Ngā Tau Ā-Ira me ngā Tau Hauātanga
Ko ngā tau ā-ira me ngā tau haurua he tikanga e rua e whakamahia whānuitia ana mō te whakaatu i ngā haurua, i ngā tau whaitake rānei. He rite tonu te mahi a ēnei e rua, engari he rerekē te whakaaturanga me te whakamahinga. Ka whakamāramahia e tēnei tuhinga ngā ariā e rua me te whakamahinga o ēnei i roto i te oranga o ia rā.
Ngā Tau Ā-ira
Ko te ira tekau he pūnaha tau turanga-tekau e whakamahi ana i te ira tekau hei wehe i ngā tau katoa mai i ngā hautau. Ko ngā mati kei te taha maui o te ira tekau ko te wāhanga katoa o te tau, ko ngā mati kei te taha matau o te ira tekau ko te hautau. Hei tauira, i roto i te tau 45.67, ko te 45 te wāhanga katoa, ā, ko te 67 te wāhanga hautau, arā, ko te 67/100, arā, 67 ōrau.
He whānuitia te whakamahinga o ngā tātai ira i roto i te oranga o ia rā, inā koa i roto i ngā horopaki pūtea, pūtaiao, me te hangarau. Hei tauira, he maha ngā wā ka whakaatuhia te moni i roto i te āhua tātai ira. Ki te hoko tetahi i tetahi mea mō te $5.75, ko te $5 he tāra katoa, ā, ko te $0.75 he haurua o te tāra.
Te Tuhi Ira-ā-ira
Ko te tuhi i ngā tau ira-ira ka whai i ētahi ture:
1. Ira-ā-ira: Ka whakamahia te ira-ā-ira hei wehe i te wāhanga tauoti mai i te wāhanga hautanga.
2. Ngā Kore: Ka whakanohoia ngā kore ki te taha mauī o te ira-ira mēnā he iti iho i te kotahi te mati hautanga, hei tauira, 0.25.
3. Te Whakaawhiwhi: He maha ngā wā ka whakaawhiwhia ngā tau ira ki tētahi maha o ngā mati ira i roto i ētahi horopaki pēnei i ngā pūrongo pūtea.
Te Tahuri i ngā Tau Hautau ki ngā Tau Ira
Ka taea te huri i te tau haurua ki te tau ira mā te wehewehe i te taupū ki te tauwehe. Hei tauira, hei huri i te 1/2 ki te tau ira, ka mahi mātou i te wehewehenga māmā: 1 ÷ 2 = 0.5.
Ngā Tau Hauātanga
Ko ngā tau haurua, arā, ngā haurua e mōhiotia whānuitia ana, he tohu anō tēnei mō ngā tau whaitake. Ka tuhia te haurua ki te āhua a/b, ko 'a' te taunga, e tohu ana i te maha o ngā wāhanga kei a tātou, ā, ko 'b' te tauwehe, e tohu ana i te maha o ngā wāhanga e hiahiatia ana hei hanga i tētahi katoa.
Te Tuhi i ngā Hautau
Ko te tuhi i ngā tau haurua e whai ana i ngā ture motuhake:
1. Te Taupū me te Tauira: Kei runga ake te taupū i te rārangi hautau, ā, kei raro iho te tauira. Hei tauira, i roto i te 3/4, ko te 3 te tauira, ā, ko te 4 te tauira.
2. Whakangāwaritia: He maha ngā wā ka whakangāwaritia ngā hautau kia māmā ake ai te mārama. Hei tauira, ka taea te whakangāwari i te 4/8 ki te 1/2.
3. Ngā Hautau Whakaranu: Mena he nui ake te taupū i te tauwehe, ka taea te tuhi hei tau whakauru. Hei tauira, ka taea te tuhi i te 7/4 hei 1 3/4.
Te Tahuri i ngā Tau Ā-ira ki ngā Tau Hautau
Ko te huri mai i te tau ira-ira ki te tau haurua ka mahia mā te tautuhi i te ira-ira me te whakangawari i taua tau. Hei tauira, ka taea te tuhi i te 0.75 hei 75/100, ka taea hoki te whakangawari ake ki te 3/4.
Te Whakataurite i ngā Ira me ngā Hautau
He painga me he ngoikoretanga ō ngā pūnaha e rua, tae atu ki ngā tono e hangai ana ki ētahi horopaki.
1. Ngāwari ki te Whakamahi: He māmā ake te whakamahi i ngā tau ā-ira mō te whakatairite me ngā mahi whakatairite nā te mea he māmā ake te whakarōpū me te whakataurite.
2. Te Tika: He tika ake te whakaaturanga o ngā hautau. He tika ake te hautau pēnei i te 1/3 i te tau ira 0.333… he mea whakaawhiwhi.
3. Māmā, Matatini rānei: He māmā ake te āhua o ngā hautau i roto i tō rātou āhua māmā, engari he roa, he uaua hoki ngā tau ira.
Ngā Taupānga i roto i te Oranga o Ia Rā
1. Pāngarau me te Mātauranga: He maha ngā wā ka akohia ngā hautau i te tīmatanga o te kura tuatahi kia mārama ai ki ngā ariā o te rahinga, ngā wāhanga o te katoa, me te ōwehenga.
2. Pūtea me te Ōhanga: He maha ngā wā ka whakamahia ngā ira-ira i roto i ngā whakawhitiwhitinga moni hei tohu i ngā utu, ngā reiti huamoni, me ngā rawa.
3. Pūtaiao me te Hangarau: E whakamahia ana ngā ariā e rua i roto i te whānuitanga o ngā tono, mai i ngā inenga māmā ki ngā huringa waeine uaua.
Ngā Tātaitanga Ā-ira me te Ā-Hautanga
Ka taea te mahi i ngā mahi pāngarau taketake pēnei i te tāpiri, te tango, te whakarea, me te wehewehe mā te whakamahi i ngā tau ira me ngā tau hautau.
1. Tāpiri me te Tango: Mō ngā hautau, me rite te tauwehenga mō te tāpiri me te tango. Heoi, mō ngā tau ā-ira, me whakarārangi noa ngā tau ā-ira.
Tauira:
– 1/4 + 1/2 = 1/4 + 2/4 = 3/4
– 0.25 + 0.5 = 0.75
2. Te Whakarea me te Wehewehe: He māmā noa te whakarea i ngā hautau me ngā tau ā-ira. Hei tauira, 0.5 0.4 = 0.2, me te 1/2 1/4 = 1/8.
Te Hononga ki ngā Tau Whakamārama
He momo tau taurite ngā tau ira me ngā tau haurua, arā, he tau ka taea te whakaatu hei wehenga o ngā tau katoa e rua. Ko ngā tau ira ā-wā, ngā tau ira tāruarua rānei, pērā i te 0.333…, ka taea hoki te whakaatu hei haurua, i tēnei wā ko te 1/3.
Whakamutunga
He pūkenga nui te mārama ki ngā tau ā-ira me ngā tau haurua i roto i te pāngarau me te oranga o ia rā. He rerekē ngā huarahi e rua hei whakaatu i ngā tau whaitake, engari he tautoko. Mā ngā tau ā-ira ka taea te whakamahi i ngā tatau me ngā whakatairite i roto i te ao hou, engari mā ngā tau haurua ka taea te whakaatu i ngā tau e tika ake ana, e māmā ake ana hoki. Mā te mōhio ki ngā tau e rua ka nui ake te ngāwari me ngā pūkenga tau hei whakahaere i ngā āhuatanga maha, ahakoa i roto i te mātauranga, te pūtea, te pūtaiao, te hangarau rānei.
