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6.1: Kutathmini Maneno

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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:

    1. \(|8−2|− |4−7|\)
    2. \(5|−3|+|−9|^2\)
    3. \(\dfrac{3}{5}|6 + (−3)^3|\)
    4. \(\left|\dfrac{(−2)^2 + 12}{3} +5 \right|+|−4+2|\)

    Suluhisho

    1. Kutathmini\(|8 − 2| − |4 − 7|\), kwanza kurahisisha ndani ya thamani kamili.

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

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

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

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

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

    1. 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:

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