He Ara Tere hei Whakaoti i ngā Raru Ōrau
Ko te ōrau he ariā pāngarau e tūtaki pinepine ana tātou i roto i te ao o ia rā, i roto i te ao mātauranga me ngā āhuatanga mahi pēnei i ngā hekenga hokohoko, te huamoni peeke, ngā hua rangahau rānei. Ahakoa te āhua māmā noa iho, tera pea ētahi tāngata e uaua ki te whakaoti rapanga ōrau i roto i te wā poto me te tika. Ko te whāinga o tēnei tuhinga he whakarato i tētahi huarahi tere me te whai hua ki te whakaoti rapanga ōrau, me ngā mahi me ngā tauira ngāwari ki te whai hei whakahōhonu ake i tō māramatanga.
1. Te Mārama ki ngā Kaupapa Taketake o ngā Ōrau
I mua i te kōrero mō ngā huarahi tere, he mea nui kia mārama ki ngā kaupapa matua o ngā ōrau. Ko te ōrau te ōwehenga o te nui ki te 100. Hei tauira, ko te 25% he 25 o te 100, 25/100 rānei. He maha ngā wā ka whakamahia ngā ōrau hei whakaahua i te nui o te uara e whakaritea ana ki te tapeke.
Tātai Ōrau Taketake:
1. Ōrau (P) = (Hea / Tapeke) × 100%
2. Te Wāhanga = (Ōrau × Tapeke) / 100
3. Tapeke = Hea / (Ōrau / 100)
Mā te mōhio ki tēnei tauira taketake, ka whai turanga pakari koe mō te whakaoti rapanga ōrau rerekē.
2. Tāutuhia te momo pātai
Ko ngā pātai ōrau ka taea te whakarōpū kia maha ngā momo:
1. Te Whakatau i te Ōrau: Te kimi i te ōrau o tētahi uara o te tapeke.
2. Whakatauhia te Wāhanga o te Tapeke: Whakatauhia he uara motuhake i runga i te ōrau kua hoatu.
3. Te Whakatau i te Tapeke: Te whakatau i te uara tapeke mēnā e mōhiotia ana ngā wāhanga me ngā ōrau.
4. Pikinga, Whakahekenga rānei o te Ōrau: Ka tatau i te huringa ōrau mai i te uara tīmatanga ki te uara whakamutunga.
Mā te mōhio ki te momo raruraru e pā ana ki a koe ka āwhina i a koe ki te whiriwhiri i te huarahi tika hei whakaoti.
3. Te Ara Tere mā te Whakamahi i te Tātai
Te Whakatau i te Ōrau
Mō ngā pātai e tono ana mō ngā ōrau, whakamahia te tātai:
\[ P = \left(\frac{\text{Wāhanga}}{\text{Tapeke}}\right) \whakareatia ki te 100\]
Tauira:
He aha te ōrau o te 25 o te 200?
Whakauruhia ngā uara ki roto i te tātai:
\[ P = \left(\frac{25}{200}\right) \times 100 = 12.5\% \]
Te Whakatau i te Wāhanga o te Tapeke
Whakamahia te tātai tika:
\[ \text{Wāhanga} = \left(\frac{P \times \text{Tapeke}}{100}\right) \]
Tauira:
Mena e mōhiotia ana ko te 20% o tētahi tau he 50, he aha te tapeke?
Whakamahia tātai hei whakatau wāhanga:
\[ 50 = \left(\frac{20 \times \text{Total}}{100}\right) \]
\[
\text{Tapeke} = \left(\frac{50 \times 100}{20}\right) = 250
\]
Te Whakatau i te Tapeke
Whakamahia te tātai whakamuri o te wāhanga:
\[ \kuputuhi{Tapeke} = \left(\frac{\kuputuhi{Wāhanga}}{\left(\frac{P}{100}\right)}\right) \]
Tauira:
He aha te tapeke mēnā ko te 15% o taua moni he 60?
