6.1: Kutathmini Maneno

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Page ID: 164692

Victoria Dominguez, Cristian Martinez, and Sanaa Saykali
Citrus College via ASCCC Open Educational Resources Initiative

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Ufafanuzi: Thamani kamili

Thamani kamili ya namba halisi$a$, iliyoandikwa$|a|$, ni umbali kutoka$a$ hadi$0$ kwenye mstari wa nambari.

Ili kupata$|−4|$, waulize: “ni umbali gani kutoka$−4$ kwenda$0$?”. Chora mstari wa nambari na uone hiyo$|−4| = 4$. Vile vile$|4| = 4$, kama inavyoonekana katika takwimu hapa chini.

$clipboard_eb8163436d100cbff9fa7ef8e4f2fd943.png$

Mfano Template:index

Tathmini maneno yafuatayo:

$|8−2|− |4−7|$
$5|−3|+|−9|^2$
$\dfrac{3}{5}|6 + (−3)^3|$
$\left|\dfrac{(−2)^2 + 12}{3} +5 \right|+|−4+2|$

Suluhisho

Kutathmini$|8 − 2| − |4 − 7|$, kwanza kurahisisha ndani ya thamani kamili.

$\begin{array} &&|8 − 2| − |4 − 7| &\text{Given} \\ &= |6| − |− 3| &\text{Simplify inside the absolute value} \\ &= (6) − (3) &\text{Absolute value definition} \\ &= 3 & \end{array}$

Kwanza, kurahisisha maadili kamili, kisha tumia operesheni inayohitajika ya hesabu.

$\begin{array} &&5| − 3| + | − 9|^2 &\text{Given} \\ &= 5(3) + (9)^2 &\text{Absolute value definition} \\ &= 15 + 81 &\text{Simplify} \\ &= 96 & \end{array}$

Tumia utaratibu wa shughuli” PEMDAS” ili kurahisisha ndani ya thamani kamili.

$\begin{array} &&\dfrac{3}{5}|6 + (−3)^3| &\text{Given} \\ &=\dfrac{3}{5}|6 + (−27)| &\text{Evaluate the exponent term} \\ &= \dfrac{3}{5} − 21 &\text{Simplify inside the absolute value} \\ &= \dfrac{3}{5} (21) &\text{Absolute value definition} \\ &= \dfrac{63}{5} & \end{array}$

Ili kutathmini maneno katika sehemu hii, kwanza tumia utaratibu wa operesheni” PEMDAS” ndani ya thamani kamili ili kurahisisha.

$\begin{array} &&\left|\dfrac{(−2)^2 + 12}{3} +5 \right|+|−4+2| &\text{Given} \\ &= \left|\dfrac{(4 + 12)}{3} +5 \right|+|−2| &\text{Simplify} \\ &= \left|\dfrac{16}{3} +5 \right|+|−2| &\text{Note that \(3$ni LCD ya$\dfrac{16}{3}$ na$5$. $5$inaweza kuandikwa kama$\dfrac{5}{1}$}\\ &=\ kushoto|\ dfrac {16} {3} +\ dfrac {5 (3)} {1 (3)}\ haki|+||-2| &\ text {Kuzidisha nambari na denominator ya$\dfrac{5}{1}$ kwa LCD ili kuongeza maneno ndani ya thamani kamili.}\\ &=\ left|\ dfrac {31} {3}\ haki|+|-1 2| &\\ &=\ kushoto (\ dfrac {31} {3}\ haki) + (2) & amp;\ maandishi {thamani kamili ufafanuzi}\\ &=\ dfrac {31} {3} + 2 &\ maandishi {Sawa na hapo juu,$3$ ni LCD ya$\dfrac{31}{3}$ na$2$. $2$inaweza kuandikwa kama$\dfrac{2}{1}$.}\\ &=\ dfrac {31} {3} +\ dfrac {2 (3)} {1 (3)} &\ maandishi {$\dfrac{3}{3}$Kuzidisha$\dfrac{2}{1}$ kwa kuongeza maneno mawili.}\\ &=\ dfrac {37} {3} &\ mwisho {safu}\)

Zoezi Template:index

Tathmini maneno yaliyotolewa:

$|8 − 15|$
$|− 3 −12|$
$\left|− 2 + 11 − \left( −\dfrac{6}{4} \right) \right|$
$\left|−\dfrac{1 + 5}{12} − 5\right|− 1$
$|2 (5 + 6) − 20|$
$\left|\dfrac{1}{2} (21 − 5) − |(−2)^3 \right|$
$\left|−5 |− 2(−13 + 10) \right|$
$\dfrac{3}{2} \left| 12 \left( \dfrac{−7 + 17}{(6 − 2)} \right) \right| + |− (−2)|$