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Sura ya 1 Mazoezi Mapitio

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    177960
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    Sura ya Mapitio ya mazoezi

    Utangulizi wa Hesabu nzima

    Tumia Thamani ya Mahali na Nambari Nzima

    Katika mazoezi yafuatayo kupata thamani ya mahali ya kila tarakimu.

    Zoezi\(\PageIndex{1}\)

    26,915

    1. 1
    2. 2
    3. 9
    4. 5
    5. 6
    Jibu
    1. makumi
    2. maelfu kumi
    3. mamia
    4. mmojammoja
    5. maelfu
    Zoezi\(\PageIndex{2}\)

    359,417

    1. 9
    2. 3
    3. 4
    4. 7
    5. 1
    Zoezi\(\PageIndex{3}\)

    58,129,304

    1. 5
    2. 0
    3. 1
    4. 8
    5. 2
    Jibu
    1. mamilioni kumi
    2. makumi
    3. maelfu mia
    4. mamilioni
    5. maelfu kumi
    Zoezi\(\PageIndex{4}\)

    9,430,286,157

    1. 6
    2. 4
    3. 9
    4. 0
    5. 5

    Katika mazoezi yafuatayo, jina la kila namba.

    Zoezi\(\PageIndex{5}\)

    6,104

    Jibu

    elfu sita, mia moja na nne

    Zoezi\(\PageIndex{6}\)

    493,068

    Zoezi\(\PageIndex{7}\)

    3,975,284

    Jibu

    milioni tatu, mia tisa sabini na tano elfu, mia mbili themanini na nne

    Zoezi\(\PageIndex{8}\)

    85,620,435

    Katika mazoezi yafuatayo, weka kila namba kama namba nzima kwa kutumia tarakimu.

    Zoezi\(\PageIndex{9}\)

    mia tatu kumi na tano

    Jibu

    315

    Zoezi\(\PageIndex{10}\)

    sitini na tano elfu, mia tisa kumi na mbili

    Zoezi\(\PageIndex{11}\)

    milioni tisini, mia nne ishirini na tano elfu, kumi na sita

    Jibu

    90,425,016

    Zoezi\(\PageIndex{12}\)

    bilioni moja, milioni arobaini na tatu, mia tisa ishirini na mbili elfu, mia tatu kumi na moja

    Katika mazoezi yafuatayo, pande zote kwa thamani ya mahali iliyoonyeshwa.

    Zoezi\(\PageIndex{13}\)

    Pande zote kwa kumi karibu.

    1. 407
    2. 8,564
    Jibu
    1. 410
    2. 8,560
    Zoezi\(\PageIndex{14}\)

    Pande zote kwa mia karibu.

    1. 25,846
    2. 25,864

    Katika mazoezi yafuatayo, pande zote namba kwa karibu 1. mia 2. elfu 3. elfu kumi.

    Zoezi\(\PageIndex{15}\)

    864,951

    Jibu
    1. 865,000865,000
    2. 865,000865,000
    3. 860,000
    Zoezi\(\PageIndex{16}\)

    3,972,849

    Tambua Multiples na Mambo

    Katika mazoezi yafuatayo, tumia vipimo vya mgawanyiko ili kuamua kama kila namba inagawanyika na 2, na 3, na 5, na 6, na 10.

    Zoezi\(\PageIndex{17}\)

    168

    Jibu

    na 2,3,6

    Zoezi\(\PageIndex{18}\)

    264

    Zoezi\(\PageIndex{19}\)

    375

    Jibu

    na 3,5

    Zoezi\(\PageIndex{20}\)

    750

    Zoezi\(\PageIndex{21}\)

    1430

    Jibu

    na 2,5,10

    Zoezi\(\PageIndex{22}\)

    1080

    Kupata factorizations Mkuu na Multiples angalau kawaida

    Katika mazoezi yafuatayo, pata factorization kuu.

    Zoezi\(\PageIndex{23}\)

    420

    Jibu

    2\(\cdot 2 \cdot 3 \cdot 5 \cdot 7\)

    Zoezi\(\PageIndex{24}\)

    115

    Zoezi\(\PageIndex{25}\)

    225

    Jibu

    3\(\cdot 3 \cdot 5 \cdot 5\)

    Zoezi\(\PageIndex{26}\)

    2475

    Zoezi\(\PageIndex{27}\)

    1560

    Jibu

    \(2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 13\)

    Zoezi\(\PageIndex{28}\)

    56

    Zoezi\(\PageIndex{29}\)

    72

    Jibu

    \(2 \cdot 2 \cdot 2 \cdot 3 \cdot 3\)

    Zoezi\(\PageIndex{30}\)

    168

    Zoezi\(\PageIndex{31}\)

    252

    Jibu

    \(2 \cdot 2 \cdot 3 \cdot 3 \cdot 7\)

    Zoezi\(\PageIndex{32}\)

    391

    Katika mazoezi yafuatayo, pata idadi ndogo ya kawaida ya namba zifuatazo kwa kutumia njia ya wingi.

    Zoezi\(\PageIndex{33}\)

    6,15

    Jibu

    30

    Zoezi\(\PageIndex{34}\)

    60, 75

    Katika mazoezi yafuatayo, pata idadi ndogo ya kawaida ya namba zifuatazo kwa kutumia njia kuu ya sababu.

    Zoezi\(\PageIndex{35}\)

    24,30

    Jibu

    120

    Zoezi\(\PageIndex{36}\)

    70, 84

    Tumia Lugha ya Algebra

    Tumia Vigezo na Algebraic Algebraic

    Katika mazoezi yafuatayo, tafsiri zifuatazo kutoka kwa algebra hadi Kiingereza.

    Zoezi\(\PageIndex{37}\)

    25-7

    Jibu

    25 minus 7, tofauti ya ishirini na tano na saba

    Zoezi\(\PageIndex{38}\)

    5\(\cdot 6\)

    Zoezi\(\PageIndex{39}\)

    \(45 \div 5\)

    Jibu

    45 kugawanywa na 5, quotient ya arobaini na tano na tano

    Zoezi\(\PageIndex{40}\)

    x+8

    Zoezi\(\PageIndex{41}\)

    \(42 \geq 27\)

    Jibu

    arobaini na mbili ni kubwa kuliko au sawa na ishirini na saba

    Zoezi\(\PageIndex{42}\)

    3n=24

    Zoezi\(\PageIndex{43}\)

    \(3 \leq 20 \div 4\)

    Jibu

    3 ni chini ya au sawa na 20 imegawanywa na 4, tatu ni chini ya au sawa na quotient ya ishirini na nne

    Zoezi\(\PageIndex{44}\)

    \(a \neq 7 \cdot 4\)

    Katika mazoezi yafuatayo, onyesha kama kila mmoja ni kujieleza au equation.

    Zoezi\(\PageIndex{45}\)

    \(6 \cdot 3+5\)

    Jibu

    kujieleza

    Zoezi\(\PageIndex{46}\)

    y-8=32

    Kurahisisha Maneno Kutumia Utaratibu wa Uendeshaji

    Katika mazoezi yafuatayo, kurahisisha kila kujieleza.

    Zoezi\(\PageIndex{47}\)

    \(3^{5}\)

    Jibu

    243

    Zoezi\(\PageIndex{48}\)

    \(10^{8}\)

    Katika mazoezi yafuatayo, kurahisisha

    Zoezi\(\PageIndex{49}\)

    6+10/2+2

    Jibu

    13

    Zoezi\(\PageIndex{50}\)

    9+12/3+4

    Zoezi\(\PageIndex{51}\)

    \(20 \div(4+6) \cdot 5\)

    Jibu

    10

    Zoezi\(\PageIndex{52}\)

    \(33 \div(3+8) \cdot 2\)

    Zoezi\(\PageIndex{53}\)

    \(4^{2}+5^{2}\)

    Jibu

    41

    Zoezi\(\PageIndex{54}\)

    \((4+5)^{2}\)

    Tathmini ya Kuelezea

    Katika mazoezi yafuatayo, tathmini maneno yafuatayo.

