1.10E: Mazoezi

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Mazoezi hufanya kamili

Tumia Mali za Comutative na Associative

Katika mazoezi yafuatayo, tumia mali ya ushirika ili kurahisisha.

Zoezi 1

$3(4x)$

Jibu: $12x$

Zoezi la 2

$4(7m)$

Zoezi la 3

$(y+12)+28$

Jibu: $y+40$

Zoezi la 4

$(n+17)+33$

Katika mazoezi yafuatayo, kurahisisha.

Zoezi 5

$\frac{1}{2}+\frac{7}{8}+\left(-\frac{1}{2}\right)$

Jibu: $\frac{7}{8}$

Zoezi la 6

$\frac{2}{5}+\frac{5}{12}+\left(-\frac{2}{5}\right)$

Zoezi la 7

$\frac{3}{20} \cdot \frac{49}{11} \cdot \frac{20}{3}$

Jibu: $\frac{49}{11}$

Zoezi la 8

$\frac{13}{18} \cdot \frac{25}{7} \cdot \frac{18}{13}$

Zoezi la 9

$-24 \cdot 7 \cdot \frac{3}{8}$

Jibu: $-63$

Zoezi la 10

$-36 \cdot 11 \cdot \frac{4}{9}$

Zoezi 11

$\left(\frac{5}{6}+\frac{8}{15}\right)+\frac{7}{15}$

Jibu: $1 \frac{5}{6}$

Zoezi 12

$\left(\frac{11}{12}+\frac{4}{9}\right)+\frac{5}{9}$

Zoezi 13

$17(0.25)(4)$

Jibu: $17$

Zoezi 14

$36(0.2)(5)$

Zoezi 15

$[2.48(12)](0.5)$

Jibu: $14.88$

Zoezi 16

$[9.731(4)](0.75)$

Zoezi 17

$7(4a)$

Jibu: $28a$

Zoezi 18

$9(8w)$

Zoezi la 19

$-15(5m)$

Jibu: $-75m$

Zoezi la 20

$-23(2n)$

Zoezi 21

$12(\frac{5}{6}p)$

Jibu: $10p$

Zoezi la 22

$20(\frac{3}{5}q)$

Zoezi 23

$43 m+(-12 n)+(-16 m)+(-9 n)$

Jibu: $27m+(-21n)$

Zoezi 24

$-22p+17q+(-35p)+(-27q)$

Zoezi 25

$\frac{3}{8} g+\frac{1}{12} h+\frac{7}{8} g+\frac{5}{12} h$

Jibu: $\frac{5}{4}g+\frac{1}{2}h$

Zoezi 26

$\frac{5}{6} a+\frac{3}{10} b+\frac{1}{6} a+\frac{9}{10} b$

Zoezi 27

$6.8 p+9.14 q+(-4.37 p)+(-0.88 q)$

Jibu: $2.43p+8.26q$

Zoezi 28

$9.6 m+7.22 n+(-2.19 m)+(-0.65 n)$

Tumia Utambulisho na Mali ya Inverse ya Kuongeza na Kuzidisha

Katika mazoezi yafuatayo, tafuta inverse ya nyongeza ya kila nambari

Zoezi 29

$\frac{2}{5}$
$4.3$
$-8$
$-\frac{10}{3}$

Jibu

$-\frac{2}{5}$
$-4.3$
$8$
$\frac{10}{3}$

Zoezi 30

$\frac{5}{9}$
$2.1$
$-3$
$-\frac{9}{5}$

Zoezi 31

$-\frac{7}{6}$
$-0.075$
$23$
$\frac{1}{4}$

Jibu

$\frac{7}{6}$
$0.075$
$-23$
$-\frac{1}{4}$

Zoezi 32

$-\frac{8}{3}$
$-0.019$
$52$
$\frac{5}{6}$

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

Zoezi la 33

$6$
$-\frac{3}{4}$
$0.7$

Jibu

$\frac{1}{6}$
$-\frac{4}{3}$
$\frac{10}{7}$

Zoezi 34

$12$
$-\frac{9}{2}$
$0.13$

Zoezi 35

$\frac{11}{12}$
$-1.1$
$-4$

Jibu

$\frac{12}{11}$
$-\frac{10}{11}$
$-\frac{1}{4}$

Zoezi 36

$\frac{17}{20}$
$-1.5$
$-3$

Tumia Mali ya Zero

Katika mazoezi yafuatayo, kurahisisha.

