Les opérations : corrigés des exercices de maths en CM1.

Exercice 1 : compléter jusqu’à 100
$50\,%2B\,50\,=\,100$
$70\,%2B\,30\,=\,100$
$90\,%2B\,10\,=\,100$
$25\,%2B\,75\,=\,100$
$65\,%2B\,35\,=\,100$
$85\,%2B\,15\,=\,100$
$16\,%2B\,84\,=\,100$
$37\,%2B\,63\,=\,100$
$49\,%2B\,51\,=\,100$
$54\,%2B\,46\,=\,100$
$68\,%2B\,32\,=\,100$
$77\,%2B\,23\,=\,100$

Exercice 2 : multiplication par 10,100, 1 000
\begin{array}{|c|c|c|c|}
\hline
5 \times 10 = 50 7 \times 100 = 700 9 \times 1\,000 = 9\,000 305 \times 100 = 30\,500 \\
\hline
24 \times 10 = 240 32 \times 100 = 3\,200 87 \times 1\,000 = 87\,000 520 \times 1\,000 = 520\,000 \\
\hline
187 \times 10 = 1\,870 456 \times 100 = 45\,600 923 \times 1\,000 = 923\,000 4\,865 \times 10 = 48\,650 \\
\hline
\end{array}

Exercice 3 : division par 10, 100, 1 000
\begin{align*}
560 : 10 = 56 \\
800 : 100 = 8 \\
4000 : 1000 = 4 \\
3500 : 100 = 35 \\
2700 : 10 = 270 \\
9500 : 100 = 95 \\
17000 : 1000 = 17 \\
47000 : 1000 = 47 \\
41000 : 10 = 4100 \\
11000 : 100 = 110 \\
820000 : 1000 = 820 \\
6800 : 10 = 680 \\
\end{align*}

Exercice 4 : division euclidienne
$\begin{array}{%7Cc%7Cc%7Cc%7C}%0D%0A\hline%0D%0A26\,: \,3\,%26\,26\,=\,3\,\times \,8\,%2B\,2\,%26\,quotient%3A\,\,8%2C\,\,reste%3A\,\,2\,\\%0D%0A26\,: \,5\,%26\,26\,=\,5\,\times \,5\,%2B\,1\,%26\,quotient%3A\,\,5%2C\,\,reste%3A\,\,1\,\\%0D%0A26\,: \,7\,%26\,26\,=\,7\,\times \,3\,%2B\,5\,%26\,quotient%3A\,\,3%2C\,\,reste%3A\,\,5\,\\%0D%0A26\,: \,9\,%26\,26\,=\,9\,\times \,2\,%2B\,8\,%26\,quotient%3A\,\,2%2C\,\,reste%3A\,\,8\,\\%0D%0A\hline%0D%0A43\,: \,4\,%26\,43\,=\,4\,\times \,10\,%2B\,3\,%26\,quotient%3A\,\,10%2C\,\,reste%3A\,\,3\,\\%0D%0A43\,: \,6\,%26\,43\,=\,6\,\times \,7\,%2B\,1\,%26\,quotient%3A\,\,7%2C\,\,reste%3A\,\,1\,\\%0D%0A43\,: \,8\,%26\,43\,=\,8\,\times \,5\,%2B\,3\,%26\,quotient%3A\,\,5%2C\,\,reste%3A\,\,3\,\\%0D%0A43\,: \,9\,%26\,43\,=\,9\,\times \,4\,%2B\,7\,%26\,quotient%3A\,\,4%2C\,\,reste%3A\,\,7\,\\%0D%0A\hline%0D%0A59\,: \,6\,%26\,59\,=\,6\,\times \,9\,%2B\,5\,%26\,quotient%3A\,\,9%2C\,\,reste%3A\,\,5\,\\%0D%0A59\,: \,7\,%26\,59\,=\,7\,\times \,8\,%2B\,3\,%26\,quotient%3A\,\,8%2C\,\,reste%3A\,\,3\,\\%0D%0A59\,: \,8\,%26\,59\,=\,8\,\times \,7\,%2B\,3\,%26\,quotient%3A\,\,7%2C\,\,reste%3A\,\,3\,\\%0D%0A59\,: \,10\,%26\,59\,=\,10\,\times \,5\,%2B\,9\,%26\,quotient%3A\,\,5%2C\,\,reste%3A\,\,9\,\\%0D%0A\hline%0D%0A\end{array}$

Exercice 5 : entourer la bonne réponse pour chaque calcul
Pour chaque calcul, entoure la bonne réponse sans effectuer précisément l’opération.