    Zoezi\(\PageIndex{55}\)

    9x+7 wakati x=3

    Jibu

    34

    Zoezi\(\PageIndex{56}\)

    5x-4 wakati x=6

    Zoezi\(\PageIndex{57}\)

    \(x^{4}\)lini\(x=3\)

    Jibu

    81

    Zoezi\(\PageIndex{58}\)

    \(3^{x}\)lini\(x=3\)

    Zoezi\(\PageIndex{59}\)

    \(x^{2}+5 x-8\)lini\(x=6\)

    Jibu

    58

    Zoezi\(\PageIndex{60}\)

    \(2 x+4 y-5\)lini
    \(x=7, y=8\)

    Kurahisisha Maneno kwa Kuchanganya Kama Masharti

    Katika mazoezi yafuatayo, tambua mgawo wa kila neno.

    Zoezi\(\PageIndex{61}\)

    12n

    Jibu

    12

    Zoezi\(\PageIndex{62}\)

    9\(x^{2}\)

    Katika mazoezi yafuatayo, tambua maneno kama hayo.

    Zoezi\(\PageIndex{63}\)

    \(3 n, n^{2}, 12,12 p^{2}, 3,3 n^{2}\)

    Jibu

    12\(3, n^{2}\) na 3\(n^{2}\)

    Zoezi\(\PageIndex{64}\)

    \(5,18 r^{2}, 9 s, 9 r, 5 r^{2}, 5 s\)

    Katika mazoezi yafuatayo, tambua maneno katika kila kujieleza.

    Zoezi\(\PageIndex{65}\)

    \(11 x^{2}+3 x+6\)

    Jibu

    \(11 x^{2}, 3 x, 6\)

    Zoezi\(\PageIndex{66}\)

    \(22 y^{3}+y+15\)

    Katika mazoezi yafuatayo, kurahisisha maneno yafuatayo kwa kuchanganya maneno kama hayo.

    Zoezi\(\PageIndex{67}\)

    17a+9a

    Jibu

    26a

    Zoezi\(\PageIndex{68}\)

    18z+9z

    Zoezi\(\PageIndex{69}\)

    9x+3x+8

    Jibu

    12x+8

    Zoezi\(\PageIndex{70}\)

    8a+5a+9

    Zoezi\(\PageIndex{71}\)

    7p+6+5p-4

    Jibu

    12p+2

    Zoezi\(\PageIndex{72}\)

    8x+7+4x-5

    Tafsiri Maneno ya Kiingereza kwa kujieleza Algebraic

    Katika mazoezi yafuatayo, tafsiri maneno yafuatayo katika maneno ya algebraic.

    Zoezi\(\PageIndex{73}\)

    jumla ya 8 na 12

    Jibu

    8+12

    Zoezi\(\PageIndex{74}\)

    jumla ya 9 na 1

    Zoezi\(\PageIndex{75}\)

    tofauti ya x na 4

    Jibu

    x-4

    Zoezi\(\PageIndex{76}\)

    tofauti ya x na 3

    Zoezi\(\PageIndex{77}\)

    bidhaa ya 6 na y

    Jibu

    6y

    Zoezi\(\PageIndex{78}\)

    bidhaa ya 9 na y

    Zoezi\(\PageIndex{79}\)

    Adele alinunua skirt na blouse. Sketi iligharimu $15 zaidi kuliko blouse. Hebu bb inawakilisha gharama ya blouse. Andika maneno kwa gharama ya skirt.

    Jibu

    b+15

    Zoezi\(\PageIndex{80}\)

    Marcella ina binamu 6 wachache wa kijana kuliko binamu wa msichana. Hebu g kuwakilisha idadi ya binamu msichana. Andika maneno kwa idadi ya binamu za kijana.

    Kuongeza na Ondoa Integers

    Tumia Negatives na Kupinga ya Integers

    Katika mazoezi yafuatayo, tengeneza kila jozi zifuatazo za namba, ukitumia < or >.

    Zoezi\(\PageIndex{81}\)
    1. 6___2
    2. -7___4
    3. -9___-1
    4. 9___1-3

    Jibu
    1. >
    2. <
    3. <
    4. >
    Zoezi\(\PageIndex{82}\)
    1. -5___1
    2. -4___-9
    3. 6___10
    4. 3___18-8

    Katika mazoezi yafuatayo, tafuta kinyume cha kila nambari.

    Zoezi\(\PageIndex{83}\)
    1. —8
    2. 1
    Jibu
    1. 8
    2. -1
    Zoezi\(\PageIndex{84}\)
    1. -2
    2. 6

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{85}\)

    - (19-19)

    Jibu

    19

    Zoezi\(\PageIndex{86}\)

    - (-53)

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{87}\)

    -m wakati

    1. m=3
    2. m=—3
    Jibu
    1. —3
    2. 3
    Zoezi\(\PageIndex{88}\)

    -p wakati

    1. p=6
    2. p=-6

    Rahisisha Maneno na Thamani kamili

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{89}\)
    1. |7|
    2. |—25|
    3. |0|
    Jibu
    1. 7
    2. 25
    3. 0
    Zoezi\(\PageIndex{90}\)
    1. |5|
    2. |0|
    3. |19|

    Katika mazoezi yafuatayo, jaza <>, au = kwa kila jozi zifuatazo za namba.

    Zoezi\(\PageIndex{91}\)
    1. -8___|—8|
    2. -|—2|___ї 2
    Jibu
    1. <
    2. =
    Zoezi\(\PageIndex{92}\)
    1. |—3|___—|—3|
    2. 4___—|—4|

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{93}\)

    |8,14|

    Jibu

    4

    Zoezi\(\PageIndex{94}\)

    |9—6|

    Zoezi\(\PageIndex{95}\)

    8 (14—2|2|)

    Jibu

    80

    Zoezi\(\PageIndex{96}\)

    6 (13—4||2|)

    Katika mazoezi yafuatayo, tathmini.

    Zoezi\(\PageIndex{97}\)

    1. |x| wakati x=—28

    Jibu
    1. 28
    2. 15
    Zoezi\(\PageIndex{98}\)
    1. ywakati y=-37
    2. |-z| wakati z=-24

    Ongeza integers

    Katika mazoezi yafuatayo, kurahisisha kila kujieleza.

    Zoezi\(\PageIndex{99}\)

    -200+65

    Jibu

    -135

    Zoezi\(\PageIndex{100}\)

    -150+45

    Zoezi\(\PageIndex{101}\)

    2+ (-8) +6

    Jibu

    0

    Zoezi\(\PageIndex{102}\)

    4+ (-9) +7

    Zoezi\(\PageIndex{103}\)

    140+ (-75) +67

    Jibu

    132

    Zoezi\(\PageIndex{104}\)

    -32+24+ (-6) +10

    Ondoa integers

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{105}\)

    9—3

    Jibu

    6

    Zoezi\(\PageIndex{106}\)

    -5—1 (-1)

    Zoezi\(\PageIndex{107}\)
    1. 15-6
    2. 15+ (-6)
    Jibu
    1. 9
    2. 9
    Zoezi\(\PageIndex{108}\)
    1. 129-9
    2. 12+ (-9)
    Zoezi\(\PageIndex{109}\)
    1. 8—9 (-9)
    2. 8+9
    Jibu
    1. 17
    2. 17
    Zoezi\(\PageIndex{110}\)
    1. 4—4 (-4)
    2. 4+4

    Katika mazoezi yafuatayo, kurahisisha kila kujieleza.

    Zoezi\(\PageIndex{111}\)

    10—19 (—19)

    Jibu

    29

    Zoezi\(\PageIndex{112}\)

    11-18 (18-18)

    Zoezi\(\PageIndex{113}\)

    31-79

    Jibu

    -48

    Zoezi\(\PageIndex{114}\)

    39-81

    Zoezi\(\PageIndex{115}\)

    -31-11

    Jibu

    -42

    Zoezi\(\PageIndex{116}\)

    -32-18

    Zoezi\(\PageIndex{117}\)

    -15—28 (-28) +5

    Jibu

    18

    Zoezi\(\PageIndex{118}\)

    71+ (-10) -8

    Zoezi\(\PageIndex{119}\)

    -16—( -4+1) -7

    Jibu

    -20

    Zoezi\(\PageIndex{120}\)

    -15—( -6+4) -3

    Kuzidisha integers

    Katika mazoezi yafuatayo, ongeze.