Zoezi 37

$\frac{0}{6}$

Jibu: $0$

Zoezi 38

$\frac{3}{0}$

Zoezi 39

$0 \div \frac{11}{12}$

Jibu: $0$

Zoezi 40

$\frac{6}{0}$

Zoezi 41

$\frac{0}{3}$

Jibu: $0$

Zoezi 42

$0 \cdot \frac{8}{15}$

Zoezi 43

$(-3.14)(0)$

Jibu: $0$

Zoezi 44

$\frac{\frac{1}{10}}{0}$

Mazoezi ya mchanganyiko

Katika mazoezi yafuatayo, kurahisisha.

Zoezi 45

$19 a+44-19 a$

Jibu: $44$

Zoezi 46

$27 c+16-27 c$

Zoezi 47

$10(0.1 d)$

Jibu: $1d$

Zoezi 48

$100(0.01 p)$

Zoezi 49

$\frac{0}{u-4.99}, \text { where } u \neq 4.99$

Jibu: $0$

Zoezi 50

$\frac{0}{v-65.1}, \text { where } v \neq 65.1$

Zoezi 51

$0 \div\left(x-\frac{1}{2}\right), \text { where } x \neq \frac{1}{2}$

Jibu: $0$

Zoezi 52

$0 \div\left(y-\frac{1}{6}\right), \text { where } y \neq \frac{1}{6}$

Zoezi 53

$\frac{32-5 a}{0}, \text { where } 32-5a \neq 0$

Jibu: haijafafanuliwa

Zoezi 54

$\frac{28-9 b}{0}, \text { where } 28-9b \neq 0$

Zoezi 55

$\left(\frac{3}{4}+\frac{9}{10} m\right) \div 0 \text { where } \frac{3}{4}+\frac{9}{10}m \neq 0$

Jibu: haijafafanuliwa

Zoezi 56

$\left(\frac{5}{16} n-\frac{3}{7}\right) \div 0 \text { where } \frac{5}{16} n-\frac{3}{7} \neq 0$

Zoezi 57

$15 \cdot \frac{3}{5}(4 d+10)$

Jibu: $36d+90$

Zoezi 58

$18 \cdot \frac{5}{6}(15 h+24)$

Rahisisha Maneno Kutumia Mali ya Kusambaza

Katika mazoezi yafuatayo, kurahisisha kutumia mali ya usambazaji.

Zoezi 59

$8(4 y+9)$

Jibu: $32y+72$

Zoezi 60

$9(3 w+7)$

Zoezi 61

$6(c-13)$

Jibu: $6c-78$

Zoezi 62

$7(y-13)$

Zoezi 63

$\frac{1}{4}(3 q+12)$

Jibu: $\frac{3}{4}q+3$

Zoezi 64

$\frac{1}{5}(4 m+20)$

Zoezi 65

$9\left(\frac{5}{9} y-\frac{1}{3}\right)$

Jibu: $5y-3$

Zoezi 66

$10\left(\frac{3}{10} x-\frac{2}{5}\right)$

Zoezi 67

$12\left(\frac{1}{4}+\frac{2}{3} r\right)$

Jibu: $3+8r$

Zoezi 68

$12\left(\frac{1}{6}+\frac{3}{4} s\right)$

Zoezi 69

$r(s-18)$

Jibu: $rs-18r$

Zoezi 70

$u(v-10)$

Zoezi 71

$(y+4) p$

Jibu: $yp+4p$

Zoezi 72

$(a+7) x$

Zoezi 73

$-7(4 p+1)$

Jibu: $-28p-7$

Zoezi 74

$-9(9 a+4)$

Zoezi 75

$-3(x-6)$

Jibu: $-3x+18$

Zoezi 76

$-4(q-7)$

Zoezi 77

$-(3 x-7)$

Jibu: $-3x+7$

Zoezi 78

$-(5 p-4)$

Zoezi 79

$16-3(y+8)$

Jibu: $-3y-8$

Zoezi 80

$18-4(x+2)$

Zoezi 81

$4-11(3 c-2)$

Jibu: $-33c+26$

Zoezi 82

$9-6(7 n-5)$

Zoezi 83

$22-(a+3)$

Jibu: $-a+19$

Zoezi 84

$8-(r-7)$

Zoezi 85

$(5 m-3)-(m+7)$

Jibu: $4m-10$

Zoezi 86

$(4 y-1)-(y-2)$

Zoezi 87

$5(2 n+9)+12(n-3)$

Jibu: $22n+9$

Zoezi 88

$9(5 u+8)+2(u-6)$

Zoezi 89

$9(8 x-3)-(-2)$

Jibu: $72x-25$

Zoezi 90

$4(6 x-1)-(-8)$

Zoezi 91

$14(c-1)-8(c-6)$

Jibu: $6c+34$

Zoezi 92

$11(n-7)-5(n-1)$

Zoezi 93

$6(7 y+8)-(30 y-15)$

Jibu: $12y+63$

Zoezi 94

$7(3 n+9)-(4 n-13)$

kila siku Math

Zoezi 95

Malipo ya bima Carrie alikuwa na kujaza 5 kufanyika. Kila kujaza gharama $80. Bima yake ya meno ilimhitaji kulipa asilimia 20 ya gharama kama nakala. Tumia nakala ya Carrie:

