Kev Sib Npaug hla yog dab tsi?
Kev sib npaug ntawm cov lej yog ib txoj kev suav lej tseem ceeb uas feem ntau siv los daws cov teeb meem uas muaj feem cuam tshuam nrog cov piv thiab cov feem. Txawm hais tias nws zoo li yooj yim, lub tswv yim no muaj txiaj ntsig zoo kawg nkaus hauv lub neej txhua hnub - los ntawm kev xam tus nqi ntawm cov khoom, txiav txim siab qhov ntsuas ntawm daim ntawv qhia, kho cov zaub mov txawv, mus rau kev daws cov teeb meem lej hauv tsev kawm ntawv. Tsab xov xwm no yuav tham txog kev sib npaug ntawm cov lej yog dab tsi, thaum twg siv nws, yuav ua li cas, thiab piv txwv ntawm nws cov kev siv.
Nkag Siab Txog Kev Sib Npaug Sib Npaug
Feem ntau, kev sib npaug hla yog ib txoj kev los sib piv ob feem lossis daws cov kab zauv hauv daim ntawv ntawm cov feem los ntawm "hla" qhov kev sib npaug ntawm tus lej suav thiab tus lej faib.
Piv txwv li, muaj ob feem:
\[
\frac{a}{b} = \frac{c}{d}
\]
Nrog kev sib npaug ntawm cov lej, peb muab a los ntawm d thiab b los ntawm c, kom peb tau txais:
\[
a\times d = b\times c
\]
Qhov no yog lub ntsiab lus ntawm kev sib npaug ntawm ob feem: hloov qhov sib npaug ntawm ob feem mus rau hauv daim ntawv sib npaug uas yooj yim dua rau kev suav.
Vim li cas nws thiaj hu ua "Cross"?
Nws hu ua "cross" vim tias yog peb sau ob feem sib luag, cov khub ntawm cov lej uas raug sib npaug tsim ib qho qauv hla:
\[
\frac{a}{b} = \frac{c}{d}
\]
Kev sib npaug ntawm cov lej siv:
- tus lej sab laug (a) zaug tus lej sab xis (d)
- tus lej sab laug (b) npaug tus lej sab xis (c)
uas zoo li kab hla.
Thaum twg siv Cross Multiplication?
Feem ntau siv kev sib npaug ntawm cov lej thaum:
1. Daws cov teeb meem sib piv
Piv txwv li: "Yog tias 2 kg ntawm txiv apples raug nqi 30.000, 5 kg raug nqi ntau npaum li cas?"
2. Sib piv ob feem
Piv txwv li, txiav txim seb qhov twg loj dua ntawm 3/5 thiab 4/7.
3. Nrhiav cov nqi tsis paub (cov hloov pauv)
Piv txwv li hauv qhov teeb meem lej: 3/4 = x/12, nrhiav x.
4. Teeb meem ntawm qhov ntsuas
Piv txwv li: daim ntawv qhia teev 1:100.000, qhov deb ntawm daim ntawv qhia yog 5 cm, qhov deb tiag tiag yog dab tsi?
5. Teeb meem ntawm kev ceev, lub sijhawm, thiab qhov deb (hauv daim ntawv sib piv)
Thaum muab teeb tsa ua feem, kev sib npaug hla tuaj yeem pab tau.
Yuav Ua Li Cas Thiaj Ua Tau Kev Sib Npaug
Yuav kom yooj yim dua, ua raws li cov kauj ruam no:
1. Xyuas kom tseeb tias lo lus nug yog nyob rau hauv daim ntawv ntawm ib qho kev faib ua feem:
\[
\frac{a}{b} = \frac{c}{d}
\]
2. Ua kev sib npaug ntawm cov lej sib txawv:
\[
a\times d = b\times c
\]
3. Yog tias muaj ib qho variable (piv txwv li x), ua kom qhov variable ntawd yog qhov tseem ceeb rau kev tshawb nrhiav.
4. Daws qhov equation li niaj zaus.
Piv txwv 1: Nrhiav Tus Nqi ntawm x
Muab:
\[
\frac{3}{4} = \frac{x}{12}
\]
Ua kev sib npaug ntawm cov lej:
\[
3 zaug 12 = 4 zaug x
\]
\[
36 = 4x
\]
\[
x = \frac{36}{4} = 9
\]
Yog li, tus nqi ntawm x = 9.
Piv txwv 2: Xam Tus Nqi Raws Li Qhov Hnyav
Yog tias 2 kg suab thaj raug nqi Rp. 28.000, 5 kg raug nqi ntau npaum li cas?