    Zoezi\(\PageIndex{121}\)

    -5 (7)

    Jibu

    -35

    Zoezi\(\PageIndex{122}\)

    -8 (6)

    Zoezi\(\PageIndex{123}\)

    -18 (ї2)

    Jibu

    36

    Zoezi\(\PageIndex{124}\)

    -10 (-6)

    Kugawanya Integers

    Katika mazoezi yafuatayo, ugawanye.

    Zoezi\(\PageIndex{125}\)

    \(-28 \div 7\)

    Jibu

    -4

    Zoezi\(\PageIndex{126}\)

    \(56 \div(-7)\)

    Zoezi\(\PageIndex{127}\)

    \(-120 \div(-20)\)

    Jibu

    6

    Zoezi\(\PageIndex{128}\)

    \(-200 \div 25\)

    Kurahisisha Maneno na Integers

    Katika mazoezi yafuatayo, kurahisisha kila kujieleza.

    Zoezi\(\PageIndex{129}\)

    -8 (ї2) -3 (-9)

    Jibu

    43

    Zoezi\(\PageIndex{130}\)

    -7 (-4) -5 (1-3)

    Zoezi\(\PageIndex{131}\)

    \((-5)^{3}\)

    Jibu

    -125

    Zoezi\(\PageIndex{132}\)

    \((-4)^{3}\)

    Zoezi\(\PageIndex{133}\)

    \(-4 \cdot 2 \cdot 11\)

    Jibu

    -88

    Zoezi\(\PageIndex{134}\)

    \(-5 \cdot 3 \cdot 10\)

    Zoezi\(\PageIndex{135}\)

    \(-10(-4) \div(-8)\)

    Jibu

    -5

    Zoezi\(\PageIndex{136}\)

    \(-8(-6) \div(-4)\)

    Zoezi\(\PageIndex{137}\)

    31-4 (3—9)

    Jibu

    55

    Zoezi\(\PageIndex{138}\)

    24-3 (2,110)

    Tathmini Maneno ya kutofautiana na Integers

    Katika mazoezi yafuatayo, tathmini kila kujieleza.

    Zoezi\(\PageIndex{139}\)

    x+8 wakati

    1. x=18-26
    2. x=-95
    Jibu
    1. -18
    2. -87
    Zoezi\(\PageIndex{140}\)

    y+9 wakati

    1. y=-29
    2. y=-84
    Zoezi\(\PageIndex{141}\)

    Wakati b=-11, tathmini:

    1. b+6
    2. -b+6
    Jibu
    1. -5
    2. 17
    Zoezi\(\PageIndex{142}\)

    Wakati c=-9, tathmini:

    1. c+ (-4) c+ (-4)
    2. -c+ (—4)
    Zoezi\(\PageIndex{143}\)

    \(p^{2}-5 p+2\)lini
    \(p=-1\)

    Jibu

    8

    Zoezi\(\PageIndex{144}\)

    \(q^{2}-2 q+9\)lini\(q=-2\)

    Zoezi\(\PageIndex{145}\)

    \(6 x-5 y+15\)lini\(x=3\) na\(y=-1\)

    Jibu

    38

    Zoezi\(\PageIndex{146}\)

    \(3 p-2 q+9\)lini\(p=8\) na\(q=-2\)

    Tafsiri Maneno ya Kiingereza kwa Maneno ya Algebraic

    Katika mazoezi yafuatayo, tafsiri kwa kujieleza kwa algebraic na kurahisisha iwezekanavyo.

    Zoezi\(\PageIndex{147}\)

    jumla ya -4 na -17, iliongezeka kwa 32

    Jibu

    (-4+ (-17) +32; 11

    Zoezi\(\PageIndex{148}\)
    1. tofauti ya 15 na -7
    2. Ondoa 15 kutoka -7
    Zoezi\(\PageIndex{149}\)

    quotient ya -45 na -9

    Jibu

    \(\frac{-45}{-9} ; 5\)

    Zoezi\(\PageIndex{150}\)

    bidhaa ya -12 na tofauti ya c na d

    Tumia Integers katika Maombi

    Katika mazoezi yafuatayo, tatua.

    Zoezi\(\PageIndex{151}\)

    Joto Joto la juu siku moja huko Miami Beach, Florida, lilikuwa 76°. Siku hiyo hiyo, joto la juu huko Buffalo, New York lilikuwa -8°. Ilikuwa tofauti kati ya joto katika Miami Beach na joto katika Buffalo?

    Jibu

    digrii 84

    Zoezi\(\PageIndex{152}\)

    Kuangalia Akaunti Adrianne ana usawa wa -$22 katika akaunti yake ya kuangalia. Yeye amana $301 kwa akaunti. Usawa mpya ni nini?

    Tazama sehemu ndogo

    Pata FRACTIONS sawa

    Katika mazoezi yafuatayo, pata sehemu tatu sawa na sehemu iliyotolewa. Onyesha kazi yako, kwa kutumia takwimu au algebra.

    Zoezi\(\PageIndex{153}\)

    \(\frac{1}{4}\)

    Jibu

    \(\frac{2}{8}, \frac{3}{12}, \frac{4}{16}\)majibu yanaweza kutofautiana

    Zoezi\(\PageIndex{154}\)

    \(\frac{1}{3}\)

    Zoezi\(\PageIndex{155}\)

    \(\frac{5}{6}\)

    Jibu

    \(\frac{10}{12}, \frac{15}{18}, \frac{20}{24}\)majibu yanaweza kutofautiana

    Zoezi\(\PageIndex{156}\)

    \(\frac{2}{7}\)

    Kurahisisha Fractions

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{157}\)

    \(\frac{7}{21}\)

    Jibu

    \(\frac{1}{3}\)

    Zoezi\(\PageIndex{158}\)

    \(\frac{8}{24}\)

    Zoezi\(\PageIndex{159}\)

    \(\frac{15}{20}\)

    Jibu

    \(\frac{3}{4}\)

    Zoezi\(\PageIndex{160}\)

    \(\frac{12}{18}\)

    Zoezi\(\PageIndex{161}\)

    \(-\frac{168}{192}\)

    Jibu

    \(-\frac{7}{8}\)

    Zoezi\(\PageIndex{162}\)

    \(-\frac{140}{224}\)

    Zoezi\(\PageIndex{163}\)

    \(\frac{11 x}{11 y}\)

    Jibu

    \(\frac{x}{y}\)

    Zoezi\(\PageIndex{164}\)

    \(\frac{15 a}{15 b}\)

    Kuzidisha vipande

    Katika mazoezi yafuatayo, ongeze.

