Identity shanduko yemashoko

Muchinyorwa chino, tichatarisa mhando huru dzeshanduko dzakafanana dzemataurirwo ealgebraic, tichiaperekedza nemafomula nemienzaniso yekuratidza kushanda kwawo mukuita. Chinangwa cheshanduko dzakadai ndechekutsiva chirevo chepakutanga neicho chakaenzana.

Kuronga patsva mazwi uye zvinhu

Mune chero huwandu, unogona kuronga zvakare mazwi.

a + b = b + a

Mune chero chigadzirwa, iwe unogona kugadzirisa zvakare zvinhu.

a ⋅ b = b ⋅ a

mienzaniso:

• 1 + 2 = 2 + 1
• 128 ⋅ 32 = 32 ⋅ 128

Matemu ekuronga (zviwandu)

Kana paine mazwi anodarika maviri muhuwandu, anogona kuiswa mumapoka nemaparenthesi. Kana zvichidiwa, unogona kutanga wachinjanisa.

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

Muchigadzirwa, iwe unogonawo kuunganidza zvinhu.

a ⋅ b ⋅ c ⋅ d = (a ⋅ d) ⋅ (b ⋅ c)

mienzaniso:

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

Kuwedzera, kubvisa, kuwanza kana kupatsanura nenhamba imwe chete

Kana nhamba imwe chete yakawedzerwa kana kubviswa kumativi ose ekuzivikanwa, zvino inoramba iri chokwadi.

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

Zvakare, kuenzana hakuzotyorwe kana zvikamu zvaro zvese zvikawanzwa kana kupatsanurwa nenhamba imwechete.

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

mienzaniso:

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

Kutsiva Musiyano neSum (kazhinji Chigadzirwa)

Chero musiyano unogona kumiririrwa sehuwandu hwematemu.

a – b = a + (-b)

Manomano mamwe chete anogona kushandiswa pakukamuranisa, kureva kutsiva kazhinji nechigadzirwa.

a: b = a ⋅ b^-1

mienzaniso:

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

Kuita arithmetic mashandiro

Unogona kurerutsa kutaura kwemasvomhu (dzimwe nguva zvakanyanya) nekuita arithmetic mashandiro (kuwedzera, kubvisa, kuwanda uye kupatsanura), uchifunga nezve inogamuchirwa kazhinji. kurongeka kwekuuraya:

• kutanga tinosimudza kune simba, kubvisa midzi, kuverenga logarithms, trigonometric nemamwe mabasa;
• zvino tinoita zviito mumabhuraketi;
• pakupedzisira - kubva kuruboshwe kuenda kurudyi, ita zviito zvakasara. Kuwanza nekupatsanura kunotungamira pane kuwedzera nekubvisa. Izvi zvinoshandawo kumataurirwo ari mumaparentheses.

mienzaniso:

• 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 kuwedzera

Maparentheses mune arithmetic kutaura anogona kubviswa. Chiito ichi chinoitwa maererano nezvimwe - zvichienderana nezviratidzo zvipi ("plus", "minus", "wanza" kana "kupatsanura") zviri pamberi kana mushure mezvibodzwa.

mienzaniso:

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

Kubatanidza The Common Factor

Kana mazwi ese ari mukutaura aine chinhu chakafanana, anogona kutorwa kubva mumabhuraketi, umo mazwi akakamurwa nechinhu ichi acharamba aripo. Hunyanzvi uhu hunoshandawo kumabhii chaiwo.

mienzaniso:

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

Kushandiswa kwemafomula akapfupikiswa ekuwanza

Iwe unogona zvakare kushandisa kuita shanduko yakafanana yealgebraic mataurirwo.

mienzaniso:

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