Priorités opératoires : corrigés des exercices de maths en 5ème.

Exercice 1 : priorités opératoires.
### Situation 1

Calcul de A:
A\,=\,7\,%2B\,4\,\times  \,8\,=\,7\,%2B\,32\,=\,39

Calcul de B:
B\,=\,3\,\times  \,11\,-\,7\,\times  \,4\,=\,33\,-\,28\,=\,5

Calcul de C:
C\,=\,3\,\times  \,6\,-\,5\,\times  \,6\,=\,18\,-\,30\,=\,-12

Calcul de D:
D\,=\,9\,-\,4\,: \,4\,=\,9\,-\,1\,=\,8

Calcul de E:
E\,=\,32\,: \,4\,-\,2\,%2B\,7\,\times  \,3\,=\,8\,-\,2\,%2B\,21\,=\,27

Calcul de F:
F\,=\,9\,\times  \,4\,-\,2\,\times  \,5\,\times  \,2\,=\,36\,-\,20\,=\,16

### Situation 2

Calcul de x:
x\,=\,132\,-\,11\,\times  \,10\,%2B\,4\,\times  \,2%2C5\,=\,132\,-\,110\,%2B\,10\,=\,32

Calcul de y:
y\,=\,12%2C5\,-\,2\,-\,5%2C1\,%2B\,15\,-\,1%2C2\,=\,12%2C5\,-\,2\,-\,5%2C1\,%2B\,15\,-\,1%2C2\,=\,19%2C2

Calcul de z:
z\,=\,120\,-\,4\,\times  \,5\,-\,7\,\times  \,8\,%2B\,54\,%3A\,9\,=\,120\,-\,20\,-\,56\,%2B\,6\,=\,50

Calcul de t:
t\,=\,22\,%2B\,3\,\times  \,1%2C5\,-\,1%2C5\,=\,22\,%2B\,4%2C5\,-\,1%2C5\,=\,25

### Situation 3

Calcul de X:
X\,=\,2%2C9\,%2B\,0%2C8\,\times  \,5\,=\,2%2C9\,%2B\,4\,=\,6%2C9

Calcul de A:
A\,=\,10\,-\,9%2C9\,%3A\,3\,=\,10\,-\,3%2C3\,=\,6%2C7

Calcul de T:
T\,=\,4\,\times  \,0%2C3\,\times  \,1%2C36\,=\,1%2C632

Calcul de E:
E\,=\,0%2C23\,\times  \,5\,%2B\,99%2C18\,%3A\,17%2C1\,=\,1%2C15\,%2B\,5%2C8\,=\,6%2C95

Calcul de C:
C\,=\,12%2C8\,-\,0%2C7\,\times  \,9\,=\,12%2C8\,-\,6%2C3\,=\,6%2C5

Rangement par ordre croissant :
T\,=\,1%2C632\,%3C\,C\,=\,6%2C5\,%3C\,A\,=\,6%2C7\,%3C\,X\,=\,6%2C9\,%3C\,E\,=\,6%2C95

Exercice 2 : priorités opératoires (14 exercices)
Correction de l’exercice de mathématiques

Situation 1

a) 7\,%2B\,4\,\times  \,8
=\,7\,%2B\,32%0D%0A=\,39

b) 3\,\times  \,11\,-\,7\,\times  \,4
=\,33\,-\,28%0D%0A=\,5

c) 37\,-\,6\,\times  \,5
=\,37\,-\,30%0D%0A=\,7

d) 9\,-\,4\,%3A\,4
=\,9\,-\,1%0D%0A=\,8

e) 32\,-\,4\,-\,2\,%2B\,7\,\times  \,3
=\,32\,-\,4\,-\,2\,%2B\,21%0D%0A=\,28\,-\,2\,%2B\,21%0D%0A=\,26\,%2B\,21%0D%0A=\,47

f) 9\,\times  \,4\,%3A\,2\,-\,5\,\times  \,2
=\,36\,%3A\,2\,-\,10%0D%0A=\,18\,-\,10%0D%0A=\,8

