He aha te Whakareatanga Whakawhiti?
He tikanga pāngarau taketake te whakarea whakawhiti e whakamahia whānuitia ana hei whakaoti rapanga e pā ana ki ngā ōwehenga me ngā tauwehenga. Ahakoa te āhua māmā noa iho, he tino whai hua tēnei ariā i roto i te oranga o ia rā—mai i te tatau i te utu o ngā taonga, te whakatau i te tauine o ngā mapi, te whakarerekē i ngā tohutao, tae atu ki te whakaoti rapanga pāngarau i te kura. Ka matapakihia e tēnei tuhinga he aha te whakarea whakawhiti, te wā e whakamahia ai, me pēhea te mahi, me ngā tauira o ōna whakamahinga.
Te Mārama ki te Whakareatanga Whakawhiti
Ko te whakarea whakawhiti he tikanga mō te whakatairite i ngā hautau e rua, te whakaoti rānei i ngā whārite i te āhua o ngā ōwehenga mā te "whiti" i te whakarea i waenganui i te taupū me te tautō.
Hei tauira, e rua ngā wāhanga:
\[
\frac{a}{b} = \frac{c}{d}
\]
Mā te whakarea whakawhiti, ka whakareatia te a ki te d, me te b ki te c, kia whiwhi ai tātou:
\[
a \ngā d = b \ngā c
\]
Koinei te kaupapa matua o te whakarea whakawhiti: te whakarerekē i te whārite o ngā hautau e rua ki tētahi āhua whakarea e māmā ake ai te tatau.
He aha i huaina ai ko "Ripeka"?
Ka kiia tēnei he "whakawhiti" nā te mea ki te tuhia e tātou ngā hautau whakarara e rua, ka hangaia he tauira whakawhiti e ngā takirua tau e whakareatia ana:
\[
\frac{a}{b} = \frac{c}{d}
\]
Ko te whakarea whakawhiti e whai ake nei:
– taupū maui (a) whakareatia te taupū matau (d)
– taupū maui (b) whakareatia te taupū matau (c)
e āhua ana me he rārangi whakawhiti.
Āhea te Whakareatanga Whakawhiti e Whakamahia ai?
Ko te whakarea whakawhiti te tikanga e whakamahia ana ina:
1. Whakaotia ngā raruraru ōwehenga
Tauira: “Mēnā he 30.000 te utu mō te 2 kg o ngā āporo, e hia te utu mō te 5 kg?”
2. Te whakatairite i ngā hautau e rua
Hei tauira, te whakatau ko tēhea te mea nui ake i waenga i te 3/5 me te 4/7.
3. Kimihia ngā uara kāore i te mōhiotia (ngā taurangi)
Hei tauira i roto i te rapanga pāngarau: 3/4 = x/12, kimihia te x.
4. Ngā take tauine
Tauira: ko te tauine mahere 1:100.000, ko te tawhiti i runga i te mahere he 5 cm, he aha te tawhiti tuturu?
5. Ngā raruraru o te tere, te wā, me te tawhiti (i roto i te āhua whakatairite)
Ina whakaritea kia rite ki ngā ōwehenga, ka āwhina te whakarea whakawhiti.
Me pēhea te mahi i te whakarea whakawhiti
Hei whakamāmā ake, whai i ēnei mahi:
1. Kia tika te āhua o te pātai:
\[
\frac{a}{b} = \frac{c}{d}
\]
2. Whakamahi i te whakarea whakawhiti:
\[
a \ngā d = b \ngā c
\]
3. Mena he taurangi kei reira (hei tauira, x), waiho taua taurangi hei arotahi ki te rapu.
4. Whakaotia te whārite pēnei i te tikanga.
Tauira 1: Te Kimi i te Uara o x
I hoatu:
\[
\frac{3}{4} = \frac{x}{12}
\]
Whakareatia te whakarea whakawhiti:
\[
3 whakareatia ki te 12 = 4 whakareatia ki te x
\]
\[
36 = 4x
\]
\[
x = \frac{36}{4} = 9
\]
Nō reira, ko te uara o x = 9.
Tauira 2: Te Tātai i te Utu i runga i te Taumaha
Mena ko te utu mō te 2 kg huka he Rp. 28.000, e hia te utu mō te 5 kg?
