Câu 1 :
a) ` 17,28 × 43 + 57 × 17,28 `
= ` 17,28 × ( 43 + 57 ) `
= ` 17,28 × 100 `
= ` 1700 `
b) ` 43,57 × 2,6 × ( 630 - 315 × 2 )`
= ` 43,57 × 2,6 × ( 630 - 630 ) `
= ` 43,57 × 2,6 × 0 `
= `0`
c) $\dfrac{45 × 16 - 17 }{ 45 × 15 + 28}$
= $\dfrac{45 × ( 15 + 1 ) - 17 }{ 45 × 15 + 28}$
= $\dfrac{45 × 15 + ( 45 - 17 ) }{ 45 × 15 + 28}$
= $\dfrac{45 × 15 + 28 }{ 45 × 15 + 28}$ = `1`
d) ` 104 × 68 - 36 × 52 `
= ` 52 × 2 × 68 - 52 × 36 `
= ` 52 × ( 68 × 2 - 36 ) `
= ` 52 × ( 136 - 36 ) ` = ` 52 × 100 ` = ` 5200 `
Câu 2 :
a) Ta có :
Đặt phân số `23/29` là phân số trung gian .
Vì `23/29` > `22/29` ( do `23` > `22` ) và `23/29` < `23/27` ( vì `27`< `29` ) .
`⇒` `22/29` < `23/29` < `23/27`
`⇒` `22/29` < `23/27`
b) Ta có :
`12/25` = $\dfrac{12 × 49}{25 × 49}$ = `588/1225`
`25/49` = $\dfrac{25 × 25}{25 × 49}$ = `625/1225`
Vì `588/1225` < `625/1225`
`⇒` `12/25` < `25/49`
Câu 3 :
a) ` ( x × 0,25 + 1999 ) × 2000 = ( 53 + 1999 ) × 2000`
`⇒` ` x × 0,25 + 1999 = 53 + 1999 ` ( chia cả `2` vế cho `2000` )
`⇒` ` x × 0,25 = 53 ` ( trừ cả `2` vế cho `1999` )
`⇒` ` x = 53 : 0,25 = 212 `
b) ` 71 + 65 × 4 ` = $\dfrac{x + 140}{x}$ + ` 260 `
`⇒` `71 + 260 ` = `x/x` + `140/x` + `260`
`⇒` ` 331` = `1` + `140/x` + `260`
`⇒` `140/x` = ` 331 - 1 - 260 ` = `70`
`⇒` `x` = ` 140 : 70 ` = `2`