Situation 2

A = 6\,\times  \,(3\,%2B\,7)
=\,6\,\times  \,10%0D%0A=\,60

B = 23\,-\,4\,\times  \,5
=\,23\,-\,20%0D%0A=\,3

C = (3\,%2B\,5)\,\times  \,(9\,-\,7)
=\,8\,\times  \,2%0D%0A=\,16

D = (13\,-\,7)\,%3A\,2
=\,6\,%3A\,2%0D%0A=\,3

E = 5\,-\,%5B4\,-\,(2\,%2B\,1)%5D
=\,5\,-\,%5B4\,-\,3%5D%0D%0A=\,5\,-\,1%0D%0A=\,4

F = (3\,%2B\,5\,\times  \,7)\,%3A\,2\,%2B\,1
=\,(3\,%2B\,35)\,%3A\,2\,%2B\,1%0D%0A=\,38\,%3A\,2\,%2B\,1%0D%0A=\,19\,%2B\,1%0D%0A=\,20

Situation 3

Aurélie achète 5 pots de confitures à 9 € pièce et 12 baguettes à 6,50 € pièce.

Le calcul pour trouver le prix total qu’elle doit payer est :
5\,\times  \,9\,%2B\,12\,\times  \,6%2C5

Calculez les produits individuellement :
5\,\times  \,9\,=\,45
12\,\times  \,6%2C5\,=\,78

Additionnez les deux résultats :
45\,%2B\,78\,=\,123

Aurélie doit payer 123 €.

Exercice 3 : opérations et priorités
Correction de l’exercice :

Situation\,1

A\,=\,8\,\times  \,(26\,-\,14)
A\,=\,8\,\times  \,12
A\,=\,96

B\,=\,(7%2C5\,-\,2%2C5)\,%3A\,(7%2C5\,%2B\,2%2C5)
B\,=\,5\,%3A\,10
B\,=\,0%2C5

C\,=\,(0%2C5\,%2B\,15\,%2B\,35\,%2B\,8%2C5\,%2B\,1%2C75)\,\times  \,(55\,%2B\,45)
C\,=\,60%2C75\,\times  \,100
C\,=\,6075

D\,=\,(1%2C2\,%2B\,1%2C8)\,\times  \,(5%2C5\,-\,4)\,-\,(7%2C5\,-\,6)
D\,=\,3\,\times  \,1%2C5\,-\,1%2C5
D\,=\,4%2C5\,-\,1%2C5
D\,=\,3

Situation\,2

A\,=\,7\,\times  \,%5B16\,-\,(2\,%2B\,9)%5D
A\,=\,7\,\times  \,%5B16\,-\,11%5D
A\,=\,7\,\times  \,5
A\,=\,35

B\,=\,%5B9\,-\,(9\,-\,8)%5D\,\times  \,%5B(2\,%2B\,7)\,%3A\,3%5D
B\,=\,%5B9\,-\,1%5D\,\times  \,%5B9\,%3A\,3%5D
B\,=\,8\,\times  \,3
B\,=\,24

C\,=\,4\,\times  \,%5B39%2C2\,-\,(2%2C4\,%2B\,4%2C8\,%2B\,3%2C5)%5D
C\,=\,4\,\times  \,%5B39%2C2\,-\,10%2C7%5D
C\,=\,4\,\times  \,28%2C5
C\,=\,114