Whakauruhia ngā uara ki roto i te tātai:
\[ \text{Tapeke} = \left(\frac{60}{0.15}\right) = 400 \]
Te Pikinga, te Whakaheke rānei i te Ōrau
Tātaihia te ōrau huringa mā te whakamahi i te tātai:
\[ \text{Te Pikinga/Te Whakahekenga o te Ōrau} = \left(\frac{\text{Uara Whakamutunga} – \text{Uara Tīmatanga}}{\text{Uara Tīmatanga}}\right) \whakareatia ki te 100\]
Tauira:
Ko te utu tīmatanga mō tētahi taonga he RP 200.000, kātahi ka piki ki te RP 250.000. He aha te ōrau pikinga o te utu o te taonga?
Whakauruhia ngā uara ki roto i te tātai:
\[ \text{Te Pikinga Ōrau} = \left(\frac{250.000 – 200.000}{200.000}\right) \times 100 = 25\% \]
4. Te Whakamahi i ngā Tinihanga Hinengaro
Haunga te whakamahi i ngā tātai, kei reira ētahi tinihanga hinengaro hei āwhina i a koe ki te whakaoti rapanga ōrau me te kore e hiahia ki te tuhi i ia taahiraa o te tatau.
10% Tinihanga
He tino āwhina te mōhio ki te 10% o tētahi tau, nā te mea ka taea te whakarea, te tango rānei hei whakatau i tētahi atu ōrau.
Tauira:
Hei kimi i te 30% o te 400, tuatahi whakatauhia te 10% o te 400, arā, ko te 40. Kātahi ka whakareatia te 40 ki te 3 (nā te mea ko te 30% he toru whakareatia ki te 10%):
\[ 30\% \whakareatia 400 = 40 \whakareatia 3 = 120 \]
Ngā Tinihanga Hautau
Mā te huri i ngā ōrau ki ngā hautau ka māmā ake ngā tataunga.
– 50% = ½
– 25% = ¼
– 20% = ⅕
– 10% = 1/10
– 5% = 1/20
Tauira:
Hei kimi i te 25% o te 320, whakamahia:
\[ 25\% = \frac{1}{4} \]
\[ \frac{1}{4} \times 320 = 80 \]
Te whakaawhiwhi
I ētahi wā, ka taea e te whakaawhiwhinga uara te tere ake i ngā tataunga me te kore e ngaro nui te tika.
Tauira:
Hei kimi i te 18% o te 465, ka taea e koe te whakaawhiwhi i te 465 ki te 470:
\[ 18\% \whakareatia 470 = 0.18 \whakareatia 470 = 84.6 \]
He tino tata tēnei whika ki te hua tuturu o te 83.7.
5. Ngā Pātai Whakaharatau
Anei ētahi pātai whakaharatau hei whakahōhonu ake i tō māramatanga:
Pātai 1:
Ko te utu tuatahi mō tētahi taonga he 150.000 rp, ka hokona mō te hekenga 15%. He aha te utu i muri i te hekenga?
Otinga:
Utu whakaheke:
\[ 15\% \whakareatia ki te 150.000 = 22.500 \]
Utu i muri i te hekenga:
\[ 150.000 – 22.500 = 127.500 \]
Pātai 2:
Mena e mōhiotia ana ko te tapeke o ngā ākonga i roto i tētahi kura he 800, ā, 35% o ngā ākonga he wāhine, e hia ngā ākonga wāhine?
Otinga:
Te tokomaha o ngā ākonga wahine:
\[ 35\% \whakareatia ki te 800 = 280 \]
Pātai 3:
I piki ake te moni whiwhi a te kamupene mai i te rp 2.000.000 ki te rp 2.500.000. He aha te ōrau pikinga o te moni whiwhi?
Otinga:
Te pikinga ōrau:
\[ \frac{2.500.000 – 2.000.000}{2.000.000} \whakareatia ki te 100 = 25\% \]
Whakamutunga
Mā te mārama ki ngā kaupapa matua o ngā ōrau, te tautuhi i ngā momo raruraru, te whakamahi i ngā tātai tika, me te whakamahi i ngā mahi tinihanga hinengaro me te mahi tonu, ka taea e koe te whakaoti rapanga ōrau i te tere me te tika. Ko ngā tikanga kua whakaahuahia i roto i tēnei tuhinga kua hangaia hei whakahaere i te tatau ōrau kia māmā ake, kia whai hua ake hoki. Ko te tumanako ka whai hua tēnei tuhinga, ā, ka āwhina i a koe ki te whakaoti i ngā momo raruraru ōrau, i roto i ngā whakamātautau me te oranga o ia rā.