1. $789\,-\,578\,\approx\,789\,-\,600\,=\,189$ donc est proche.
2. $2382\,%2B\,411\,\approx\,2400\,%2B\,400\,=\,2800$ donc est proche.
3. $2382\,-\,411\,\approx\,2400\,-\,400\,=\,2000$ donc est proche.
4. $652\,%2B\,258\,\approx\,650\,%2B\,250\,=\,900$ donc est proche.
5. $341\,\times \,7\,\approx\,350\,\times \,7\,=\,2450$ donc est proche.
6. $260\,: \,5\,\approx\,250\,: \,5\,=\,50$ donc est proche.

Exercice 6 : donner un ordre de grandeur
$418\,%2B\,507\,\approx\,400\,%2B\,500\,=\,900$

$792\,-\,409\,\approx\,800\,-\,400\,=\,400$

$62\,\times \,49\,\approx\,60\,\times \,50\,=\,3000$

$613\,: \,3\,\approx\,600\,: \,3\,=\,200$

$125\,%2B\,682\,\approx\,100\,%2B\,700\,=\,800$

$898\,-\,122\,\approx\,900\,-\,100\,=\,800$

$51\,\times \,28\,\approx\,50\,\times \,30\,=\,1500$

$924\,: \,9\,\approx\,900\,: \,9\,=\,100$

$2\%2C135\,%2B\,703\,\approx\,2\%2C100\,%2B\,700\,=\,2\%2C800$

$3\%2C216\,-\,485\,\approx\,3\%2C200\,-\,500\,=\,2\%2C700$

$32\,\times \,787\,\approx\,30\,\times \,800\,=\,24\%2C000$

$3\%2C980\,: \,11\,\approx\,4\%2C000\,: \,10\,=\,400$

$8\%2C430\,%2B\,72\,\approx\,8\%2C400\,%2B\,100\,=\,8\%2C500$

$5\%2C044\,-\,395\,\approx\,5\%2C000\,-\,400\,=\,4\%2C600$

$212\,\times \,694\,\approx\,200\,\times \,700\,=\,140\%2C000$

$2\%2C954\,: \,52\,\approx\,3\%2C000\,: \,50\,=\,60$

Exercice 7 : effectuer les additions
$a.\quad\,\begin{array}{r}%0D%0A4432\,\\%0D%0A%2B\,5364\,\\%0D%0A\hline%0D%0A9796\,\\%0D%0A\end{array}$

$b.\quad\,\begin{array}{r}%0D%0A5489\,\\%0D%0A%2B\,3255\,\\%0D%0A\hline%0D%0A8744\,\\%0D%0A\end{array}$

$c.\quad\,\begin{array}{r}%0D%0A76593\,\\%0D%0A%2B\,18273\,\\%0D%0A\hline%0D%0A94866\,\\%0D%0A\end{array}$

Exercice 8 : poser des additions
a. $4352\,%2B\,9558$

Colonnes des unités : $2\,%2B\,8\,=\,10$ , on pose 0 et on retient 1.

Colonnes des dizaines : $5\,%2B\,5\,%2B\,1\,=\,11$ , on pose 1 et on retient 1.

Colonnes des centaines : $3\,%2B\,5\,%2B\,1\,=\,9$ , on pose 9.

Colonnes des milliers : $4\,%2B\,9\,=\,13$ , on pose 13.

Donc $4352\,%2B\,9558\,=\,13910$ .

$\begin{array}{r}%0D%0A4352\,\\%0D%0A%2B\,9558\,\\%0D%0A\hline%0D%0A13910%0D%0A\end{array}$

b. $32964\,%2B\,5756$

Colonnes des unités : $4\,%2B\,6\,=\,10$ , on pose 0 et on retient 1.

Colonnes des dizaines : $6\,%2B\,5\,%2B\,1\,=\,12$ , on pose 2 et on retient 1.

Colonnes des centaines : $9\,%2B\,7\,%2B\,1\,=\,17$ , on pose 7 et on retient 1.

Colonnes des milliers : $2\,%2B\,5\,%2B\,1\,=\,8$ , on pose 8.

Colonnes des dizaines de milliers : $3\,%2B\,0\,=\,3$ , on pose 3.

Donc $32964\,%2B\,5756\,=\,38720$ .

$\begin{array}{r}%0D%0A32964\,\\%0D%0A%2B\,5756\,\\%0D%0A\hline%0D%0A38720%0D%0A\end{array}$

c. $47837\,%2B\,77837$

Colonnes des unités : $7\,%2B\,7\,=\,14$ , on pose 4 et on retient 1.

Colonnes des dizaines : $3\,%2B\,3\,%2B\,1\,=\,7$ , on pose 7.

Colonnes des centaines : $8\,%2B\,8\,=\,16$ , on pose 6 et on retient 1.

Colonnes des milliers : $7\,%2B\,7\,%2B\,1\,=\,15$ , on pose 5 et on retient 1.

