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Welcome to PAEKUPU, words related to Te Marautanga o Aotearoa. Curriculum areas presently available on PAEKUPU: Toi Ataata, Puoro, Te Reo Pāngarau, Ngā Mahi a te Rēhia
 
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Te Reo Pāngarau

paheko

operation (number or algebraic)

tūingoa

WHAKAMĀRAMA

E whā ngā paheko tau matua, arā, ngā momo honohono i te tau - ko te tāpiri, ko te tango, ko te whakarea, ko te whakawehe. Ka kīia ēnei paheko katoa, he paheko tāhūrua nā te mea ka puta he tau tuatoru i te pāhekoheko o ētahi tau e rua.

There are four main number operations or ways of combining numbers together. They are addition, subtraction, multiplication and division. These are called binary operations because two numbers are combined to produce a third.

Tauira KŌrero

He aha te paheko e tika ana mō tēnei rapanga

Āta kōwhiria te paheko e tika ana.

Ko tēhea te paheko kōaro o te tangohanga?

WhakamĀrama Āpitihanga

Koia nei ngā tohu mō ngā paheko matua e whā:

+  mō te tāpiritanga           mō te tangohanga

× mō te whakareatanga    ÷  mō te whakawehenga

 

He paheko kōaro te tāpiritanga me te tangohanga:
6 + 2 = 8          8 – 2 = 6

He paheko kōaro te whakarea me te whakawehe:
6 × 2 = 12          12 ÷ 2 = 6

 

Ko te kore (0) te tūmau o te tāpiritanga me te tangohanga. Arā, ki te tāpiria, ki te tangohia rānei te 0 i tētahi tau, ka noho pūmau tonu te uara o taua tau:
34 + 0 = 34          34 – 0 = 34

Ko te tahi (1) te tūmau o te whakareatanga me te whakawehenga. Arā, ki te whakareatia, ki te whakawehea rānei tētahi tau ki te 1, ka noho pūmau tonu te uara o taua tau:
34 × 1 = 34          34 ÷ 1 = 34

 

He āhuatanga motuhake ō ētahi o ngā paheko:
Ko te āhuatanga kōaro e mea ana kāore he take o te raupapa o ngā tau i roto i tētahi paheko.
Hei tauira, ko te tāpiri me te whakarea:
3 + 4 = 7          4 + 3 = 7
3 × 4 = 12         4 × 3 = 12

Kāore te tango me te whakawehe e whai ana i te āhuatanga kōaro. Arā:
3 – 4 ≠ 4 – 3          12 ÷ 4 ≠ 4 ÷ 12

 

Ko te āhuatanga herekore e mea ana kāore he take o te whakarōpū i ngā tau i roto i tētahi paheko mēnā e toru, nui ake rānei ngā tau o taua paheko. Hei tauira, ko te tāpiri, me te whakarea:
5 + (3 +2) = 5 + 5          (5 + 3) + 2 = 8 + 2
                 = 10                                = 10

3 × (4 x 5) = 3 × 20         (3 × 4) × 5 = 12 × 5
                 = 60                                 = 60

 

Kāore te tango me te whakawehe e whai ana i te āhuatanga herekore. Arā:
10 – (4 – 3) = 9          (10 – 4) – 3 = 3
12 ÷ (4 ÷ 2) = 6        (12 ÷ 4) ÷ 2 = 1 1/2

 

Ko te āhuatanga tohatoha e mea ana e taea ana tētahi paheko te tohatoha ki paheko kē atu.
Hei tauira, e taea ana te whakarea te tohatoha ki te tāpiri:
3 × (4 + 5) = (3 × 4) + (3 × 5)
3 × 9              12 + 15
27                  27

Takenga Mai

paheko - join, combine

Tauira KŌrero

He aha te paheko e tika ana mō tēnei rapanga

Āta kōwhiria te paheko e tika ana.

Ko tēhea te paheko kōaro o te tangohanga?

WhakamĀrama Āpitihanga