Identity transformations ntawm kev nthuav qhia

Hauv kev tshaj tawm no, peb yuav txiav txim siab txog hom kev hloov pauv zoo ib yam ntawm cov kab lus algebraic, nrog rau lawv nrog cov qauv thiab cov piv txwv los ua kom pom lawv daim ntawv thov hauv kev xyaum. Lub hom phiaj ntawm cov kev hloov pauv no yog los hloov cov lus qhia qub nrog qhov sib npaug sib npaug.

Rearranging cov nqe lus thiab yam

Hauv txhua qhov kev suav, koj tuaj yeem hloov kho cov ntsiab lus.

ib + b = b + a

Hauv ib qho khoom lag luam, koj tuaj yeem hloov kho qhov xwm txheej.

ib ⋅ b = b ⋅ a

piv txwv:

• 1 + 2 = 2 + 1
• 128 ⋅ 32 = 32 ⋅ 128

Grouping cov ntsiab lus (multipliers)

Yog tias muaj ntau tshaj 2 nqe lus hauv cov lej, lawv tuaj yeem muab faib ua pawg. Yog tias xav tau, koj tuaj yeem hloov pauv lawv thawj zaug.

a + b + c + d = (a + c) + (b + d)

Hauv cov khoom, koj tuaj yeem pab pawg ua ke.

a ⋅ b ⋅ c ⋅ d = (a ⋅ d) ⋅ (b ⋅ c)

piv txwv:

• 15 + 6 + 5 + 4 = (15 + 5) + (6 + 4)
• 6 ⋅ 8 ⋅ 11 ⋅ 4 = (6 ⋅ 4 ⋅ 8) ⋅ 11

Ntxiv, rho tawm, sib npaug lossis faib los ntawm tib tus lej

Yog tias tib tus lej ntxiv lossis rho tawm rau ob feem ntawm tus kheej, ces nws tseem muaj tseeb.

If a + b = c + dces (a + b) ± e = (c + d) ± e.

Tsis tas li ntawd, kev sib npaug yuav tsis raug ua txhaum yog tias ob qho tib si ntawm nws qhov chaw tau muab faib los yog muab faib los ntawm tib tus lej.

If a + b = c + dces (a + b) ⋅/: e = (c + d) ⋅/: e.

piv txwv:

• 35 + 10 = 9 + 16 + 20 ⇒ (35 + 10) + 4 = (9 + 16 + 20) + 4
• 42 + 14 = 7 ⋅ 8 ⇒ (42 + 14) ⋅ 12 = (7 ⋅ 8) ⋅ 12

Hloov qhov sib txawv nrog ib qho nyiaj (feem ntau yog ib yam khoom)

Txhua qhov sib txawv tuaj yeem sawv cev raws li cov ntsiab lus.

a – b = a + (-b)

Tib qhov ua kom yuam kev tuaj yeem siv rau kev faib khoom, piv txwv li hloov nquag nrog cov khoom.

a: b = a ⋅ b^-1

piv txwv:

• 76 – 15 – 29 : kuv 76 + (-15) + (-29)
• 42:3 = 42 ⋅ 3^-1

Ua haujlwm lej lej

Koj tuaj yeem ua kom yooj yim rau kev qhia lej (qee zaum tseem ceeb) los ntawm kev ua lej lej (ntxiv, rho tawm, sib faib thiab faib), suav nrog kev lees paub feem ntau. kev txiav txim ntawm kev tua:

• ua ntej peb tsa lub zog, rho tawm cov hauv paus hniav, suav logarithms, trigonometric thiab lwm yam haujlwm;
• tom qab ntawd peb ua cov yeeb yam hauv cov kab ke;
• Thaum kawg - los ntawm sab laug mus rau sab xis, ua cov haujlwm seem. Kev sib faib thiab kev faib ua ntej tshaj qhov sib ntxiv thiab rho tawm. Qhov no kuj siv tau rau cov kab lus hauv kab lus.

piv txwv:

• 14 + 6 ⋅ (35 – 16 ⋅ 2) + 11 ⋅ 3 = 14 + 18 + 33 = 65
• 20 : 4 + 2 ⋅ (25 ⋅ 3 – 15) – 9 + 2 ⋅ 8 = 5 + 120 - 9 + 16 = 132

Bracket expansion

Cov kab lus hauv kev qhia lej lej tuaj yeem raug tshem tawm. Qhov kev txiav txim no yog ua raws li qee qhov - nyob ntawm seb cov cim ("ntxiv", "tshem tawm", "multiply" lossis "divide") yog ua ntej lossis tom qab cov kab tuav.

piv txwv:

• 117 + (90–74–38) : kuv. = 117+90–74–38 : kuv
• 1040 – 218 – 409 + 192 (ib.) = 1040 + 218 + 409 - 192 ib
• 22⋅(8+14) = 22 ⋅ 8 + 22 ⋅ 14
• 18: (4–6) hnub. = 18: 4-18: 6

Bracketing qhov Common Factor

Yog tias tag nrho cov ntsiab lus hauv cov lus qhia muaj qhov sib xws, nws tuaj yeem raug tshem tawm ntawm cov kab ke, uas cov ntsiab lus faib los ntawm qhov xwm txheej no yuav nyob twj ywm. Cov txheej txheem no kuj tseem siv tau rau cov ntaub ntawv sib txawv.

piv txwv:

• 3 ⋅ 5 + 5 ⋅ 6 = 5⋅(3+6)
• 28 + 56 - 77 = 7 ⋅ (4 + 8 - 11)
• 31 x + 50 x = x ⋅ (31 + 50)

Kev siv cov ntawv sau luv luv

Koj tuaj yeem siv los ua qhov hloov pauv zoo ib yam ntawm cov kab lus algebraic.

piv txwv:

• (31 + 4)² = 31² + 2 ⋅ 31 ⋅ 4 + 4² = 1225
• 26² - 7² = (26 - 7) ⋅ (26 + 7) = 627