Colonnes des dizaines de milliers : $4\,%2B\,7\,%2B\,1\,=\,12$ , on pose 12.

Donc $47837\,%2B\,77837\,=\,125674$ .

$\begin{array}{r}%0D%0A47837\,\\%0D%0A%2B\,77837\,\\%0D%0A\hline%0D%0A125674%0D%0A\end{array}$

Exercice 9 : compléter chaque addition
a. Complétons l’addition suivante :
$\begin{array}{cccc}%0D%0A%26\,4\,%26\,7\,%26\,4\,%26\,7\,\\%0D%0A%2B\,%26\,0\,%26\,2\,%26\,5\,%26\,1\,\\%0D%0A\hline%0D%0A=\,%26\,4\,%26\,9\,%26\,9\,%26\,8\,\\%0D%0A\end{array}$

$4747\,%2B\,251\,=\,4998$

b. Complétons l’addition suivante :
$\begin{array}{cccc}%0D%0A%26\,6\,%26\,2\,%26\,4\,%26\,3\,\\%0D%0A%2B\,%26\,2\,%26\,4\,%26\,4\,%26\,6\,\\%0D%0A\hline%0D%0A=\,%26\,8\,%26\,0\,%26\,8\,%26\,4\,\\%0D%0A\end{array}$

$6243\,%2B\,2446\,=\,8084$

c. Complétons l’addition suivante :
$\begin{array}{cccc}%0D%0A%26\,5\,%26\,4\,%26\,6\,%26\,2\,\\%0D%0A%2B\,%26\,3\,%26\,0\,%26\,9\,%26\,1\,\\%0D%0A\hline%0D%0A=\,%26\,8\,%26\,7\,%26\,5\,%26\,3\,\\%0D%0A\end{array}$

$5462\,%2B\,3091\,=\,8753$

Exercice 10 : additions à trois termes
a. $\begin{array}{c%40{c%40{c%40{c%40{c}%0D%0A%26\,8\,%26\,6\,%26\,5\,%26\,8\,\\%0D%0A%2B\,%26\,4\,%26\,8\,%26\,5\,%26\,7\,\\%0D%0A%2B\,%26\,9\,%26\,8\,%26\,5\,%26\,1\,\\%0D%0A\hline%0D%0A%26\,2\,%26\,3\,%26\,2\,%26\,6\,%26\,6\,\\%0D%0A\end{array}$

b. $\begin{array}{c%40{c%40{c%40{c%40{c%40{c}%0D%0A%26\,7\,%26\,4\,%26\,3\,%26\,5\,%26\,4\,\\%0D%0A%2B\,%26\,8\,%26\,5\,%26\,9\,%26\,8\,%26\,9\,\\%0D%0A%2B\,%26\,9\,%26\,3\,%26\,2\,%26\,5\,%26\,4\,\\%0D%0A\hline%0D%0A%26\,2\,%26\,5\,%26\,3\,%26\,5\,%26\,9\,%26\,7\,\\%0D%0A\end{array}$

c. $\begin{array}{c%40{c%40{c%40{c%40{c}%0D%0A%26\,2\,%26\,5\,%26\,3\,%26\,6\,%26\,9\,\\%0D%0A%2B\,%26\,0\,%26\,0\,%26\,6\,%26\,0\,%26\,2\,\\%0D%0A%2B\,%26\,8\,%26\,3\,%26\,6\,%26\,7\,\\%0D%0A\hline%0D%0A%26\,3\,%26\,4\,%26\,3\,%26\,3\,%26\,8\,\\%0D%0A\end{array}$

Exercice 11 : calculer des sommes
$\begin{array}{ccc}%0D%0A1689\,%26\,85569\,%26\,347\,\\%0D%0A47476\,%26\,785\,%26\,9714\,\\%0D%0A967\,%26\,5444\,%26\,71032\,\\%0D%0A\end{array}$

Calcul des sommes des lignes :
$\begin{array}{rcl}%0D%0A1689\,%2B\,47476\,%2B\,967\,%26\,=\,%26\,50132\,\\%0D%0A85569\,%2B\,785\,%2B\,5444\,%26\,=\,%26\,91852\,\\%0D%0A347\,%2B\,9714\,%2B\,71032\,%26\,=\,%26\,81193\,\\%0D%0A\end{array}$

Calcul des sommes des colonnes :
$\begin{array}{rcl}%0D%0A1689\,%2B\,85569\,%2B\,347\,%26\,=\,%26\,87505\,\\%0D%0A47476\,%2B\,785\,%2B\,9714\,%26\,=\,%26\,57975\,\\%0D%0A967\,%2B\,5444\,%2B\,71032\,%26\,=\,%26\,77443\,\\%0D%0A\end{array}$

