Question

4. Să se formeze proporții cu următoarele numere:
a) 2; 3; 4; 6
b) 3; 4; 6; 8
c) 4; 5; 12; 15
d) 2; 24; 6; 8
e) 2; 5; 6; 15
f) 4; 6; 8; 12
g) 3; 9; 16; 48
h) 4; 12; 12; 36

Answer 1

Pentru ca o proportie sa fie egala trebuie ca produsul pe diagonala al mezilor si al extremilor sa fie egal.

Fie $\frac{a}{b} =\frac{c}{d}$

a , d - extremii si b , c -mezii

$3\cdot4=2\cdot6 \implies \frac{3}{2} =\frac{6}{4}$

$3\cdot8=4\cdot6 \implies \frac{3}{4} =\frac{6}{8}$

$4\cdot15=5\cdot12 \implies \frac{4}{5} =\frac{12}{15}$

$2\cdot24=6\cdot8 \implies\frac{2}{6} =\frac{8}{24}$

$2\cdot15=5\cdot6 \implies \frac{2}{5} =\frac{6}{15}$

$4\cdot12=6\cdot8 \implies \frac{4}{6} =\frac{8}{12}$

$3\cdot48=9\cdot16 \implies \frac{3}{9} =\frac{16}{48}$

$12\cdot12=4\cdot36 \implies \frac{12}{4} =\frac{36}{12}$

Answer 2

Răspuns:

egalitatea a doua rapoarte se numeste proportie

a/b=c/d=>ad=bc unde b≠0si d≠0

2/3=4/6=>3·4=2·6

3/4=6/8=>3·8=4·6

4/5=12/15=>4·15=5·12

24/6=8/2=>24·2=6·8

2/5=6/15=>2·15=5·6

4/6=8/12=>6·8=4·12

3/9=16/48=>3·48=9·16

4/12=12/36=>12·12=4·36