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\,3\,=\,24%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F12%2520%252B%2520105%2520%252B%252024%2520%253D%2520141%22\,alt=%2212\,%2B\,105\,%2B\,24\,=\,141%22\,align=%22absmiddle%22\,%2F>%0D%0ADonc%2C%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3FA%2520%253D%2520141%22\,alt=%22A\,=\,141%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3FB%2520%253D%252025%2520-%2520%255Cleft%255B%252012%2520-%2520%25283%2520%252B%25204%2529%2520%255Cright%255D%22\,alt=%22B\,=\,25\,-\,%5B\,12\,-\,(3\,%2B\,4)\,%5D%22\,align=%22absmiddle%22\,%2F>%0D%0ACalculons\,etape\,par\,etape\,%3A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F3%2520%252B%25204%2520%253D%25207%22\,alt=%223\,%2B\,4\,=\,7%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F12%2520-%25207%2520%253D%25205%22\,alt=%2212\,-\,7\,=\,5%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F25%2520-%25205%2520%253D%252020%22\,alt=%2225\,-\,5\,=\,20%22\,align=%22absmiddle%22\,%2F>%0D%0ADonc%2C%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3FB%2520%253D%252020%22\,alt=%22B\,=\,20%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3FC%2520%253D%252081%2520%252B%2520%255Cleft%255B%2520%25287%2520%252B%252021%2529%2520-%252013%2520%255Cright%255D%2520-%2520%252817%2520-%25209%2529%22\,alt=%22C\,=\,81\,%2B\,%5B\,(7\,%2B\,21)\,-\,13\,%5D\,-\,(17\,-\,9)%22\,align=%22absmiddle%22\,%2F>%0D%0ACalculons\,etape\,par\,etape\,%3A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F7%2520%252B%252021%2520%253D%252028%22\,alt=%227\,%2B\,21\,=\,28%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F28%2520-%252013%2520%253D%252015%22\,alt=%2228\,-\,13\,=\,15%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F17%2520-%25209%2520%253D%25208%22\,alt=%2217\,-\,9\,=\,8%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F81%2520%252B%252015%2520-%25208%2520%253D%252088%22\,alt=%2281\,%2B\,15\,-\,8\,=\,88%22\,align=%22absmiddle%22\,%2F>%0D%0ADonc%2C%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3FC%2520%253D%252088%22\,alt=%22C\,=\,88%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3FD%2520%253D%2520%255Cleft%255B%2520%25287%2520%255Ctimes  %25208%2520-%25204%2520%255Ctimes  %25205%2529%2520%252B%252011%2520%255Cright%255D%2520%255Ctimes  %2520%25284%2520%252B%25203%2529%22\,alt=%22D\,=\,%5B\,(7\,\times  \,8\,-\,4\,\times  \,5)\,%2B\,11\,%5D\,\times  \,(4\,%2B\,3)%22\,align=%22absmiddle%22\,%2F>%0D%0ACalculons\,etape\,par\,etape\,%3A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F7%2520%255Ctimes  %25208%2520%253D%252056%22\,alt=%227\,\times  \,8\,=\,56%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F4%2520%255Ctimes  %25205%2520%253D%252020%22\,alt=%224\,\times  \,5\,=\,20%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F56%2520-%252020%2520%253D%252036%22\,alt=%2256\,-\,20\,=\,36%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F36%2520%252B%252011%2520%253D%252047%22\,alt=%2236\,%2B\,11\,=\,47%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F4%2520%252B%25203%2520%253D%25207%22\,alt=%224\,%2B\,3\,=\,7%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F47%2520%255Ctimes  %25207%2520%253D%2520329%22\,alt=%2247\,\times  \,7\,=\,329%22\,align=%22absmiddle%22\,%2F>%0D%0ADonc%2C%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3FD%2520%253D%2520329%22\,alt=%22D\,=\,329%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3FE%2520%253D%25206%2520%252B%2520%255Cleft%255B%2520%25287%2520%255Ctimes  %25202%2529%2520-%2520%25281%2520%255Ctimes  %25202%2529%2520%255Cright%255D%22\,alt=%22E\,=\,6\,%2B\,%5B\,(7\,\times  \,2)\,-\,(1\,\times  \,2)\,%5D%22\,align=%22absmiddle%22\,%2F>%0D%0ACalculons\,etape\,par\,etape\,%3A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F7%2520%255Ctimes  %25202%2520%253D%252014%22\,alt=%227\,\times  \,2\,=\,14%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F1%2520%255Ctimes  %25202%2520%253D%25202%22\,alt=%221\,\times  \,2\,=\,2%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F14%2520-%25202%2520%253D%252012%22\,alt=%2214\,-\,2\,=\,12%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F6%2520%252B%252012%2520%253D%252018%22\,alt=%226\,%2B\,12\,=\,18%22\,align=%22absmiddle%22\,%2F>%0D%0ADonc%2C%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3FE%2520%253D%252018%22\,alt=%22E\,=\,18%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0A%3Ca\,id=%22exercice-5%22>%3C%2Fa>%3Cspan\,class=%22titrecorrection%22>Exercice\,5\,%3A\,probleme\,du\,libraire\,et\,operations%3C%2Fspan>%0D%0ALe\,nombre\,total\,de\,tomes\,d'Harry\,Potter\,que\,le\,libraire\,a\,recus\,est\,%3A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F50%2520%252B%252080%2520%253D%2520130%2520%2520tomes%22\,alt=%2250\,%2B\,80\,=\,130\,\,tomes%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0ALe\,nombre\,d'etageres\,necessaires\,pour\,ranger\,ces\,130\,tomes%2C\,sachant\,qu'une\,etagere\,peut\,contenir\,13\,livres%2C\,est\,donne\,par\,%3A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F%255Cleft%255Clceil%2520%255Cfrac%257B130%257D%257B13%257D%2520%255Cright%255Crceil%22\,alt=%22\lceil\,\frac{130}{13}\,\rceil%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0ACalculons\,%3A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F%255Cfrac%257B130%257D%257B13%257D%2520%253D%252010%22\,alt=%22\frac{130}{13}\,=\,10%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0ADonc%2C\,le\,libraire\,remplira\,%3A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F10%22\,alt=%2210%22\,align=%22absmiddle%22\,%2F>%0D%0Aetageres.%0D%0A%0D%0AAinsi%2C\,le\,libraire\,remplira\,10\,etageres.%0D%0A%0D%0A%3Ca\,id=%22exercice-6%22>%3C%2Fa>%3Cspan\,class=%22titrecorrection%22>Exercice\,6\,%3A\,probleme\,et\,expression\,numerique%3C%2Fspan>%0D%0A1)\,Un\,eleveur\,possede\,102\,%C5%93ufs\,et\,en\,ramasse\,18\,autres.\,Il\,doit\,expedier\,ses\,%C5%93ufs\,par\,boite\,de\,12.\,Combien\,expediera-t-il\,de\,boites\,%3F%0D%0A%0D%0AOn\,additionne\,le\,nombre\,total\,d'%C5%93ufs\,%3A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F102%2520%252B%252018%2520%253D%2520120%22\,alt=%22102\,%2B\,18\,=\,120%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0AEnsuite%2C\,on\,divise\,le\,nombre\,total\,d'%C5%93ufs\,par\,le\,nombre\,d'%C5%93ufs\,par\,boite\,%3A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F120%2520%255Cdiv%252012%2520%253D%252010%22\,alt=%22120\,: \,12\,=\,10%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0AIl\,expediera\,donc\,10\,boites.\,La\,bonne\,expression\,est\,donc\,\(\,(102\,%2B\,18)\,: \,12
D\,=\,120\,%3A\,40\,%3B\,2\,%2B\,3
D\,=\,3\,%3B\,2\,%2B\,3
D\,=\,3\,%3B\,5 (Depend de l’interpretation de l’utilisation du « ; » qui peut etre l’equivalent du signe de separation de deux valeurs/items)