    Zoezi\(\PageIndex{165}\)

    \(\frac{2}{5} \cdot \frac{1}{3}\)

    Jibu

    \(\frac{2}{15}\)

    Zoezi\(\PageIndex{166}\)

    \(\frac{1}{2} \cdot \frac{3}{8}\)

    Zoezi\(\PageIndex{167}\)

    \(\frac{7}{12}\left(-\frac{8}{21}\right)\)

    Jibu

    \(-\frac{2}{9}\)

    Zoezi\(\PageIndex{168}\)

    \(\frac{5}{12}\left(-\frac{8}{15}\right)\)

    Zoezi\(\PageIndex{169}\)

    \(-28 p\left(-\frac{1}{4}\right)\)

    Jibu

    7p

    Zoezi\(\PageIndex{170}\)

    \(-51 q\left(-\frac{1}{3}\right)\)

    Zoezi\(\PageIndex{172}\)

    \(\frac{14}{5}(-15)\)

    Jibu

    -42

    Zoezi\(\PageIndex{173}\)

    \(-1\left(-\frac{3}{8}\right)\)

    Gawanya FRACTIONS

    Katika mazoezi yafuatayo, ugawanye

    Zoezi\(\PageIndex{174}\)

    \(\frac{1}{2} \div \frac{1}{4}\)

    Jibu

    2

    Zoezi\(\PageIndex{175}\)

    \(\frac{1}{2} \div \frac{1}{8}\)

    Zoezi\(\PageIndex{176}\)

    \(-\frac{4}{5} \div \frac{4}{7}\)

    Jibu

    \(-\frac{7}{5}\)

    Zoezi\(\PageIndex{177}\)

    \(-\frac{3}{4} \div \frac{3}{5}\)

    Zoezi\(\PageIndex{178}\)

    \(\frac{5}{8} \div \frac{a}{10}\)

    Jibu

    \(\frac{25}{4 a}\)

    Zoezi\(\PageIndex{179}\)

    \(\frac{5}{6} \div \frac{c}{15}\)

    Zoezi\(\PageIndex{180}\)

    \(\frac{7 p}{12} \div \frac{21 p}{8}\)

    Jibu

    \(\frac{2}{9}\)

    Zoezi\(\PageIndex{181}\)

    \(\frac{5 q}{12} \div \frac{15 q}{8}\)

    Zoezi\(\PageIndex{182}\)

    \(\frac{2}{5} \div(-10)\)

    Jibu

    \(-\frac{1}{25}\)

    Zoezi\(\PageIndex{183}\)

    \(-18 \div-\left(\frac{9}{2}\right)\)

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{184}\)

    \(\frac{\frac{2}{3}}{\frac{8}{9}}\)

    Jibu

    \(\frac{3}{4}\)

    Zoezi\(\PageIndex{185}\)

    \(\frac{\frac{4}{5}}{\frac{8}{15}}\)

    Zoezi\(\PageIndex{186}\)

    \(\frac{-\frac{9}{10}}{3}\)

    Jibu

    \(-\frac{3}{10}\)

    Zoezi\(\PageIndex{187}\)

    \(\frac{2}{\frac{5}{8}}\)

    Zoezi\(\PageIndex{188}\)

    \(\frac{\frac{r}{5}}{\frac{s}{3}}\)

    Jibu

    \(\frac{3 r}{5 s}\)

    Zoezi\(\PageIndex{189}\)

    \(\frac{-\frac{x}{6}}{-\frac{8}{9}}\)

    Kurahisisha Maneno Imeandikwa na Bar Sehemu

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{190}\)

    \(\frac{4+11}{8}\)

    Jibu

    \(\frac{15}{8}\)

    Zoezi\(\PageIndex{191}\)

    \(\frac{9+3}{7}\)

    Zoezi\(\PageIndex{192}\)

    \(\frac{30}{7-12}\)

    Jibu

    -6

    Zoezi\(\PageIndex{193}\)

    \(\frac{15}{4-9}\)

    Zoezi\(\PageIndex{194}\)

    \(\frac{22-14}{19-13}\)

    Jibu

    \(\frac{4}{3}\)

    Zoezi\(\PageIndex{195}\)

    \(\frac{15+9}{18+12}\)

    Zoezi\(\PageIndex{196}\)

    \(\frac{5 \cdot 8}{-10}\)

    Jibu

    -4

    Zoezi\(\PageIndex{197}\)

    \(\frac{3 \cdot 4}{-24}\)

    Zoezi\(\PageIndex{198}\)

    \(\frac{15 \cdot 5-5^{2}}{2 \cdot 10}\)

    Jibu

    \(\frac{5}{2}\)

    Zoezi\(\PageIndex{199}\)

    \(\frac{12 \cdot 9-3^{2}}{3 \cdot 18}\)

    Zoezi\(\PageIndex{200}\)

    \(\frac{2+4(3)}{-3-2^{2}}\)

    Jibu

    -2

    Zoezi\(\PageIndex{201}\)

    \(\frac{7+3(5)}{-2-3^{2}}\)

    Tafsiri Maneno kwa Maneno na sehemu ndogo

    Katika mazoezi yafuatayo, tafsiri kila maneno ya Kiingereza katika kujieleza kwa algebraic.

    Zoezi\(\PageIndex{202}\)

    quotient ya c na jumla ya d na 9.

    Jibu

    \(\frac{c}{d+9}\)

    Zoezi\(\PageIndex{203}\)

    quotient ya tofauti ya h na k, na -5.

    Ongeza na Ondoa sehemu

    Ongeza na Ondoa sehemu ndogo na Denominator ya kawaida

    Katika mazoezi yafuatayo, ongeza.

    Zoezi\(\PageIndex{204}\)

    \(\frac{4}{9}+\frac{1}{9}\)

    Jibu

    \(\frac{5}{9}\)

    Zoezi\(\PageIndex{205}\)

    \(\frac{2}{9}+\frac{5}{9}\)

    Zoezi\(\PageIndex{206}\)

    \(\frac{y}{3}+\frac{2}{3}\)

    Jibu

    \(\frac{y+2}{3}\)

    Zoezi\(\PageIndex{207}\)

    \(\frac{7}{p}+\frac{9}{p}\)

    Zoezi\(\PageIndex{208}\)

    \(-\frac{1}{8}+\left(-\frac{3}{8}\right)\)

    Jibu

    \(-\frac{1}{2}\)

    Zoezi\(\PageIndex{209}\)

    \(-\frac{1}{8}+\left(-\frac{5}{8}\right)\)

    Katika mazoezi yafuatayo, toa.

    Zoezi\(\PageIndex{210}\)

    \(\frac{4}{5}-\frac{1}{5}\)

    Jibu

    \(\frac{3}{5}\)

    Zoezi\(\PageIndex{211}\)

    \(\frac{4}{5}-\frac{3}{5}\)

    Zoezi\(\PageIndex{212}\)

    \(\frac{y}{17}-\frac{9}{17}\)

    Jibu

    \(\frac{y-9}{17}\)

    Zoezi\(\PageIndex{213}\)

    \(\frac{x}{19}-\frac{8}{19}\)

    Zoezi\(\PageIndex{214}\)

    \(-\frac{8}{d}-\frac{3}{d}\)

    Jibu

    \(-\frac{11}{d}\)

    Zoezi\(\PageIndex{215}\)

    \(-\frac{7}{c}-\frac{7}{c}\)

    Ongeza au Ondoa sehemu na Denominators tofauti

    Katika mazoezi yafuatayo, ongeza au uondoe.

    Zoezi\(\PageIndex{216}\)

    \(\frac{1}{3}+\frac{1}{5}\)

    Jibu

    \(\frac{8}{15}\)

    Zoezi\(\PageIndex{217}\)

    \(\frac{1}{4}+\frac{1}{5}\)

    Zoezi\(\PageIndex{218}\)

    \(\frac{1}{5}-\left(-\frac{1}{10}\right)\)

    Jibu

    \(\frac{3}{10}\)

    Zoezi\(\PageIndex{219}\)

    \(\frac{1}{2}-\left(-\frac{1}{6}\right)\)

    Zoezi\(\PageIndex{220}\)

    \(\frac{2}{3}+\frac{3}{4}\)

    Jibu

    \(\frac{17}{12}\)

    Zoezi\(\PageIndex{221}\)

    \(\frac{3}{4}+\frac{2}{5}\)

    Zoezi\(\PageIndex{222}\)

    \(\frac{11}{12}-\frac{3}{8}\)

    Jibu

    \(\frac{13}{24}\)

    Zoezi\(\PageIndex{223}\)

    \(\frac{5}{8}-\frac{7}{12}\)

    Zoezi\(\PageIndex{224}\)

    \(-\frac{9}{16}-\left(-\frac{4}{5}\right)\)

    Jibu

    \(\frac{19}{80}\)

    Zoezi\(\PageIndex{225}\)

    \(-\frac{7}{20}-\left(-\frac{5}{8}\right)\)

    Zoezi\(\PageIndex{226}\)

    \(1+\frac{5}{6}\)

    Jibu

    \(\frac{11}{6}\)

    Zoezi\(\PageIndex{227}\)

    \(1-\frac{5}{9}\)

    Tumia Utaratibu wa Uendeshaji ili kurahisisha sehemu ndogo

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{228}\)

    \(\frac{\left(\frac{1}{5}\right)^{2}}{2+3^{2}}\)

    Jibu

    \(\frac{1}{275}\)

    Zoezi\(\PageIndex{229}\)

    \(\frac{\left(\frac{1}{3}\right)^{2}}{5+2^{2}}\)

    Zoezi\(\PageIndex{230}\)

    \(\frac{\frac{2}{3}+\frac{1}{2}}{\frac{3}{4}-\frac{2}{3}}\)

    Jibu

    14

    Zoezi\(\PageIndex{231}\)

    \(\frac{\frac{3}{4}+\frac{1}{2}}{\frac{5}{6}-\frac{2}{3}}\)

    Tathmini Maneno ya kutofautiana na FRACTIONS

    Katika mazoezi yafuatayo, tathmini.