Calcul de la somme totale :
$50132\,%2B\,91852\,%2B\,81193\,=\,223177$

Exercice 12 : effectuer chaque soustraction

a.
$\begin{array}{r}%0D%0A5637\\%0D%0A-214\\%0D%0A\hline%0D%0A5423%0D%0A\end{array}$

b.
$\begin{array}{r}%0D%0A6957\\%0D%0A-3241\\%0D%0A\hline%0D%0A3716%0D%0A\end{array}$

c.
$\begin{array}{r}%0D%0A43749\\%0D%0A-21401\\%0D%0A\hline%0D%0A22348%0D%0A\end{array}$

d.
$\begin{array}{r}%0D%0A7257\\%0D%0A-631\\%0D%0A\hline%0D%0A6626%0D%0A\end{array}$

e.
$\begin{array}{r}%0D%0A94888\\%0D%0A-25666\\%0D%0A\hline%0D%0A69222%0D%0A\end{array}$

f.
$\begin{array}{r}%0D%0A65421\\%0D%0A-12630\\%0D%0A\hline%0D%0A52791%0D%0A\end{array}$

Exercice 13 : poser des soustractions
$a.\,\quad\,632\,-\,251$

$\begin{array}{r}%0D%0A632\,\\%0D%0A-\,251\,\\%0D%0A\hline%0D%0A381\,\\%0D%0A\end{array}$

$b.\,\quad\,854\,-\,249$

$\begin{array}{r}%0D%0A854\,\\%0D%0A-\,249\,\\%0D%0A\hline%0D%0A605\,\\%0D%0A\end{array}$

$c.\,\quad\,1\%3B000\,-\,695$

$\begin{array}{r}%0D%0A1\%3B000\,\\%0D%0A-\,\%3B695\,\\%0D%0A\hline%0D%0A\%3B305\,\\%0D%0A\end{array}$

Exercice 14 : compléter chaque soustraction
a.
$\begin{array}{cccc}%0D%0A5\,%26\,4\,%26\,8\,%26\,2\,\\%0D%0A-\,%26\,.\,%26\,.\,%26\,.\,\\%0D%0A\hline%0D%0A5\,%26\,2\,%26\,3\,%26\,1\,\\%0D%0A\end{array}$
$5\,-\,0\,=\,5$ \\
$4\,-\,2\,=\,2$ \\
$8\,-\,5\,=\,3$ \\
$2\,-\,1\,=\,1$

b.
$\begin{array}{ccccc}%0D%0A%26\,%26\,6\,%26\,.\,%26\,.\,\\%0D%0A-\,%26\,2\,%26\,1\,%26\,2\,%26\,5\,\\%0D%0A\hline%0D%0A.\,%26\,6\,%26\,3\,%26\,3\,%26\,3\,\\%0D%0A\end{array}$
$10\,-\,2\,=\,8$ \\
$8\,-\,5\,=\,3$ \\
$11\,-\,3\,-\,3\,-\,2$ \\
$10\,-\,3\,=\,7\,-\,3\,-\,2$

c.
$\begin{array}{cccc}%0D%0A6\,%26\,4\,%26\,.\,%26\,2\,\\%0D%0A-\,%26\,3\,%26\,.\,%26\,1\,\\%0D%0A\hline%0D%0A5\,%26\,4\,%26\,2\,%26\,0\,\\%0D%0A\end{array}$
$4\,-\,2\,=\,2$ \\
$6\,-\,3\,=\,3$ \\
$4\,-\,1\,=\,4$ \\
$5\,-\,4\,=\,1$

d.
$\begin{array}{cccc}%0D%0A6\,%26\,6\,%26\,0\,%26\,0\,\\%0D%0A-\,%26\,.\,%26\,.\,%26\,.\,\\%0D%0A\hline%0D%0A6\,%26\,2\,%26\,4\,%26\,4\,\\%0D%0A\end{array}$
$6\,-\,2\,=\,4$ \\
$8\,-\,4\,=\,4$ \\
$6\,=\,4\,=\,6\,=\,4\,-\,4\,=\,2$

e.
$\begin{array}{ccccc}%0D%0A%26\,3\,%26\,.\,%26\,.\,%26\,.\,\\%0D%0A-\,%26\,4\,%26\,5\,%26\,2\,%26\,7\,\\%0D%0A\hline%0D%0A.\,%26\,3\,%26\,3\,%26\,6\,%26\,9\,\\%0D%0A\end{array}$
$3\,-\,1\,-\,0\,-\,4\,-\,2\,=\,1$ \\
$3\,-\,4\,-\,2\,-\,2\,-\,3$