Situation\,3

a. La somme de 7,5 et du produit de 3 par 1,5 :
7%2C5\,%2B\,(3\,\times  \,1%2C5)
7%2C5\,%2B\,4%2C5
12

b. Le produit de 7,5 par la somme de 3 et 1,5 :
7%2C5\,\times  \,(3\,%2B\,1%2C5)
7%2C5\,\times  \,4%2C5
33%2C75

c. Le quotient de la somme de 12 et 8 par 10 :
\frac{(12\,%2B\,8)}{10}
\frac{20}{10}
2

d. La somme du produit de 3 par 6 et du resultat de la soustraction de 7 a 15 :
(3\,\times  \,6)\,%2B\,(15\,-\,7)
18\,%2B\,8
26

Exercice 4 : calcul numerique et parentheses
A\,=\,12\,%2B\,%5B\,3\,\times  \,(\,5\,%2B\,(4\,\times  \,7)\,%2B\,2\,)\,%5D\,%2B\,(8\,\times  \,3)
Calculons etape par etape :
4\,\times  \,7\,=\,28
5\,%2B\,28\,=\,33
33\,%2B\,2\,=\,35
3\,\times  \,35\,=\,105
8\,\times  \,3\,=\,24
12\,%2B\,105\,%2B\,24\,=\,141
Donc,
A\,=\,141

B\,=\,25\,-\,%5B\,12\,-\,(3\,%2B\,4)\,%5D
Calculons etape par etape :
3\,%2B\,4\,=\,7
12\,-\,7\,=\,5
25\,-\,5\,=\,20
Donc,
B\,=\,20

C\,=\,81\,%2B\,%5B\,(7\,%2B\,21)\,-\,13\,%5D\,-\,(17\,-\,9)
Calculons etape par etape :
7\,%2B\,21\,=\,28
28\,-\,13\,=\,15
17\,-\,9\,=\,8
81\,%2B\,15\,-\,8\,=\,88
Donc,
C\,=\,88