    Zoezi\(\PageIndex{232}\)

    \(x+\frac{1}{2}\)lini

    1. \(x=-\frac{1}{8}\)
    2. \(x=-\frac{1}{2}\)
    Jibu
    1. \(\frac{3}{8}\)
    2. \(0\)
    Zoezi\(\PageIndex{233}\)

    \(x+\frac{2}{3}\)lini

    1. \(x=-\frac{1}{6}\)
    2. \(x=-\frac{5}{3}\)
    Zoezi\(\PageIndex{234}\)

    4\(p^{2} q\) wakati\(p=-\frac{1}{2}\) na\(q=\frac{5}{9}\)

    Jibu

    \(\frac{5}{9}\)

    Zoezi\(\PageIndex{235}\)

    5\(m^{2} n\) wakati\(m=-\frac{2}{5}\) na\(n=\frac{1}{3}\)

    Zoezi\(\PageIndex{236}\)

    \(\frac{u+v}{w}\)lini
    \(u=-4, v=-8, w=2\)

    Jibu

    -6

    Zoezi\(\PageIndex{237}\)

    \(\frac{m+n}{p}\)lini
    \(m=-6, n=-2, p=4\)

    Desimali

    Jina na Andika Decimals

    Katika mazoezi yafuatayo, andika kama decimal.

    Zoezi\(\PageIndex{238}\)

    Hundredths nane na tatu

    Jibu

    8.03

    Zoezi\(\PageIndex{239}\)

    Hundredths tisa na saba

    Zoezi\(\PageIndex{240}\)

    Elfu moja

    Jibu

    0.001

    Zoezi\(\PageIndex{241}\)

    Elfu tisa

    Katika mazoezi yafuatayo, jina la kila decimal.

    Zoezi\(\PageIndex{242}\)

    7.8

    Jibu

    kumi saba na nane

    Zoezi\(\PageIndex{243}\)

    5.01

    Zoezi\(\PageIndex{244}\)

    0.005

    Jibu

    elfu tano

    Zoezi\(\PageIndex{245}\)

    0.381

    Decimals pande zote

    Katika mazoezi yafuatayo, pande zote namba kwa karibu

    1. mia moja
    2. ya kumi
    3. idadi nzima.
    Zoezi\(\PageIndex{246}\)

    5.7932

    Jibu
    1. 5.79
    2. 5.8
    3. 6
    Zoezi\(\PageIndex{247}\)

    3.6284

    Zoezi\(\PageIndex{248}\)

    12.4768

    Jibu
    1. 12.48
    2. 12.5
    3. 12
    Zoezi\(\PageIndex{249}\)

    25.8449

    Kuongeza na Ondoa Decimals

    Katika mazoezi yafuatayo, ongeza au uondoe.

    Zoezi\(\PageIndex{250}\)

    18.37+9.36

    Jibu

    27.73

    Zoezi\(\PageIndex{251}\)

    256.37-85.49

    Zoezi\(\PageIndex{252}\)

    15.35-20.88

    Jibu

    -5.53

    Zoezi\(\PageIndex{253}\)

    37.5+12.23

    Zoezi\(\PageIndex{254}\)

    -4.2+ (-9.3)

    Jibu

    -13.5

    Zoezi\(\PageIndex{255}\)

    -8.6+ (-8.6)

    Zoezi\(\PageIndex{256}\)

    100-64.2

    Jibu

    35.8

    Zoezi\(\PageIndex{257}\)

    100-65.83

    Zoezi\(\PageIndex{258}\)

    2.51+40

    Jibu

    42.51

    Zoezi\(\PageIndex{259}\)

    9.38+60

    Kuzidisha na Gawanya Decimals

    Katika mazoezi yafuatayo, ongeze.

    Zoezi\(\PageIndex{260}\)

    (0.3) (0.4)

    Jibu

    0.12

    Zoezi\(\PageIndex{261}\)

    (0.6) (0.7)

    Zoezi\(\PageIndex{262}\)

    (8.52) (3.14)

    Jibu

    26.7528

    Zoezi\(\PageIndex{263}\)

    (5.32) (4.86)

    Zoezi\(\PageIndex{264}\)

    (0.09) (24.78)

    Jibu

    2.2302

    Zoezi\(\PageIndex{265}\)

    (0.04) (36.89)

    Katika mazoezi yafuatayo, ugawanye.

    Zoezi\(\PageIndex{266}\)

    \(0.15 \div 5\)

    Jibu

    0.03

    Zoezi\(\PageIndex{267}\)

    \(0.27 \div 3\)

    Zoezi\(\PageIndex{268}\)

    \(\$ 8.49 \div 12\)

    Jibu

    $0.71

    Zoezi\(\PageIndex{269}\)

    \(\$ 16.99 \div 9\)

    Zoezi\(\PageIndex{270}\)

    \(12 \div 0.08\)

    Jibu

    150

    Zoezi\(\PageIndex{271}\)

    \(5 \div 0.04\)

    Badilisha Decimals, Fractions, na asilimia

    Katika mazoezi yafuatayo, andika kila decimal kama sehemu.

    Zoezi\(\PageIndex{272}\)

    0.08

    Jibu

    \(\frac{2}{25}\)

    Zoezi\(\PageIndex{273}\)

    0.17

    Zoezi\(\PageIndex{274}\)

    0.425

    Jibu

    \(\frac{17}{40}\)

    Zoezi\(\PageIndex{275}\)

    0.184

    Zoezi\(\PageIndex{276}\)

    1.75

    Jibu

    \(\frac{7}{4}\)

    Zoezi\(\PageIndex{277}\)

    0.035

    Katika mazoezi yafuatayo, kubadilisha kila sehemu kwa decimal.

    Zoezi\(\PageIndex{278}\)

    \(\frac{2}{5}\)

    Jibu

    0.4

    Zoezi\(\PageIndex{279}\)

    \(\frac{4}{5}\)

    Zoezi\(\PageIndex{280}\)

    \(-\frac{3}{8}\)

    Jibu

    -0.375

    Zoezi\(\PageIndex{281}\)

    \(-\frac{5}{8}\)

    Zoezi\(\PageIndex{282}\)

    \(\frac{5}{9}\)

    Jibu

    \(0 . \overline{5}\)

    Zoezi\(\PageIndex{283}\)

    \(\frac{2}{9}\)

    Zoezi\(\PageIndex{284}\)

    \(\frac{1}{2}+6.5\)

    Jibu

    7

    Zoezi\(\PageIndex{285}\)

    \(\frac{1}{4}+10.75\)

    Katika mazoezi yafuatayo, kubadilisha kila asilimia kwa decimal.

    Zoezi\(\PageIndex{286}\)

    5%

    Jibu

    0.05

    Zoezi\(\PageIndex{287}\)

    9%

    Zoezi\(\PageIndex{288}\)

    40%

    Jibu

    0.4

    Zoezi\(\PageIndex{289}\)

    50%

    Zoezi\(\PageIndex{290}\)

    115%

    Jibu

    1.15

    Zoezi\(\PageIndex{291}\)

    125%

    Katika mazoezi yafuatayo, kubadilisha kila decimal kwa asilimia.