Peb ua qhov sib piv:
\[
\frac{2}{5} = \frac{28000}{x}
\]
Los yog koj kuj tseem tuaj yeem ua tau:
\[
\frac{2 kg}}{28000} = \frac{5 kg}}{x}
\]
Tab sis qhov yooj yim tshaj plaws:
\[
\frac{2}{28000} = \frac{5}{x}
\]
Kev sib tshooj hla:
\[
2x = 28000 x 5
\]
\[
2x = 140000
\]
\[
x = 70000 os
\]
Yog li tus nqi ntawm 5 kg ntawm qab zib yog IDR 70.000.
Piv txwv 3: Txheeb xyuas cov feem loj dua
Piv txwv:
\[
\frac{3}{5} \text{ thiab } \frac{4}{7}
\]
Siv kev sib npaug ntawm cov lej:
– 3 × 7 = 21
– 4 × 5 = 20
Txij li thaum 21 > 20, ces:
\[
\frac{3}{5} > \frac{4}{7}
\]
Kev sib npaug ua rau nws yooj yim dua rau peb los sib piv cov feem pua yam tsis tas yuav hloov lawv mus rau hauv cov lej kaum.
Cov Yuam Kev Feem Ntau Hauv Kev Sib Npaug
Txawm hais tias nws zoo li yooj yim los xij, muaj ntau qhov yuam kev uas feem ntau tshwm sim:
1. Hla cov lej tsis raug
Piv txwv li, muab a los ntawm c (nws yuav tsum yog a los ntawm d).
2. Tsis tswj cov feem pua
Kev sib npaug ntawm ob feem sib npaug (hauv daim ntawv "=").
3. Tso cov chav tsis raug
Hauv cov teeb meem dab neeg, cov chav ntsuas yuav tsum sib xws (kg nrog kg, cm nrog cm, thiab lwm yam).
4. Tsis nco qab faib tom qab tau txais qhov sib npaug
Piv txwv li: koj twb tau 36 = 4x, tab sis tsis tau txuas ntxiv mus rau x = 9.
Yuav kom tsis txhob ua yuam kev, ib txwm xyuas ob zaug cov kauj ruam thiab xyuas kom meej tias cov hloov pauv nyob rau hauv qhov chaw raug.
Kev Sib Npaug Hauv Lub Neej Txhua Hnub
Kev sib npaug ntawm cov lej tsis yog siv rau hauv kev xeem lej xwb. Hauv ntau qhov xwm txheej hauv ntiaj teb tiag tiag, lub tswv yim no tshwm sim yam tsis tau peb paub txog.
1. Cov Zaub Mov Txawv Ua Noj
Yog tias daim ntawv qhia hu rau 2 diav suab thaj rau 4 qhov kev pabcuam, ces rau 10 qhov kev pabcuam:
\[
\frac{2}{4} = \frac{x}{10}
\sab xis 2 \times 10 = 4x
\Xub Sab Xis 20 = 4x
\Xub Sab Xis x = 5
\]
Xav tau 5 diav suab thaj.
2. Daim Ntawv Qhia Qhov Ntsuas
Yog tias qhov ntsuas yog 1:50.000, nws txhais tau tias 1 cm ntawm daim ntawv qhia = 50.000 cm hauv qhov tseeb (500 m). Yog tias qhov deb ntawm daim ntawv qhia yog 3 cm, qhov deb tiag tiag yog 1.500 m.
Nrog cov piv txwv:
\[
\frac{1}{500} = \frac{3}{x}
\]
Kev sib npaug hla tuaj yeem siv los nrhiav x.
3. Ceev thiab Lub Sijhawm
Yog tias lub tsheb mus ncig 120 km hauv 2 teev, ces hauv 5 teev (ntawm qhov ceev tas li):
\[
\frac{120}{2} = \frac{x}{5}
\sab xis 120 \times 5 = 2x
\Xub Sab Xis 600 = 2x
\Xub Sab Xis x = 300
\]
Qhov ntev ntawm txoj kev taug kev yog 300 km.
Xaus
Kev sib npaug sib npaug yog ib txoj hauv kev tseem ceeb rau kev daws cov piv thiab cov feem. Nws ua haujlwm los ntawm kev sib npaug ntawm tus lej ntawm ib feem los ntawm tus lej ntawm lwm tus, ua rau muaj qhov sib npaug uas yooj yim dua los daws. Kev nkag siab txog kev sib npaug sib npaug tso cai rau peb daws ntau yam teeb meem lej sai dua thiab raug, thiab nws kuj tuaj yeem siv rau ntau qhov xwm txheej txhua hnub, xws li xam tus nqi, xam cov nplai, cov zaub mov txawv, thiab xam qhov deb thiab lub sijhawm.
Yog tias koj xav tau, kuv kuj tuaj yeem pab koj tsim ib qho version yooj yim dua ntawm tsab xov xwm no rau cov tub ntxhais kawm ntawv qib pib / theem nrab, lossis ib qho version kev kawm ntxiv nrog cov lus nug xyaum thiab kev sib tham.
