Đáp án:

Bài 1:

51162 - (14015 + x) = 1111

                14015 + x = 51162 - 1111

                14015 + x = 50051

                              x = 50051 - 14015

                              x = 36035

                    Vậy x = 36035

(7654 – x) – 1008 = 2222

              7654 – x = 2222 + 1008

              7654 – x = 3230

                          x = 7654 – 3230

                          x = 4424

                Vậy x = 4424

  36  : x = x

       36 = x . x

       36 = x²

       6² = x²

⇒ x = 6

   Vậy x = 6

Bài 2:

`3``\frac{17}{24}` + `2``\frac{8}{15}`+`1``\frac{7}{8}`

= `\frac{89}{24}` + `\frac{38}{15}`+ `\frac{15}{8}`

= `\frac{445}{120}` + `\frac{304}{120}`+ `\frac{225}{120}`

= `\frac{487}{60}`

Bài 3:

`\frac{1}{2}`+ `\frac{1}{6}` + `\frac{1}{12}` +`\frac{1}{20}`  +  `\frac{1}{30}` +`\frac{1}{42}`

= `\frac{1}{1 . 2}`+ `\frac{1}{2.3}` + `\frac{1}{3.4}` + `\frac{1}{4.5}` +`\frac{1}{5.6}` +`\frac{1}{6.7}`

= `1` - `\frac{1}{2}` + `\frac{1}{2}` - `\frac{1}{3}` + `\frac{1}{3}` - `\frac{1}{4}` + `\frac{1}{4}`-`\frac{1}{5}` + `\frac{1}{5}`- `\frac{1}{6}` + `\frac{1}{6}` - `\frac{1}{7}`

= `1` - `\frac{1}{7}`

= `\frac{6}{7}`

`\frac{1}{3}`+ `\frac{1}{15}` + `\frac{1}{35}` +`\frac{1}{63}`  +  `\frac{1}{99}`

= `\frac{1}{1.3}`+ `\frac{1}{3.5}` + `\frac{1}{5.7}` +`\frac{1}{7.9}`  +  `\frac{1}{9.11}` 

= `1` - `\frac{1}{3}`+ `\frac{1}{3}` - `\frac{1}{5}` + `\frac{1}{5}` - `\frac{1}{7}` +`\frac{1}{7}` - `\frac{1}{9}` +  `\frac{1}{9}` - `\frac{1}{11}`

= `1` - `\frac{1}{11}`

= `\frac{10}{11}`

Giải thích các bước giải: 

`51162 - (14015 + x) = 1111`

`⇒ 51162 - 14015 - x = 1111`

`⇒ 37147 - x = 1111`

`⇒ x = 37147 - 1111`

`⇒ x = 36036`

.

`(7654 - x) - 1008 = 2222`

`⇒ 7654 - x - 1008 = 2222`

`⇒ -x = 2222 - 7654 + 1008`

`⇒ -x = -4424`

`⇒ x = 4424`

.

`36 : x = x`

`⇒ x^2 = 36`

`⇒ x = ± 6`

Vậy `x= ± 6`

.

`3 17/24 + 2 8/15 + 1 7/8`

`= 89/24 + 38/15 + 15/8`

`= 445/120 + 304/120 + 225/120`

`= 974/120 = 487/60`

.

`1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42`

`= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7`

`= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7`

`= 1 - 1/7 = 6/7`

.

`1/3 + 1/15 + 1/35 + 1/63 + 1/99`

`= 1/1.3 + 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11`

`= 1/2 . (2/1.3 + 2/3.5 + 2/5.7 + 2/7.9 + 2/9.11)`

`= 1/2 . (1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 -1/11)`

`= 1/2 . (1 - 1/11)`

`= 1/2 . 10/11 = 5/11`