    Zoezi\(\PageIndex{292}\)

    0.18

    Jibu

    18%

    Zoezi\(\PageIndex{293}\)

    0.15

    Zoezi\(\PageIndex{294}\)

    0.009

    Jibu

    0.9%

    Zoezi\(\PageIndex{295}\)

    0.008

    Zoezi\(\PageIndex{296}\)

    1.5

    Jibu

    150%

    Zoezi\(\PageIndex{297}\)

    2.2

    Hesabu halisi

    Rahisisha maneno na Mizizi ya Mraba

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{298}\)

    \(\sqrt{64}\)

    Jibu

    8

    Zoezi\(\PageIndex{299}\)

    \(\sqrt{144}\)

    Zoezi\(\PageIndex{300}\)

    \(-\sqrt{25}\)

    Jibu

    -5

    Zoezi\(\PageIndex{301}\)

    \(-\sqrt{81}\)

    Tambua Integers, Hesabu za busara, Hesabu zisizofaa, na Hesabu halisi

    Katika mazoezi yafuatayo, andika kama uwiano wa integers mbili.

    Zoezi\(\PageIndex{302}\)
    1. 9
    2. 8.47
    Jibu
    1. \(\frac{9}{1}\)
    2. \(\frac{847}{100}\)
    Zoezi\(\PageIndex{303}\)
    1. -15
    2. 3.591

    Katika mazoezi yafuatayo, orodha

    1. idadi ya busara,
    2. idadi irrational.
    Zoezi\(\PageIndex{304}\)

    \(0.84,0.79132 \ldots, 1 . \overline{3}\)

    Jibu
    1. \(0.84,1.3\)
    2. \(0.79132 \ldots\)
    Zoezi\(\PageIndex{305}\)

    \(2.3 \overline{8}, 0.572,4.93814 \ldots\)

    Katika mazoezi yafuatayo, tambua kama kila nambari ni ya busara au isiyo ya maana.

    Zoezi\(\PageIndex{306}\)
    1. \(\sqrt{121}\)
    2. \(\sqrt{48}\)
    Jibu
    1. busara
    2. isiyo na maana
    Zoezi\(\PageIndex{307}\)
    1. \(\sqrt{56}\)
    2. \(\sqrt{16}\)

    Katika mazoezi yafuatayo, tambua kama kila namba ni namba halisi au si namba halisi.

    Zoezi\(\PageIndex{308}\)
    1. \(\sqrt{-9}\)
    2. \(-\sqrt{169}\)
    Jibu
    1. si idadi halisi
    2. nambari halisi
    Zoezi\(\PageIndex{309}\)
    1. \(\sqrt{-64}\)
    2. \(-\sqrt{81}\)

    Katika mazoezi yafuatayo, orodha

    1. idadi nzima,
    2. integers,
    3. idadi ya busara,
    4. nambari zisizo na maana,
    5. idadi halisi kwa kila seti ya idadi.
    Zoezi\(\PageIndex{310}\)

    \(-4,0, \frac{5}{6}, \sqrt{16}, \sqrt{18}, 5.2537 \ldots\)

    Jibu
    1. \(0, \sqrt{16}\)
    2. \(-4,0, \sqrt{16}\)
    3. \(-4,0, \frac{5}{6}, \sqrt{16}\)
    4. \(\sqrt{18}, 5.2537 \ldots\)
    5. \(-4,0, \frac{5}{6}, \sqrt{16}, \sqrt{18}, 5.2537 \ldots\)
    Zoezi\(\PageIndex{311}\)

    \(-\sqrt{4}, 0 . \overline{36}, \frac{13}{3}, 6.9152 \ldots, \sqrt{48}, 10 \frac{1}{2}\)

    Pata sehemu ndogo kwenye Mstari wa Idadi

    Katika mazoezi yafuatayo, Pata namba kwenye mstari wa nambari.

    Zoezi\(\PageIndex{312}\)

    \(\frac{2}{3}, \frac{5}{4}, \frac{12}{5}\)

    Jibu

    Takwimu hii ni mstari wa nambari unaoanzia 0 hadi 6 na alama za alama kwa kila integer. Theluthi 2, nne za 5, na tano za 12 zimepangwa.

    Zoezi\(\PageIndex{313}\)

    \(\frac{1}{3}, \frac{7}{4}, \frac{13}{5}\)

    Zoezi\(\PageIndex{314}\)

    \(2 \frac{1}{3},-2 \frac{1}{3}\)

    Jibu

    Takwimu hii ni mstari wa namba kuanzia hasi 4 hadi 4 na alama za kupe kwa kila integer. Hasi 2 na 1 ya tatu, na 2 na 1 ya tatu ni njama.

    Zoezi\(\PageIndex{315}\)

    \(1 \frac{3}{5},-1 \frac{3}{5}\)

    Katika mazoezi yafuatayo, tengeneza kila jozi zifuatazo za namba, ukitumia < or >.

    Zoezi\(\PageIndex{316}\)

    -1___\(-\frac{1}{8}\)

    Jibu

    <

    Zoezi\(\PageIndex{317}\)

    \(-3 \frac{1}{4}\)___-4

    Zoezi\(\PageIndex{318}\)

    \(-\frac{7}{9}\)___\(\frac{4}{9}\)

    Jibu

    >

    Zoezi\(\PageIndex{319}\)

    \(-2\)___\(\frac{19}{8}\)

    Pata Decimals kwenye Mstari wa Idadi

    Katika mazoezi yafuatayo, tafuta kwenye mstari wa nambari.

    Zoezi\(\PageIndex{320}\)

    0.3

    Jibu

    Takwimu hii ni mstari wa namba kuanzia 0 hadi 1 na alama za alama kwa kila kumi ya integer. 0.3 imepangwa.

    Zoezi\(\PageIndex{321}\)

    -0.2

    Zoezi\(\PageIndex{322}\)

    -2.5

    Jibu

    Takwimu hii ni mstari wa namba kuanzia hasi 5 hadi 5 na alama za kupe kwa kila integer. Hasi 2.5 imepangwa.

    Zoezi\(\PageIndex{323}\)

    2.7

    Katika mazoezi yafuatayo, tengeneza kila jozi zifuatazo za namba, ukitumia < or >.

    Zoezi\(\PageIndex{324}\)

    0.9___0.6

    Jibu

    >

    Zoezi\(\PageIndex{325}\)

    0.7___0.8

    Zoezi\(\PageIndex{326}\)

    -0.6___-0.59

    Jibu

    >

    Zoezi\(\PageIndex{327}\)

    -0.27___-0.3

    Mali ya Hesabu halisi

    Tumia Mali za Comutative na Associative

    Katika mazoezi yafuatayo, tumia Mali ya Associative ili kurahisisha.

    Zoezi\(\PageIndex{328}\)

    -12 (4m)

    Jibu

    -48m

    Zoezi\(\PageIndex{329}\)

    30\(\left(\frac{5}{6} q\right)\)

    Zoezi\(\PageIndex{330}\)

    (a+16) +31

    Jibu

    a+47

    Zoezi\(\PageIndex{331}\)

    (c+0.2) +0.7

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{332}\)

    6y+37+ (-6y)

    Jibu

    37

    Zoezi\(\PageIndex{333}\)

    \(\frac{1}{4}+\frac{11}{15}+\left(-\frac{1}{4}\right)\)

    Zoezi\(\PageIndex{334}\)

    \(\frac{14}{11} \cdot \frac{35}{9} \cdot \frac{14}{11}\)

    Jibu

    \(\frac{35}{9}\)

    Zoezi\(\PageIndex{335}\)

    \(-18 \cdot 15 \cdot \frac{2}{9}\)

    Zoezi\(\PageIndex{336}\)

    \(\left(\frac{7}{12}+\frac{4}{5}\right)+\frac{1}{5}\)

    Jibu

    1\(\frac{7}{12}\)

    Zoezi\(\PageIndex{337}\)

    (3.98d+0.75d) +1.25d

    Zoezi\(\PageIndex{338}\)

    11x+8y+16x+15y

    Jibu

    27x+23y

    Zoezi\(\PageIndex{339}\)

    52m+ (-20n) + (-18m) + (-5n)

    Tumia Utambulisho na Mali ya Inverse ya Kuongeza na Kuzidisha

    Katika mazoezi yafuatayo, tafuta inverse ya nyongeza ya kila nambari.

