Bài luyện tập

a) 12.18 + 14.3 – 255:17

= 216 + 42 – 15

= 273 

b)  13 + 42.5 – (198:11 – 8)

= 13 + 210 – 10

= 213

c) 25.8 – 12.5 + 272:17 – 8

= 200 – 60 +16 – 8

= 148

d, $2^3-5^3:5^2+12.2^2$

= 8 – 5 +48

= 51

a, $5^3+\left(3^4+4\right).2+\left(27-3\right):4$

= 125+170+6

= 301

b, $124:\left[3^2.7-\left(1^{10}+24\right):5^2\right]$

= 124:[9.7–(1+24):25]

= 124 : [63–25:25]

= 124:62

= 2

c, $245-4\left[16:8+2\left(4.3^2-9\right)\right]$

= 245–4[2+2.27]

= 245–4.45

= 29

d, $375:5^3-\left(3^8:3^6-2.2^3\right)$

= 375 : 125 – (9–16)

= 3–9+16

= 10

a, $15.\{32:[6-5+5(9:3)]+3\}-{2018}^0$

= 15.{32:[1+15]+3}–1

= 15.5–1

= 74

b, $25.\{2^7:[12-4+2^2.\left(16:2^3\right)]-2^4\}$

= 25.{128:[8+4.2]–16}

= 25.24

= 600

c, $2019.\{101-1000:[\left(2^2.2^3+5^6:5^3-6^2\right):11-{2018}^0\left]\right\}$

= 2019.{101–1000:[(32+125–36):11–1]}

= 2019.{101–1000:[121:11–1]}

= 2019.{101–1000:10}

= 2019.1

= 2019

a, 5(x – 7) = 0

x – 7 = 0

x = 7

b, 95 – 5(x+2) = 45

5(x+2) = 40

x+2 = 8

x = 6

c, $6\left(2x+2^3\right)+40=100$

6(2x+8) = 60

2x+8 = 10

x = 1

d, 3(3x+9)+6 = 96

3(3x+9) = 90

3x+9 = 30

3x = 27

x = 9

e, $2^6+\left(5+x\right)=3^4$

5+x = 81–64

5+x = 17

x = 12

a, $10x+2^2.5={10}^2$

10x = 100–20

10x = 80

x = 8

b, $5^2+\left(15-x\right)=30$

15–x = 5

x = 10

c, $2^2.5^2-\left(25+x\right)=40$

100–(25+x) = 40

25+x = 60

x = 35

d, $7^{2}x-6^{2}x=13.2^3-26$

49x–36x = 104–26

13x = 78

x = 6

a, $2^{3}x+5^{2}x=2\left(5^2+2^3\right)-33$

8x+25x = 33

33x = 33

x = 1

b, $260:\left(x+4\right)=5\left(2^3+5\right)-3\left(3^2+2^2\right)$

260:(x+4) = 5.13–3.13

x+4 = 260:26

x+4 = 10

x = 6

c, $720:[41-\left(2x-5\right)]=2^3.5$

41–(2x–5) = 720:40

2x–5 = 41–18

2x = 28

x = 14

d, $\left(3^2-2\right)\left(x-12\right)+35=5^2+279:3^2$

7(x–12)+35 = 56

7(x–12) = 21

x–12 = 3

x = 15

a, $4.24.5^2-\left(3^3.18+3^3.12\right)$

= 100.24–27.30

= 2400 – 810

= 1590

b, $2^3.7.5^3-\left(5^2.65+5^2.35\right)$

= 7.1000 – 25.100

= 7000 – 2500

= 4500

c, $2^2.74.5^2+5^2.26.4-7000$

= 100.74 + 100.26 – 70.100

= 100.(74+26–70)

= 100.30

= 3000

d, $55.2^2.5+4.89.5^2-3^2.{10}^3$

= 25.4.11 + 4.25.89 – 90.100

= 100.11 + 100.89 – 100.90

= 100.(11+89–90)

= 100.10

= 1000

e, [(315+372).3+(372+315).7]:(26.13+74.13+74)

= [687.3+687.7]:(13.(26+74)+74)

= (687.10):(13.100+74)

= 6870:1374

= 5

a, Ta thấy có 11 số hạng ta nhóm được 5 nhóm

7+11+15+19+…+43+47

= (7+47)+(11+43)+(15+39)+…+(23+31)+27

= 54+54+54+…+54+27

= 54.5 + 27

= 297

b, Có 11 số hạng ta nhóm 5 nhóm có tổng 50

10+13+16+…+37+40

= (10+40)+(13+37)+…+(22+28)+25

= 50.5 + 25

= 275

c, Có 672 số hạng ta nhóm 336 nhóm có tổng là 2019

3+6+…+2016

= (3+2016)+(6+2013)+…+(1009+1010)

= 2019.336

= 678384

a, Ta thấy: $3^{n+2}+3^n=3^n.3^2+3^n$

= $3^n\left(3^2+1\right)$ = $3^n.10$ chia hết cho 10

=> $3^{n+2}+3^n$ chia hết cho 10, n$\in$N

b, $7^{n+4}-7^n=7^n.7^4-7^n$

$7^n\left(7^4-1\right)=7^n.2400$ chia hết cho 30

=> $7^{n+4}-7^n$ chia hết cho 30, n$\in$N

a, (x+1)+(x+2)+(x+3)+...+(x+100) = 7450

(x+x+...+x)+(1+2+...+100) = 7450

$100x+\frac{101.100}{2}=7450$

100x = 2400

x = 24

b, 1+2+3+...+x = 500500

Đặt: A = 1+2+3+...+x

số hạng A (x$-$1) : 1 + 1 = x

Tổng của A

$A=\frac{\left(x+1\right).x}{2}=500500$

(x+1).x = 1001000

Ta thấy

1000.1001 = 1001000

=> x = 1000

A = 2019.20182018 – 2018.20192019

= 2019.(20180000+2018) – 2018.(20190000+2019)

= 2019.2018.${10}^4$ + 2019.2018 – 2018.2019.${10}^4$ – 2018.2019

= (2019.2018.${10}^4$ – 2018.2019.${10}^4$) + (2019.2018 – 2018.2019)

= 0 + 0 = 0

1+2+3 – 4 +5+6+78+9 = 100

1+2+34 – 5 +67 – 8 +9 = 100

12+3 – 4 +5+67+8+9 = 100

123 – 4 – 5 – 6 – 7 +8 – 9 =100

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