™oµ˜°o Š„µ¦™°—ªŠÁ¨È š‡¸É ¨¤» „¨»¤n ‹ÎµœªœÄ—¨³¤Á¸ ‡¦°Éº Š®¤µ¥ª„°¥n®¼ œµo ªŠÁ¨È Ä®o™°— ªŠÁ¨È°°„¨³‡ŠÁ‡¦ºÉ°Š®¤µ¥Á—¤· —Š´ ˜´ª°¥µn Š 12 + (3 + 5) = 12 + 3 + 5 12 + (3 – 5) = 12 + 3 – 5 Ĝ„¦–¸š¸É¤¸Á‡¦°Éº Š®¤µ¥¨°¥®¼n œµo ªŠÁ¨È Á¤°Éº ™°—ªŠÁ¨È°°„Ä®oÁž¨¥¸É œÁ‡¦°Éº Š®¤µ¥šÉ¸Á‡¥ °¥nļ œªŠÁ¨ÈÁžœ} ˜¦Š„´œ…oµ¤ —Š´ ˜´ª°¥µn Š 12 – (3 – 5) = 12 – 3 + 5 12 – (3 + 5) = 12 – 3 – 5 Ĝ„¦–¸šÉ¤¸ ø ‹š¥„r µ¦ª„¨³¨‹µÎ œªœÁ˜¤È ®¨µ¥ Ç ‹µÎ œªœ ˜Ån ¤¤n ¸ªŠÁ¨È ¦³ª» µn ‹³ —µÎ Áœ·œ„µ¦Ä—„n°œ®¨´Š Ánœ 100 – 15 – 18 – 20 – 10 Á¦µ‹³™º°ªµn Ä®o—µÎ Áœ·œ„µ¦‹µ„Žµo ¥Åž…ªµ ­—Š—ªo ¥ž¦³Ã¥‡‡–·˜«µ­˜¦År —o—Š´ œÊ¸ [{(100 – 15) – 18} – 20] – 10 = 37 ĜšÉœ¸ Äʸ ªo ŠÁ¨È Á¨„È ( ) ªŠÁ¨È ž„e „µ { } ¨³ªŠÁ¨È Ä®n®¦º°ªŠÁ¨È „µo ¤ž¼ [ ] ×¥ čoªŠÁ¨ÈÁ¨„È ­—Š„µ¦‡Îµœª–Ážœ} ¨Îµ—´ ¦„ ªŠÁ¨Èže„„µ‡¨»¤ªŠÁ¨ÈÁ¨„È ­—Š„µ¦‡µÎ œª–Äœ ¨Îµ—´˜°n Ş ¨³ªŠÁ¨È Ä®n®¦º°ªŠÁ¨È „µo ¤ž‡¼ ¨¤» ªŠÁ¨Èže„„µ ­—Š„µ¦‡µÎ œª–Ážœ} ¨µÎ —´ ­»—šoµ¥—Š´ ˜°n ޜʸ

86 [{(100 – 15) – 18} – 20] – 10 = [{85 – 18} – 20] – 10 ‡Îµœª–ÄœªŠÁ¨ÈÁ¨È„ 100 – 15 = 85 = [67 – 20] – 10 = 47 – 10 ‡Îµœª–ÄœªŠÁ¨Èže„„µ = 37 85 – 18 = 67 ˜´ª°¥nµŠšÉ¸ 1 ‹Š®µŸ¨¨´¡›r 11 – 20 + 32 – 12 + 55 – 35 ª·›š¸ ε 11 – 20 + 32 – 12 + 55 – 35 = 11 + 32 + 55 – 20 – 12 – 35 = (11 + 32 + 55) – (20 + 12 + 35) = 98 – 67 = 31 ˜° 31 ˜ª´ °¥nµŠš¸É 2 ‹Š®µŸ¨¨´¡›r 48 + {125 – (125 – 2)} ª·›š¸ µÎ 48 + {125 – (125 – 2)} = 48 + {125 – 125 + 2} = 48 + 2 = 50 ˜° 50 „µ¦™°—ªŠÁ¨È Ĝ˚¥rš¸¤É ª¸ ŠÁ¨ÈÂ­—Š¨µÎ —´„µ¦‡µÎ œª–°¥®n¼ ¨µ¥œ—· µŠ‡¦ŠÊ´ Á¤Éº° ‡Îµœª–ÄœªŠÁ¨È Ä®n®¦°º ªŠÁ¨Èže„„µÂ¨ªo °µ‹Áž¨¸É¥œÅžÄªo ŠÁ¨È °´œ—´ ¦°Š¨Š¤µ —Š´ ˜´ª°¥µn Š ˜n°Åžœ¸Ê

87 ˜ª´ °¥µn ŠšÉ¸ 3 ‹Š®µŸ¨¨¡´ ›r 12 – [15 + {(-3) – 10}] ª·›¸šÎµ 12 – [15 + {(-3) – 10}] = 12 – {15 + (-13)} = 12 – 2 = 10 ˜° 10 Ä®oœ„´ Á¦¥¸ œ®µŸ¨¨¡´ ›˜r n°ÅžœÊ¸ 1. 11 + 12 – 13 + 14 – 15 + 16 – 17 2. 18 + 14 – 20 – 12 + 40 – 9 3. (-35) + 17 – 22 – 43 + 60 4. {(-9) + 24} – {(-40) – (28 – 40)} 5. 3 + {18 – (-19)} – (15 – 22) 6. (-5) – [(-2) + {(-10) – 16}] œ°„‹µ„œ´„Á¦¥¸ œ˜°o Š¤‡¸ ªµ¤­µ¤µ¦™Äœ„µ¦‡—· ‡µÎ œª–¨oª œ´„Á¦¥¸ œ‡ª¦¦o‹¼ ´„Á¨°º „čªo ›· ¸ šÉ‹¸ ³ªn ¥Ä®o‡µÎ œª–Å—o¦ª—Á¦ªÈ —´Š˜ª´ °¥nµŠ 1. ‹Š®µŸ¨ª„ 32 + 15 + 18 + 9 + 45 ª·›¸šÉ¸ 1 ®µŸ¨ª„šÉš¸ µÎ Ä®Åo —‹o 圪œÁ˜¤È ­· ץč­o ¤˜´ „· µ¦­¨´š¸É¨³­¤´˜· „µ¦Áž¨É¥¸ œ®¤¼n (ĜšÉœ¸ ʸåŠÁ­oœÁ¡°Éº nª¥Ä®Áo ®Èœ„µ¦‹—´ „¨¤n» ) 32 + 15 + 18 + 9 + 45 = (32 + 18) + (15 + 45) + 9 = 50 + 60 + 9 = 119

88 วธิ ีที 2 ก กก ก 32 + 15 + 18 + 9 + 45 = (30 + 2) + (10 + 5) + (10 + 8) + 9 + (40 + 5) = (30 + 10 + 10 + 40) + (2 + 5 + 8 + 9 + 5) = 90 + 29 = 119 ตอบ 119 2. F 10 3 + 9 7 13 7+9 7 13 วธิ ีที 1 10 3 + 9 7 13 = 9 13 -4 วธิ ีที 2 = = วธิ ีที 3 10 3 + 9 7 13 = 10 3 + 9 20 = -10 + 6 = -4 10 3 + 9 7 13 = 10 10 + 9 13 = 9 13 = -4 ตอบ -4 3. ก 99 + 399 + 298 วธิ ีทาํ 99 + 399 + 298 = (100 1) + (400 1) + (300 2) 100 1 + 400 1 + 300 2 = (100 + 400 + 300) (1 + 1 + 2) 800 4 = 796 = = ตอบ 796