    Zoezi\(\PageIndex{340}\)
    1. \(\frac{1}{3}\)
    2. 5.1
    3. \(-14\)
    4. \(-\frac{8}{5}\)
    Jibu
    1. \(-\frac{1}{3}\)
    2. \(-5.1\)
    3. -14
    4. \(-\frac{8}{5}\)
    Zoezi\(\PageIndex{341}\)
    1. \(-\frac{7}{8}\)
    2. \(-0.03\)
    3. 17
    4. \(\frac{12}{5}\)

    Katika mazoezi yafuatayo, tafuta inverse ya kuzidisha ya kila nambari.

    Zoezi\(\PageIndex{342}\)
    1. \(10\)
    2. \(-\frac{4}{9}\)
    3. 0.6
    Jibu
    1. \(\frac{1}{10}\)
    2. \(-\frac{9}{4}\)
    3. \(\frac{5}{3}\)
    Zoezi\(\PageIndex{343}\)
    1. \(-\frac{9}{2}\)
    2. -7
    3. 2.1

    Tumia Mali ya Zero

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{344}\)

    83\(\cdot 0\)

    Jibu

    0

    Zoezi\(\PageIndex{345}\)

    \(\frac{0}{9}\)

    Zoezi\(\PageIndex{346}\)

    \(\frac{5}{0}\)

    Jibu

    haijafafanuliwa

    Zoezi\(\PageIndex{347}\)

    \(0 \div \frac{2}{3}\)

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{348}\)

    43+39+ (-43)

    Jibu

    39

    Zoezi\(\PageIndex{349}\)

    (n+6.75) +0.25

    Zoezi\(\PageIndex{350}\)

    \(\frac{5}{13} \cdot 57 \cdot \frac{13}{5}\)

    Jibu

    57

    Zoezi\(\PageIndex{351}\)

    \(\frac{1}{6} \cdot 17 \cdot 12\)

    Zoezi\(\PageIndex{352}\)

    \(\frac{2}{3} \cdot 28 \cdot \frac{3}{7}\)

    Jibu

    8

    Zoezi\(\PageIndex{353}\)

    \(9(6 x-11)+15\)

    Rahisisha Maneno Kutumia Mali ya Kusambaza

    Katika mazoezi yafuatayo, kurahisisha kutumia Mali ya Usambazaji.

    Zoezi\(\PageIndex{354}\)

    7 (x+9)

    Jibu

    7x+63

    Zoezi\(\PageIndex{355}\)

    9 (u-4)

    Zoezi\(\PageIndex{356}\)

    —3 (6m-1)

    Jibu

    -18m+3

    Zoezi\(\PageIndex{357}\)

    -8 (-7a—12)

    Zoezi\(\PageIndex{358}\)

    \(\frac{1}{3}(15 n-6)\)

    Jibu

    5n-2

    Zoezi\(\PageIndex{359}\)

    \((y+10) \cdot p\)

    Zoezi\(\PageIndex{360}\)

    (a-4) - (6a+9)

    Jibu

    -5a—13

    Zoezi\(\PageIndex{361}\)

    4 (x+3) -8 (x-7)

    Mifumo ya Upimaji

    1.1 Eleza Units za Upimaji wa Marekani na Kubadilisha kutoka Kitengo kimoja hadi Kingine

    Katika mazoezi yafuatayo, kubadilisha vitengo. Pande zote hadi kumi ya karibu.

    Zoezi\(\PageIndex{362}\)

    Arbor ya maua ni urefu wa miguu 7. Badilisha urefu kwa inchi.

    Jibu

    84 inchi

    Zoezi\(\PageIndex{363}\)

    Muundo wa picha ni upana wa inchi 42. Badilisha upana kwa miguu.

    Zoezi\(\PageIndex{364}\)

    Kelly ni 5 futi 4 inches mrefu. Kubadili urefu wake kwa inchi.

    Jibu

    64 inches

    Zoezi\(\PageIndex{365}\)

    Uwanja wa michezo ni upana wa futi 45. Badilisha upana kwa yadi.

    Zoezi\(\PageIndex{366}\)

    Urefu wa Mlima Shasta ni futi 14,179. Badilisha urefu hadi maili.

    Jibu

    maili 2.7

    Zoezi\(\PageIndex{367}\)

    Shamu ina uzito wa tani 4.5. Badilisha uzito kwa paundi.

    Zoezi\(\PageIndex{368}\)

    kucheza ilidumu\(1\frac{3}{4}\) masaa. Badilisha muda hadi dakika.

    Jibu

    Dakika 105

    Zoezi\(\PageIndex{369}\)

    Vijiko ngapi viko katika quart?

    Zoezi\(\PageIndex{370}\)

    Mtoto wa Naomi alikuwa na uzito wa paundi 5 14 ounces wakati wa kuzaliwa. Badilisha uzito kwa ounces.

    Jibu

    94 ounsi

    Zoezi\(\PageIndex{371}\)

    Trinh anahitaji vikombe 30 vya rangi kwa ajili ya mradi wake wa sanaa ya darasa. Badilisha kiasi kwa galoni.

    Tumia Units Mchanganyiko wa Upimaji katika mfumo wa Marekani.

    Katika mazoezi yafuatayo, tatua.

    Zoezi\(\PageIndex{372}\)

    John hawakupata lobsters 4. Uzito wa lobsters ulikuwa 1 pound 9 ounces, 1 pound 12 ounces, paundi 4 2 ounces, na paundi 2 ounces 15. Uzito wa jumla wa lobsters ulikuwa nini?

    Jibu

    10 lbs. 6 oz.

    Zoezi\(\PageIndex{373}\)

    Kila siku wiki iliyopita Pedro aliandika idadi ya dakika alizozitumia kusoma. Idadi ya dakika ilikuwa 50, 25, 83, 45, 32, 60, 135. Pedro alitumia masaa ngapi kusoma?

    Zoezi\(\PageIndex{374}\)

    Fouad ni 6 futi 2 inches mrefu. Kama yeye anasimama juu ya rung ya ngazi 8 futi 10 inchi juu, jinsi ya juu mbali ya ardhi ni juu ya kichwa Fouad?

    Jibu

    Futi 15

    Zoezi\(\PageIndex{375}\)

    Dalila anataka kufanya kutupa mto inashughulikia. Kila kifuniko kinachukua inchi 30 za kitambaa. Anahitaji yadi ngapi za kitambaa kwa vifuniko 4?

    Fanya Waongofu Kitengo katika Mfumo wa Metric

    Katika mazoezi yafuatayo, kubadilisha vitengo.

    Zoezi\(\PageIndex{376}\)

    Donna ni urefu wa mita 1.7. Badilisha urefu wake kwa sentimita.

    Jibu

    Sentimita 170

    Zoezi\(\PageIndex{377}\)

    Mlima Everest una urefu wa mita 8,850. Badilisha urefu hadi kilomita.

    Zoezi\(\PageIndex{378}\)

    Kikombe kimoja cha mtindi kina miligramu 488 za kalsiamu. Badilisha hii kwa gramu.

    Jibu

    0.488 gramu

    Zoezi\(\PageIndex{379}\)

    Kikombe kimoja cha mtindi kina gramu 13 za protini. Badilisha hii kwa miligramu.

    Zoezi\(\PageIndex{380}\)

    Sergio alikuwa na uzito wa kilo 2.9 wakati wa kuzaliwa. Badilisha hii kwa gramu.

    Jibu

    2,900 gramu

    Zoezi\(\PageIndex{381}\)

    Chupa ya maji ilikuwa na mililita 650. Badilisha hii kwa lita.

    Tumia Vipimo vya Mchanganyiko wa Kipimo katika Mfumo wa Metriki

    Katika mazoezi yafuatayo, tatua.

