Question

1) a=6,5 la puterea a 2 a:[5/8+(12,5-5)×2/5]-3,75-2,75
2) Comparati fractiile 17/7 si 19/8
3) a)0,1:1/5
b)6/17×(0,75+2/3)
c)6/17+0,1
d)[(0,75+2/3)×6/17+0,1:1/5]0,(3)

Answer 1

☆2) 17/7 si 19/8=>17×8 si 19×7 =>136>133, deci: 17/7>19/8.

☆3)a) 0,1÷1/5=1/10×5/1=5/10=1/2.

☆b)6/17×(0,75+2/3)=6/17×(75/100+2/3)=(se simpl. "75/100" cu" 25")=6/17×(3/4+2/3)=(se aduc fr.la numit."12")=6/17×(9+8)/12=6/17×17/12(se simpl.pe diagonală)=1/2.

☆c)6/17+0,1=6/17+1/10=(se aduce la numit.com."170")=(60+17)/170=77/170.

☆d)[(0,75+2/3)×6/17+0,1÷1,5]×0,3=[(3/4+2/3)×6/17+1/10÷15/10]×3/10=(aducem la numit.com."12")=[(9+8)/12×6/17+1/10×10/15]×3/10=(17/10×6/17+1/15)×3/10=(se simpl.pe diagonală primele două fr.)=(1/2+1/15)×3/10=(aducem la numit.com."30")=(15+2)/30×3/10=17/30×3/10 (se simpl.pe diag.)=17/100.

Answer 2

1) a=(6,5)²:[5/8+7,5×2/5]-6,5
a=42,25:[5/8+15/2×2/5]-6,5
a=42,25:[5/8+3]-6,5  (am simplificat in diagonala)
a=42,25:29/8-6,5
a=42,25×8/29-6,5
a=338/29 -6,5
a=(338-188,5)/29
a=149,5/29
a=299/58
2. 17/7 si 19/8
(17×8)/56 si (19×7)/56 (am adus la numitor comun)
136/56 >133/56
deci 17/7>19/8
3. a. 0,1:1/5 =1/10×5/1=5/10=1/2 (impartire la o fractie inseamna inmultire cu inversul)
b. 6/17×(3/4+2/3)=6/17×(9/12+8/12) = 6/17×17/12 =1/1×1/2=1/2 (am simplificat in diagonala)
c. 6/17+0,1=6/17+1/10=60/170+17/170=77/170
d. [(3/4+2/3)×6/17+0,1:1/5]×3/9= (folosim rezultatele de la pct b si a)
=[1/2+1/2]×1/3=1×1/3=1/3=0,(3)