D\,=\,%5B\,(7\,\times  \,8\,-\,4\,\times  \,5)\,%2B\,11\,%5D\,\times  \,(4\,%2B\,3)
Calculons etape par etape :
7\,\times  \,8\,=\,56
4\,\times  \,5\,=\,20
56\,-\,20\,=\,36
36\,%2B\,11\,=\,47
4\,%2B\,3\,=\,7
47\,\times  \,7\,=\,329
Donc,
D\,=\,329

E\,=\,6\,%2B\,%5B\,(7\,\times  \,2)\,-\,(1\,\times  \,2)\,%5D
Calculons etape par etape :
7\,\times  \,2\,=\,14
1\,\times  \,2\,=\,2
14\,-\,2\,=\,12
6\,%2B\,12\,=\,18
Donc,
E\,=\,18

Exercice 5 : probleme du libraire et operations
Le nombre total de tomes d’Harry Potter que le libraire a recus est :
50\,%2B\,80\,=\,130\,\,tomes

Le nombre d’etageres necessaires pour ranger ces 130 tomes, sachant qu’une etagere peut contenir 13 livres, est donne par :
\lceil\,\frac{130}{13}\,\rceil

Calculons :
\frac{130}{13}\,=\,10

Donc, le libraire remplira :
10
etageres.

Ainsi, le libraire remplira 10 etageres.

Exercice 6 : probleme et expression numerique
1) Un eleveur possede 102 œufs et en ramasse 18 autres. Il doit expedier ses œufs par boite de 12. Combien expediera-t-il de boites ?

On additionne le nombre total d’œufs :
102\,%2B\,18\,=\,120

Ensuite, on divise le nombre total d’œufs par le nombre d’œufs par boite :
120\,: \,12\,=\,10

Il expediera donc 10 boites. La bonne expression est donc \( (102 + 18) : 12″ align= »absmiddle » />, soit la réponse c.

2) L’intendance du collège achète 102 cartons de papier blanc et 12 de papier de couleur. Un carton coûte 18 €. Quel est le prix total à payer ?

On additionne le nombre total de cartons :
102\,%2B\,12\,=\,114

Ensuite, on multiplie le nombre total de cartons par le prix par carton :
114\,\times  \,18\,=\,2052

Le prix total à payer est donc de 2052 €. La bonne expression est donc (102\,%2B\,12)\,\times  \,18, soit la réponse b.

3) Un grand magasin reçoit sa livraison de jus de fruit, soit 18 cartons de 12 bouteilles. Il reste en réserve 102 bouteilles. Combien y a-t-il maintenant de bouteilles de jus de fruit dans ce grand magasin ?

On calcule le nombre de bouteilles dans les 18 cartons :
18\,\times  \,12\,=\,216

Ensuite, on additionne les bouteilles reçues et celles en réserve :
216\,%2B\,102\,=\,318

Il y a maintenant 318 bouteilles de jus de fruit dans ce grand magasin. La bonne expression est donc 18\,\times  \,12\,%2B\,102, soit la réponse a.

Résumé des correspondances :

1) c. \frac{(102\,%2B\,18)}{12}
2) b. (102\,%2B\,12)\,\times  \,18
3) a. 18\,\times  \,12\,%2B\,102

Exercice 7 : priorités opératoires
Correction de l’exercice :

a) 7\,%2B\,4\,\times  \,8
7\,%2B\,4\,\times  \,8\,=\,7\,%2B\,32\,=\,39

b) 3\,\times  \,11\,-\,7\,\times  \,4
3\,\times  \,11\,-\,7\,\times  \,4\,=\,33\,-\,28\,=\,5

c) 37\,-\,6\,\times  \,5
37\,-\,6\,\times  \,5\,=\,37\,-\,30\,=\,7

d) 9\,-\,\frac{4}{4}
9\,-\,\frac{4}{4}\,=\,9\,-\,1\,=\,8

e) \frac{32}{4}\,-\,2\,%2B\,7\,\times  \,3
\frac{32}{4}\,-\,2\,%2B\,7\,\times  \,3\,=\,8\,-\,2\,%2B\,21\,=\,6\,%2B\,21\,=\,27

f) 9\,\times  \,4\,: \,2\,-\,5\,\times  \,2
9\,\times  \,4\,: \,2\,-\,5\,\times  \,2\,=\,36\,: \,2\,-\,10\,=\,18\,-\,10\,=\,8

Exercice 8 : brocante et prix d’un DVD
Soit x le prix d’un DVD.

