Kusintha kwa mawu

M'bukuli, tiwona mitundu yayikulu yakusintha kofananira kwa mawu a algebra, kuwatsagana ndi mafomu ndi zitsanzo zowonetsera kagwiritsidwe ntchito kake. Cholinga cha masinthidwe oterowo ndikusintha mawu oyamba ndi mawu ofanana.

Kukonzanso mawu ndi zinthu

Mwachidule chilichonse, mutha kusinthanso mawuwo.

+ b = b + a

Muzogulitsa zilizonse, mutha kusinthanso zinthu.

a ⋅ b = b ⋅ a

zitsanzo:

• 1 + 2 = 2 + 1
• 128 ⋅ 32 = 32 ⋅ 128

Mawu amagulu (ochulukitsa)

Ngati pali mawu opitilira 2 pakuwerengera, atha kugawidwa ndi mabatani. Ngati pangafunike, mutha kusinthana kaye.

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

Muzogulitsa, muthanso kugawa zinthuzo.

a ⋅ b ⋅ c ⋅ d = (a ⋅ d) ⋅ (b ⋅ c)

zitsanzo:

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

Kuwonjezera, kuchotsa, kuchulukitsa kapena kugawa ndi nambala yomweyo

Ngati nambala yomweyi ionjezedwa kapena kuchotsedwa mbali zonse ziwiri za chizindikiritso, ndiye kuti imakhala yowona.

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

Komanso, kufanana sikudzaphwanyidwa ngati mbali zake zonse zichulukitsidwa kapena kugawidwa ndi chiwerengero chomwecho.

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

zitsanzo:

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

Kusintha Kusiyana ndi Sum (nthawi zambiri Zogulitsa)

Kusiyana kulikonse kungathe kuimiridwa ngati chiŵerengero cha mawu.

a – b = a + (-b)

Chinyengo chomwecho chingagwiritsidwe ntchito pa magawano, mwachitsanzo, m'malo pafupipafupi ndi mankhwala.

a: b = a ⋅ b^-1

zitsanzo:

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

Kuchita masamu

Mutha kufewetsa mawu a masamu (nthawi zina kwambiri) pochita masamu (kuwonjezera, kuchotsa, kuchulukitsa ndi kugawa), poganizira zomwe zimavomerezedwa dongosolo la kuphedwa:

• choyamba timakweza ku mphamvu, kuchotsa mizu, kuwerengera logarithms, trigonometric ndi ntchito zina;
• Kenako timachita ntchitozo m'mabulaketi;
• potsiriza - kuchokera kumanzere kupita kumanja, chitani zotsalira. Kuchulukitsa ndi kugawa kumakhala patsogolo kuposa kuwonjezera ndi kuchotsa. Izi zimagwiranso ntchito ku mawu omwe ali m'makolo.

zitsanzo:

• 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

Kukula kwa bracket

Mabokosi mu mawu a masamu amatha kuchotsedwa. Izi zimachitika molingana ndi zina - kutengera zizindikiro ("kuphatikiza", "kuchotsa", "chulukitsani" kapena "gawaniza") zomwe zili patsogolo kapena pambuyo pa mabulaketi.

zitsanzo:

• 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

Kukhazikitsa Common Factor

Ngati mawu onse omwe ali m'mawuwa ali ndi chinthu chofanana, amatha kuchotsedwa m'mabokosi, momwe mawu omwe amagawidwa ndi ichi adzakhalapo. Njira imeneyi imagwiranso ntchito pazosintha zenizeni.

zitsanzo:

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

Kugwiritsa ntchito njira zazifupi zochulutsa

Mukhozanso kugwiritsa ntchito kusintha kofanana kwa mawu a algebraic.

zitsanzo:

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