Kwanza, kwa kuzidisha 0.20 na 80 ili kupata copay yake kwa kila kujaza na kisha kuzidisha jibu lako kwa 5 ili kupata nakala yake ya jumla kwa kujaza 5.
Kisha, kwa kuzidisha [5 (0.20)] (80)
Ni ipi kati ya mali ya namba halisi inasema kuwa majibu yako kwa sehemu (a), ambapo uliongeza 5 [(0.20) (80)] na (b), ambapo uliongeza [5 (0.20)] (80), lazima iwe sawa?

Jibu

$80
$80
majibu yatatofautiana

Zoezi 96

Kupika wakati Helen kununuliwa 24-pauni Uturuki kwa ajili ya familia yake Shukrani chakula cha jioni na anataka kujua ni muda gani wa kuweka Uturuki katika tanuri. Anataka kuruhusu 20 dakika kwa pauni wakati kupikia. Tumia urefu wa muda unaohitajika kuchoma Uturuki:

Kwanza, kwa kuzidisha 24·20 kupata jumla ya idadi ya dakika na kisha kuzidisha jibu$\frac{1}{60}$ kwa kubadilisha dakika katika masaa.
Kisha, kwa kuzidisha$24(20 \cdot \frac{1}{60})$.
Ni ipi kati ya mali ya namba halisi inasema kwamba majibu yako kwa sehemu (a), ambapo uliongezeka$(24 \cdot 20) \frac{1}{60}$, na (b), ambako umeongezeka$24(20 \cdot \frac{1}{60})$, lazima iwe sawa?

Zoezi 97

Kununua kwa kesi Mfanyabiashara Joe maduka ya vyakula kuuzwa chupa ya mvinyo wao kuitwa “Mbili Buck Chuck” kwa $1.99. Waliuza kesi ya chupa 12 kwa $23.88. Ili kupata gharama ya chupa 12 kwa $1.99, angalia kuwa 1.99 ni 2,10.01.

Panua 12 (1.99) kwa kutumia mali ya usambazaji ili kuzidisha 12 (2—0.01).
Ilikuwa ni biashara ya kununua “Mbili Buck Chuck” na kesi?

Jibu

$23.88
Hapana, bei ni sawa

Zoezi 98

Multi-pakiti kununua shampoo Adele ya kuuza kwa $3.99 kwa chupa katika duka la vyakula. Katika duka la ghala, shampoo hiyo inauzwa kama pakiti ya 3 kwa $10.49. Ili kupata gharama ya chupa 3 kwa $3.99, angalia kuwa 3.99 ni 4—0.01.

Panua 3 (3.99) kwa kutumia mali ya usambazaji ili kuzidisha 3 (4—0.01).
Kiasi gani Adele ingeweza kuokoa kwa kununua chupa za 3 kwenye duka la ghala badala ya duka la vyakula?

Mazoezi ya kuandika

Zoezi 99

Kwa maneno yako mwenyewe, sema mali ya kubadilisha ya kuongeza.

Jibu: $Answers may vary$

Zoezi 100

Ni tofauti gani kati ya inverse ya kuongezea na inverse ya kuzidisha ya idadi?

Zoezi 101

Kurahisisha$8(x-\frac{1}{4})$ kutumia mali ya usambazaji na kuelezea kila hatua.

Jibu: $Answers may vary$

Zoezi 102

Eleza jinsi unavyoweza kuzidisha 4 ($5.97) bila karatasi au calculator kwa kufikiria $5.97 kama 6—0.03 na kisha kutumia mali ya kusambaza.

Self Check

ⓐ Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

$Hii ni meza ambayo ina safu tano na nguzo nne. Katika mstari wa kwanza, ambayo ni mstari wa kichwa, seli zinasoma kutoka kushoto kwenda kulia “Ninaweza...,” “Kwa ujasiri,” “Kwa msaada fulani,” na “Hakuna-Siipati!” Safu ya kwanza chini ya “naweza...” inasoma “tumia mali za kubadilisha na ushirika,” “tumia utambulisho na mali ya kinyume ya kuongeza na kuzidisha,” “tumia mali ya sifuri,” na “kurahisisha maneno kwa kutumia mali ya usambazaji.” Wengine wa seli ni tupu.$

ⓑ Baada ya kuchunguza orodha hii, utafanya nini ili uwe na ujasiri kwa malengo yote?