    Zoezi\(\PageIndex{382}\)

    Minh ni urefu wa mita 2. Binti yake ni urefu wa sentimita 88. Minh ni mrefu zaidi kuliko binti yake?

    Jibu

    1.12 mita

    Zoezi\(\PageIndex{383}\)

    Selma alikuwa na chupa ya lita 1 ya maji. Ikiwa alinywa mililita 145, ni kiasi gani cha maji kilichoachwa katika chupa?

    Zoezi\(\PageIndex{384}\)

    Huduma moja ya juisi ya cranberry ina gramu 30 za sukari. Ni kilo ngapi za sukari ziko katika huduma 30 za juisi ya cranberry?

    Jibu

    0.9 kilo

    Zoezi\(\PageIndex{385}\)

    Ounce moja ya tofu ilitoa gramu 2 za protini. Ni miligramu ngapi za protini zinazotolewa na ounces 5 za tofu?

    Badilisha kati ya Marekani na Mifumo ya Metric ya Upimaji

    Katika mazoezi yafuatayo, fanya mabadiliko ya kitengo. Pande zote hadi kumi ya karibu.

    Zoezi\(\PageIndex{386}\)

    Majid ni urefu wa inchi 69. Badilisha urefu wake hadi sentimita.

    Jibu

    175.3 sentimita

    Zoezi\(\PageIndex{387}\)

    Mahakama ya mpira wa kikapu ya chuo ni urefu wa miguu 84. Badilisha urefu huu kwa mita.

    Zoezi\(\PageIndex{388}\)

    Caroline alitembea kilomita 2.5. Badilisha urefu huu kwa maili.

    Jibu

    1.6 maili

    Zoezi\(\PageIndex{389}\)

    Lucas ina uzito wa kilo 78. Kubadilisha uzito wake kwa paundi.

    Zoezi\(\PageIndex{390}\)

    Gari la Steve lina lita 55 za gesi. Badilisha hii kwa galoni.

    Jibu

    14.6 galoni

    Zoezi\(\PageIndex{391}\)

    Sanduku la vitabu lina uzito wa paundi 25. Badilisha uzito kwa kilo.

    Badilisha kati ya joto la Fahrenheit na Celsius

    Katika mazoezi yafuatayo, kubadilisha joto la Fahrenheit kwa digrii Celsius. Pande zote hadi kumi ya karibu.

    Zoezi\(\PageIndex{392}\)

    95° Fahrenheit

    Jibu

    35° C

    Zoezi\(\PageIndex{393}\)

    23° Fahrenheit

    Zoezi\(\PageIndex{394}\)

    20° Fahrenheit

    Jibu

    —6.7° C

    Zoezi\(\PageIndex{395}\)

    64° Fahrenheit

    Katika mazoezi yafuatayo, kubadilisha joto la Celsius kwa digrii Fahrenheit. Pande zote hadi kumi ya karibu.

    Zoezi\(\PageIndex{396}\)

    30° Celsius

    Jibu

    86° YA

    Zoezi\(\PageIndex{397}\)

    —5° Celsius

    Zoezi\(\PageIndex{398}\)

    —12° Celsius

    Jibu

    10.4° YA

    Zoezi\(\PageIndex{399}\)

    24° Celsius

    Sura ya Mazoezi mtihani

    Zoezi\(\PageIndex{1}\)

    Andika kama namba nzima kwa kutumia tarakimu: mia mbili elfu tano, mia sita kumi na saba.

    Jibu

    205,617

    Zoezi\(\PageIndex{2}\)

    Kupata factorization mkuu wa 504.

    Zoezi\(\PageIndex{3}\)

    Kupata angalau kawaida nyingi ya 18 na 24.

    Jibu

    72

    Zoezi\(\PageIndex{4}\)

    Kuchanganya kama maneno: 5n+8+2n-1.

    Katika mazoezi yafuatayo, tathmini.

    Zoezi\(\PageIndex{5}\)

    \(-|x|\)lini\(x=-2\)

    Jibu

    -2

    Zoezi\(\PageIndex{6}\)

    11—a wakati =—3

    Zoezi\(\PageIndex{7}\)

    Tafsiri kwa kujieleza kwa algebraic na kurahisisha: ishirini chini ya hasi 7.

    Jibu

    -7—20; -27

    Zoezi\(\PageIndex{8}\)

    Monique ana usawa wa -$18 katika akaunti yake ya kuangalia. Yeye amana $152 kwa akaunti. Usawa mpya ni nini?

    Zoezi\(\PageIndex{9}\)

    Pande zote 677.1348 kwa karibu mia moja.

    Jibu

    677.13

    Zoezi\(\PageIndex{10}\)

    Badilisha\(\frac{4}{5}\) hadi decimal.

    Zoezi\(\PageIndex{11}\)

    Badilisha 1.85 kwa asilimia.

    Jibu

    185%

    Zoezi\(\PageIndex{12}\)

    Pata\(\frac{2}{3},-1.5,\) na\(\frac{9}{4}\) kwenye mstari wa nambari.

    Katika mazoezi yafuatayo, kurahisisha kila kujieleza.

    Zoezi\(\PageIndex{13}\)

    \(4+10(3+9)-5^{2}\)

    Jibu

    99

    Zoezi\(\PageIndex{14}\)

    -85+42

    Zoezi\(\PageIndex{15}\)

    -19-25

    Jibu

    -44

    Zoezi\(\PageIndex{16}\)

    \((-2)^{4}\)

    Zoezi\(\PageIndex{17}\)

    \(-5(-9) \div 15\)

    Jibu

    3

    Zoezi\(\PageIndex{18}\)

    \(\frac{3}{8} \cdot \frac{11}{12}\)

    Zoezi\(\PageIndex{19}\)

    \(\frac{4}{5} \div \frac{9}{20}\)

    Jibu

    \(\frac{16}{9}\)

    Zoezi\(\PageIndex{20}\)

    \(\frac{12+3 \cdot 5}{15-6}\)

    Zoezi\(\PageIndex{21}\)

    \(\frac{m}{7}+\frac{10}{7}\)

    Jibu

    \(\frac{m+10}{7}\)

    Zoezi\(\PageIndex{22}\)

    \(\frac{7}{12}-\frac{3}{8}\)

    Zoezi\(\PageIndex{23}\)

    \(-5.8+(-4.7)\)

    Jibu

    -10.5

    Zoezi\(\PageIndex{24}\)

    100-64.25

    Zoezi\(\PageIndex{25}\)

    (0.07) (31.95)

    Jibu

    2.2365

    Zoezi\(\PageIndex{26}\)

    \(9 \div 0.05\)

    Zoezi\(\PageIndex{27}\)

    \(-14\left(\frac{5}{7} p\right)\)

    Jibu

    -10p

    Zoezi\(\PageIndex{28}\)

    (u+8) -9

    Zoezi\(\PageIndex{29}\)

    6x+ (-4y) +9x+8y

    Jibu

    15x+4y

    Zoezi\(\PageIndex{30}\)

    \(\frac{0}{23}\)

    Zoezi\(\PageIndex{31}\)

    \(\frac{75}{0}\)

    Jibu

    haijafafanuliwa

    Zoezi\(\PageIndex{32}\)

    -2 (13q-5)

    Zoezi\(\PageIndex{33}\)

    Filamu ilidumu\(\frac{2}{3}\) saa 1. Je! Dakika ngapi ilidumu? (\(=60\)Dakika ya saa 1)

    Jibu

    Dakika 100

    Zoezi\(\PageIndex{34}\)

    SUV Mike ni 5 futi 11 inches mrefu. Anataka kuweka mfuko wa mizigo ya dari kwenye SUV. Mfuko wa mizigo ni mguu 1 urefu wa inchi 6. Urefu wa jumla utakuwa wa SUV na mfuko wa mizigo juu ya paa? (Mguu 1 = inchi 12)

    Zoezi\(\PageIndex{35}\)

    Jennifer mbio 2.8 maili. Badilisha urefu huu hadi kilomita. (1 maili = 1.61 kilomita)

    Jibu

    4.508 km