Ka hanga e mātou te ōwehenga:
\[
\frac{2}{5} = \frac{28000}{x}
\]
Ka taea rānei e koe:
\[
\frac{2 \text{ kg}}{28000} = \frac{5 \text{ kg}}{x}
\]
Engari ko te mea tino māmā:
\[
\frac{2}{28000} = \frac{5}{x}
\]
Whakareatanga whakawhiti:
\[
2x = 28000 \whakareatia ki te 5
\]
\[
2x = 140000
\]
\[
x = 70000
\]
Nō reira, ko te utu mō te 5 kg huka he IDR 70.000.
Tauira 3: Te Whakatau i ngā Hautau Nui Ake
Whakataurite:
\[
\frac{3}{5} \text{ me } \frac{4}{7}
\]
Whakamahia te whakarea whakawhiti:
– 3 × 7 = 21
– 4 × 5 = 20
Nā te mea ko te 21 > 20, kāti:
\[
\frac{3}{5} > \frac{4}{7}
\]
Mā te whakarea whakawhiti ka māmā ake te whakatairite i ngā hautau me te kore e hiahiatia kia huri hei tau ā-ira.
Ngā Hapa Noa i roto i te Whakarea Whakawhiti
Ahakoa te āhua ngāwari, he maha ngā hapa e puta pinepine ana:
1. Te whakawhiti hē i ngā tau
Hei tauira, te whakarea i te a ki te c (me a ki te d).
2. Kāore e pupuri i ngā ōwehenga
E pā ana te whakarea whakawhiti ki ngā hautau ōrite e rua (i te āhua “=”).
3. Te whakanoho hē i ngā waeine
Mō ngā rapanga kōrero, me ōrite ngā waeine (kg ki te kg, cm ki te cm, me ētahi atu).
4. Te wareware ki te wehewehe i muri i te whiwhinga i te whārite
Tauira: kua whiwhi kē koe i te 36 = 4x, engari kāore i haere tonu ki te x = 9.
Hei karo i ngā hapa, tirohia anō ngā mahi, kia tika ai te tūnga o ngā taurangi.
Te Whakareatanga Whakawhiti i te Oranga o Ia Rā
Kāore te whakarea whakawhiti e whakamahia ana i roto i ngā whakamātautau pāngarau anake. I roto i ngā āhuatanga o te ao tūturu, ka puta ake tēnei ariā me te kore e mōhiotia e tātou.
1. Ngā Tohutao Tunu Kai
Mena e rua punetēpu huka te nui e hiahiatia ana mō ngā tūnga e whā, mō ngā tūnga e 10:
\[
\frac{2}{4} = \frac{x}{10}
\Rightarrow 2 \whakanuia te 10 = 4x
\Pere Matau 20 = 4x
\Pere Matau x = 5
\]
E hiahia ana koe kia 5 punetēpu o te huka.
2. Tauine Mahere
Mena ko te tauine he 1:50.000, ko te tikanga ko te 1 henimita i runga i te mapi = 50.000 henimita i te ao tūturu (500 m). Mena ko te tawhiti i runga i te mapi he 3 henimita, ko te tawhiti tuturu he 1.500 m.
Me ngā ōwehenga:
\[
\frac{1}{500} = \frac{3}{x}
\]
Ka taea te whakamahi i te whakarea whakawhiti hei kimi i te x.
3. Tere me te Wā
Mena ka haere te waka i te 120 km i roto i ngā hāora e 2, kāti i roto i ngā hāora e 5 (i te tere pumau):
\[
\frac{120}{2} = \frac{x}{5}
\Rightarrow 120 \whakanuia te 5 = 2x
\Pere Matau 600 = 2x
\Pere Matau x = 300
\]
Ko te tawhiti i haerea he 300 kiromita.
Whakamutunga
He tikanga nui te whakarea whakawhiti mō te whakaoti rapanga ōwehenga me ngā ōwehenga. Mā te whakarea whakawhiti i te taupū o tētahi hautau ki te taupū o tētahi atu, ka hua ake he whārite e māmā ake ai te whakaoti. Mā te mārama ki te whakarea whakawhiti ka taea e tātou te whakaoti rapanga pāngarau tere me te tika, ā, ka taea hoki te whakamahi i roto i ngā āhuatanga o ia rā, pērā i te tatau i ngā utu, te tatau i ngā tauine, ngā tohutao, me te tatau i ngā tawhiti me te wā.
Ki te hiahia koe, ka taea e au te āwhina i a koe ki te waihanga i tētahi putanga māmā ake o tēnei tuhinga mō ngā ākonga kura tuatahi/kura waenga, i tētahi putanga mātauranga ake rānei me ngā pātai whakaharatau me ngā kōrero.