f.
$\begin{array}{ccccc}%0D%0A%26\,9\,%26\,.\,%26\,3\,%26\,8\,\\%0D%0A-\,%26\,4\,%26\,.\,%26\,3\,%26\,.\,\\%0D%0A\hline%0D%0A3\,%26\,0\,%26\,8\,%26\,8\,%26\,6\,\\%0D%0A\end{array}$
$9\,-\,3\,-\,8\,=\,4$ \\
$5\,-\,8\,-\,3\,-\,8\,=\,6$ \\
$4\,-\,3\,=\,3%0D%0A%0D%0A%3Ca\,id=%22exercice-15%22>%3C%2Fa>%3Cspan\,class=%22titrecorrection%22>Exercice\,15\,%3A\,tables\,de\,multiplications%3C%2Fspan>%0D%0A%0D%0Aa.%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F%255Cbegin%257Barray%257D%257B%257Cc%257Cc%257Cc%257Cc%257Cc%257C%257D%250D%250A%255Chline%250D%250A%2524%255Ctimes %2524%2520%2526%25205%2520%2526%25203%2520%2526%25202%2520%2526%25209%2520%255C%255C%250D%250A%255Chline%250D%250A4%2520%2526%252020%2520%2526%252012%2520%2526%25208%2520%2526%252036%2520%255C%255C%250D%250A%255Chline%250D%250A7%2520%2526%252035%2520%2526%252021%2520%2526%252014%2520%2526%252063%2520%255C%255C%250D%250A%255Chline%250D%250A6%2520%2526%252030%2520%2526%252018%2520%2526%252012%2520%2526%252054%2520%255C%255C%250D%250A%255Chline%250D%250A5%2520%2526%252025%2520%2526%252015%2520%2526%252010%2520%2526%252045%2520%255C%255C%250D%250A%255Chline%250D%250A%255Cend%257Barray%257D%22\,alt=%22\begin{array}{%7Cc%7Cc%7Cc%7Cc%7Cc%7C}%0D%0A\hline%0D%0A%24\times %24\,%26\,5\,%26\,3\,%26\,2\,%26\,9\,\\%0D%0A\hline%0D%0A4\,%26\,20\,%26\,12\,%26\,8\,%26\,36\,\\%0D%0A\hline%0D%0A7\,%26\,35\,%26\,21\,%26\,14\,%26\,63\,\\%0D%0A\hline%0D%0A6\,%26\,30\,%26\,18\,%26\,12\,%26\,54\,\\%0D%0A\hline%0D%0A5\,%26\,25\,%26\,15\,%26\,10\,%26\,45\,\\%0D%0A\hline%0D%0A\end{array}%22\,align=%22absmiddle%22\,%2F>%0D%0Ab%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F%255Cbegin%257Barray%257D%257B%257Cc%257Cc%257Cc%257Cc%257C%257D%250D%250A%255Chline%250D%250A%2524%255Ctimes %2524%2520%2526%25202%2520%2526%25203%2520%2526%25205%2520%255C%255C%250D%250A%255Chline%250D%250A6%2520%2526%252012%2520%2526%252018%2520%2526%252030%2520%255C%255C%250D%250A%255Chline%250D%250A9%2520%2526%252018%2520%2526%252027%2520%2526%252045%2520%255C%255C%250D%250A%255Chline%250D%250A4%2520%2526%25208%2520%2526%252012%2520%2526%252020%2520%255C%255C%250D%250A%255Chline%250D%250A7%2520%2526%252014%2520%2526%252021%2520%2526%252035%2520%255C%255C%250D%250A%255Chline%250D%250A%255Cend%257Barray%257D%22\,alt=%22\begin{array}{%7Cc%7Cc%7Cc%7Cc%7C}%0D%0A\hline%0D%0A%24\times %24\,%26\,2\,%26\,3\,%26\,5\,\\%0D%0A\hline%0D%0A6\,%26\,12\,%26\,18\,%26\,30\,\\%0D%0A\hline%0D%0A9\,%26\,18\,%26\,27\,%26\,45\,\\%0D%0A\hline%0D%0A4\,%26\,8\,%26\,12\,%26\,20\,\\%0D%0A\hline%0D%0A7\,%26\,14\,%26\,21\,%26\,35\,\\%0D%0A\hline%0D%0A\end{array}%22\,align=%22absmiddle%22\,%2F>%0D%0Ac\,.%0D%0A%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F%255Cbegin%257Barray%257D%257B%257Cc%257Cc%257Cc%257Cc%257C%257D%250D%250A%255Chline%250D%250A%2524%255Ctimes %2524%2520%2526%25208%2520%2526%25209%2520%2526%25207%2520%255C%255C%250D%250A%255Chline%250D%250A8%2520%2526%252064%2520%2526%252072%2520%2526%252056%2520%255C%255C%250D%250A%255Chline%250D%250A6%2520%2526%252048%2520%2526%252054%2520%2526%252042%2520%255C%255C%250D%250A%255Chline%250D%250A9%2520%2526%252072%2520%2526%252081%2520%2526%252063%2520%255C%255C%250D%250A%255Chline%250D%250A7%2520%2526%252056%2520%2526%252063%2520%2526%252049%2520%255C%255C%250D%250A%255Chline%250D%250A%255Cend%257Barray%257D%22\,alt=%22\begin{array}{%7Cc%7Cc%7Cc%7Cc%7C}%0D%0A\hline%0D%0A%24\times %24\,%26\,8\,%26\,9\,%26\,7\,\\%0D%0A\hline%0D%0A8\,%26\,64\,%26\,72\,%26\,56\,\\%0D%0A\hline%0D%0A6\,%26\,48\,%26\,54\,%26\,42\,\\%0D%0A\hline%0D%0A9\,%26\,72\,%26\,81\,%26\,63\,\\%0D%0A\hline%0D%0A7\,%26\,56\,%26\,63\,%26\,49\,\\%0D%0A\hline%0D%0A\end{array}%22\,align=%22absmiddle%22\,%2F>%0D%0A%3Ca\,id=%22exercice-16%22>%3C%2Fa>%3Cspan\,class=%22titrecorrection%22>Exercice\,16\,%3A\,effectuer\,des\,multiplications%3C%2Fspan>%0D%0Aa.%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F5489%2520%255Ctimes %25204%2520%253D%252021956%22\,alt=%225489\,\times \,4\,=\,21956%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0Ab.%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F5489%2520%255Ctimes %25205%2520%253D%252027445%22\,alt=%225489\,\times \,5\,=\,27445%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0Ac.%0D%0A%3Cimg\,decoding=%22async%22\,class=%22LatexImg%22\,src=%22https%3A%2F%2Fmaths-pdf.fr%2Fcgi-bin%2Fmimetex.cgi%3F5489%2520%255Ctimes %25209%2520%253D%252049401%22\,alt=%225489\,\times \,9\,=\,49401%22\,align=%22absmiddle%22\,%2F>%0D%0A%0D%0A%3Ca\,id=%22exercice-17%22>%3C%2Fa>%3Cspan\,class=%22titrecorrection%22>Exercice\,17\,%3A\,poser\,des\,multiplications%3C%2Fspan>%0D%0A\(\,a.\,\quad\,6372\,\times \,3$ Exercice 15 : tables de multiplications