Marc a acheté :
– 8 livres, chaque livre coûtant 1,5 euros : 8\,\times  \,1%2C5\,=\,12 euros
– 2 bandes dessinées, chaque BD coûtant 4 euros : 2\,\times  \,4\,=\,8 euros
– 4 DVD

Le montant total payé pour les livres et les BD est :
12\,%2B\,8\,=\,20\,\,euros

Sachant qu’il a payé en tout 38 euros, la somme payée pour les 4 DVD est :
38\,-\,20\,=\,18\,\,euros

Le prix d’un DVD est donc :
x\,=\,\frac{18}{4}\,=\,4%2C5\,\,euros

Ainsi, le prix d’un DVD est de 4,5 euros.

Exercice 9 : enchaînement de calculs
\begin{align*}
A = 6 + 27 : 3 \\
= 6 + 9 \\
= 15
\end{align*}

\begin{align*}
B = 24 : 3 + 16 : 8 – 2 \\
= 8 + 2 – 2 \\
= 8
\end{align*}

\begin{align*}
C = 8 \times 6 – 23 \\
= 48 – 23 \\
= 25
\end{align*}

\begin{align*}
D = 5 \times 6 + 4 \times 3 \\
= 30 + 12 \\
= 42
\end{align*}

\begin{align*}
E = 7 + 15 : 3 \times 5 \\
= 7 + 5 \times 5 \\
= 7 + 25 \\
= 32
\end{align*}

\begin{align*}
F = 3 + 4 \times 5 – 1 \\
= 3 + 20 – 1 \\
= 23 – 1 \\
= 22
\end{align*}

\begin{align*}
G = 15 \times 5 – 2 \\
= 75 – 2 \\
= 73
\end{align*}

\begin{align*}
H = 55 – 7 \times 6 + 1 \\
= 55 – 42 + 1 \\
= 13 + 1 \\
= 14
\end{align*}

\begin{align*}
I = 12 : 4 – 15 : 3 \\
= 3 – 5 \\
= -2
\end{align*}

Exercice 10 : expressions contenant des parenthèses
Voici la correction de l’exercice en utilisant LaTeX pour les équations :

Calcul des expressions numériques suivantes :

A\,=\,(5\,%2B\,7)\,\times  \,2
A\,=\,12\,\times  \,2
A\,=\,24

B\,=\,5\,%2B\,7\,\times  \,2
B\,=\,5\,%2B\,14
B\,=\,19

C\,=\,(12\,-\,4)\,\times  \,3
C\,=\,8\,\times  \,3
C\,=\,24

D\,=\,12\,-\,4\,\times  \,3
D\,=\,12\,-\,12
D\,=\,0

E\,=\,(21\,-\,18)\,\times  \,(12\,-\,10)\,%2B\,1
E\,=\,3\,\times  \,2\,%2B\,1
E\,=\,6\,%2B\,1
E\,=\,7

F\,=\,18\,%2B\,%5B12\,-\,2\,\times  \,(13\,-\,9)%5D
F\,=\,18\,%2B\,%5B12\,-\,2\,\times  \,4%5D
F\,=\,18\,%2B\,%5B12\,-\,8%5D
F\,=\,18\,%2B\,4
F\,=\,22

G\,=\,(4.8\,-\,(2.5\,%2B\,0.3))\,\times  \,(3\,%2B\,3.5)
G\,=\,(4.8\,-\,2.8)\,\times  \,6.5
G\,=\,2\,\times  \,6.5
G\,=\,13

H\,=\,%5B18\,%2B\,2\,\times  \,(120\,-\,45)%5D\,\times  \,1.5
H\,=\,%5B18\,%2B\,2\,\times  \,75%5D\,\times  \,1.5
H\,=\,%5B18\,%2B\,150%5D\,\times  \,1.5
H\,=\,168\,\times  \,1.5
H\,=\,252

I\,=\,700\,-\,%5B300\,-\,(300\,-\,80)%5D
I\,=\,700\,-\,%5B300\,-\,220%5D
I\,=\,700\,-\,80
I\,=\,620

Ainsi, les résultats finaux sont :

A\,=\,24%2C\,\quad\,B\,=\,19%2C\,\quad\,C\,=\,24%2C\,\quad\,D\,=\,0%2C\,\quad\,E\,=\,7%2C\,\quad\,F\,=\,22%2C\,\quad\,G\,=\,13%2C\,\quad\,H\,=\,252%2C\,\quad\,I\,=\,620

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