a.
$\begin{array}{%7Cc%7Cc%7Cc%7Cc%7Cc%7C}%0D%0A\hline%0D%0A%24\times %24\,%26\,5\,%26\,3\,%26\,2\,%26\,9\,\\%0D%0A\hline%0D%0A4\,%26\,20\,%26\,12\,%26\,8\,%26\,36\,\\%0D%0A\hline%0D%0A7\,%26\,35\,%26\,21\,%26\,14\,%26\,63\,\\%0D%0A\hline%0D%0A6\,%26\,30\,%26\,18\,%26\,12\,%26\,54\,\\%0D%0A\hline%0D%0A5\,%26\,25\,%26\,15\,%26\,10\,%26\,45\,\\%0D%0A\hline%0D%0A\end{array}$
b
$\begin{array}{%7Cc%7Cc%7Cc%7Cc%7C}%0D%0A\hline%0D%0A%24\times %24\,%26\,2\,%26\,3\,%26\,5\,\\%0D%0A\hline%0D%0A6\,%26\,12\,%26\,18\,%26\,30\,\\%0D%0A\hline%0D%0A9\,%26\,18\,%26\,27\,%26\,45\,\\%0D%0A\hline%0D%0A4\,%26\,8\,%26\,12\,%26\,20\,\\%0D%0A\hline%0D%0A7\,%26\,14\,%26\,21\,%26\,35\,\\%0D%0A\hline%0D%0A\end{array}$
c .

$\begin{array}{%7Cc%7Cc%7Cc%7Cc%7C}%0D%0A\hline%0D%0A%24\times %24\,%26\,8\,%26\,9\,%26\,7\,\\%0D%0A\hline%0D%0A8\,%26\,64\,%26\,72\,%26\,56\,\\%0D%0A\hline%0D%0A6\,%26\,48\,%26\,54\,%26\,42\,\\%0D%0A\hline%0D%0A9\,%26\,72\,%26\,81\,%26\,63\,\\%0D%0A\hline%0D%0A7\,%26\,56\,%26\,63\,%26\,49\,\\%0D%0A\hline%0D%0A\end{array}$
Exercice 16 : effectuer des multiplications
a.
$5489\,\times \,4\,=\,21956$

b.
$5489\,\times \,5\,=\,27445$

c.
$5489\,\times \,9\,=\,49401$

Exercice 17 : poser des multiplications
\( a. \quad 6372 \times 3″ align= »absmiddle » />

$\begin{array}{c\,c\,c\,c}%0D%0A6\,%26\,3\,%26\,7\,%26\,2\,\\%0D%0A\times \,%26\,%26\,%26\,3\,\\%0D%0A\hline%0D%0A1\,%26\,9\,%26\,1\,%26\,1\,%26\,6\,\\%0D%0A\end{array}$

Ainsi, $6372\,\times \,3\,=\,19116$ .

$b.\,\quad\,6372\,\times \,7$

$\begin{array}{c\,c\,c\,c}%0D%0A6\,%26\,3\,%26\,7\,%26\,2\,\\%0D%0A\times \,%26\,%26\,%26\,7\,\\%0D%0A\hline%0D%0A4\,%26\,4\,%26\,6\,%26\,0\,%26\,4\,\\%0D%0A\end{array}$

Ainsi, $6372\,\times \,7\,=\,44604$ .

$c.\,\quad\,6372\,\times \,8$

$\begin{array}{c\,c\,c\,c}%0D%0A6\,%26\,3\,%26\,7\,%26\,2\,\\%0D%0A\times \,%26\,%26\,%26\,8\,\\%0D%0A\hline%0D%0A5\,%26\,0\,%26\,9\,%26\,7\,%26\,6\,\\%0D%0A\end{array}$

Ainsi, $6372\,\times \,8\,=\,50976$ .

Exercice 18 : effectuer des multiplications
Correction de l’exercice :

a.
$\begin{array}{c}%0D%0A\phantom{0}69\,\\%0D%0A\times \,\phantom{0}54\,\\%0D%0A\hline%0D%0A\phantom{0}276\,\quad\,(69\,%C3%97\,4)\,\\%0D%0A%2B\,3450\,\quad\,(69\,%C3%97\,50%2C\,decale\,d'un\,rang)\,\\%0D%0A\hline%0D%0A3726\,\\%0D%0A\end{array}$

b.
$\begin{array}{c}%0D%0A728\,\\%0D%0A\times \,31\,\\%0D%0A\hline%0D%0A\phantom{0}728\,\quad\,(728\,%C3%97\,1)\,\\%0D%0A%2B21840\,\quad\,(728\,%C3%97\,30%2C\,decale\,d'un\,rang)\,\\%0D%0A\hline%0D%0A22568\,\\%0D%0A\end{array}$

c.
$\begin{array}{c}%0D%0A573\,\\%0D%0A\times \,89\,\\%0D%0A\hline%0D%0A\phantom{0}5157\,\quad\,(573\,%C3%97\,9)\,\\%0D%0A%2B45840\,\quad\,(573\,%C3%97\,80%2C\,decale\,d'un\,rang)\,\\%0D%0A\hline%0D%0A51597\,\\%0D%0A\end{array}$

Exercice 19 : calculer des multiplications
$a.\,\quad\,46\,\times \,27\,\\%0D%0A46\,\\%0D%0A\times \,27\,\\%0D%0A\hline\,\\%0D%0A322\,\quad\,\quad\,(46\,%C3%97\,7)\,\\%0D%0A920\,%2B\,\quad\,\quad\,(46%C3%9720)\,\\%0D%0A\hline\,\\%0D%0A1242$

$b.\,\quad\,328\,\times \,609\,\\%0D%0A328\,\\%0D%0A\times \,609\,\\%0D%0A\hline\,\\%0D%0A2952\,\quad\,\quad\,(328\,%C3%97\,9)\,\\%0D%0A0\,\\%0D%0A19680\,%2B\,\quad\,\quad\,(328\,%C3%97\,600)\,\\%0D%0A\hline\,\\%0D%0A199752$

$c.\,\quad\,155\,\times \,88\,\\%0D%0A155\,\\%0D%0A\times \,88\,\\%0D%0A\hline\,\\%0D%0A1240\,\quad\,\quad\,(155\,%C3%97\,8)\,\\%0D%0A1240\,%2B\,\quad\,\quad\,(155\,%C3%97\,80)\,\\%0D%0A\hline\,\\%0D%0A13640$

Exercice 20 : colorier un chemin
Pour aller de la case 175 à la case 125 en ne passant que par des multiples de 25, nous allons suivre le chemin des cases multiples de 25 de façon continue et adjacente. Le chemin possible est le suivant :

Chemin :
$175\,\to\,350\,\to\,375\,\to\,500\,\to\,475\,\to\,450\,\to\,125$

En bleu, le chemin est :
$175\,\to\,350\,\to\,375\,\to\,500\,\to\,475\,\to\,450\,\to\,125$

Soit en LaTeX :

$\begin{array}{ccccccc}%0D%0A%26\,%26\,%26\,175\,%26\,%26\,%26\,\\%0D%0A%26\,%26\,115\,%26\,%26\,\color{blue}350\,%26\,%26\,\\%0D%0A%26\,195\,%26\,%26\,240\,%26\,%26\,225\,%26\,\\%0D%0A370\,%26\,%26\,205\,%26\,%26\,\color{blue}375\,%26\,%26\,\\%0D%0A%26\,420\,%26\,%26\,445\,%26\,%26\,325\,%26\,\\%0D%0A135\,%26\,%26\,\color{blue}500\,%26\,%26\,\colo{blue}475\,%26\,%26\,255\,\\%0D%0A%26\,420\,%26\,%26\,445\,%26\,%26\,325\,%26\,\\%0D%0A155\,%26\,%26\,\color{blue}450\,%26\,%26\,150\,%26\,%26\,\color{blue}125\,\\%0D%0A\end{array}$

Ce trace montre visuellement le chemin à suivre pour atteindre la case cible en respectant les conditions du problème.

Voir Exercices 11 à 20 ...

Exercice 21 : effectuer une division
a.
$\begin{array}{r%7Cl}%0D%0A5372\,%26\,2\,\\%0D%0A\hline%0D%0A%26\,2686\,\\%0D%0A\end{array}$
Donc, $Q\,=\,2686$ et $R\,=\,0$ .

b.
$\begin{array}{r%7Cl}%0D%0A1973\,%26\,3\,\\%0D%0A\hline%0D%0A%26\,657\,\\%0D%0A\end{array}$
Donc, $Q\,=\,657$ et $R\,=\,2$ .

c.
$\begin{array}{r%7Cl}%0D%0A3159\,%26\,4\,\\%0D%0A\hline%0D%0A%26\,789\,\\%0D%0A\end{array}$
Donc, $Q\,=\,789$ et $R\,=\,3$ .

Exercice 22 : poser des divisions
a.
Les nombres sont : $4%2C\,2%2C\,5%2C\,5$ .

Pour trouver (la moyenne) et (l’étendue) :
$Q\,=\,\frac{\sum_{i=1}^n\,a_i}{n}\,=\,\frac{4\,%2B\,2\,%2B\,5\,%2B\,5}{4}\,=\,\frac{16}{4}\,=\,4$
L’étendue est la différence entre la valeur maximale et la valeur minimale :
$R\,=\,\max(a_i)\,-\,\min(a_i)\,=\,5\,-\,2\,=\,3$

Donc, $Q\,=\,4$ et $R\,=\,3$ .

b.
Les nombres sont : $5%2C\,9%2C\,8%2C\,1%2C\,6$ .

Pour trouver (la moyenne) et (l’étendue) :
$Q\,=\,\frac{\sum_{i=1}^n\,b_i}{n}\,=\,\frac{5\,%2B\,9\,%2B\,8\,%2B\,1\,%2B\,6}{5}\,=\,\frac{29}{5}\,=\,5.8$
L’étendue est la différence entre la valeur maximale et la valeur minimale :
$R\,=\,\max(b_i)\,-\,\min(b_i)\,=\,9\,-\,1\,=\,8$

Donc, $Q\,=\,5.8$ et $R\,=\,8$ .

c.
Les nombres sont : $3%2C\,0%2C\,2%2C\,1%2C\,7$ .

Pour trouver (la moyenne) et (l’étendue) :
$Q\,=\,\frac{\sum_{i=1}^n\,c_i}{n}\,=\,\frac{3\,%2B\,0\,%2B\,2\,%2B\,1\,%2B\,7}{5}\,=\,\frac{13}{5}\,=\,2.6$
L’étendue est la différence entre la valeur maximale et la valeur minimale :
$R\,=\,\max(c_i)\,-\,\min(c_i)\,=\,7\,-\,0\,=\,7$

Donc, $Q\,=\,2.6$ et $R\,=\,7$ .

Exercice 23 : calculer chaque division
a. $\frac{5371}{11}\,=\,488$ avec un reste de \newline
$Q\,=\,488\,\\,%3B\,\\,R\,=\,3$

b. $\frac{15511}{11}\,=\,1419$ avec un reste de \newline
$Q\,=\,1419\,\\,%3B\,\\,R\,=\,2$

c. $\frac{626661}{11}\,=\,56969$ avec un reste de \newline
$Q\,=\,56969\,\\,%3B\,\\,R\,=\,2$

Exercice 24 : compléter la table du 15 puis effectuer les divisions
Pour compléter la table de multiplication de 15:

$\begin{align%2A}%0D%0A15\,\times \,1\,%26=\,15\,\\%0D%0A15\,\times \,2\,%26=\,30\,\\%0D%0A15\,\times \,3\,%26=\,45\,\\%0D%0A15\,\times \,4\,%26=\,60\,\\%0D%0A15\,\times \,5\,%26=\,75\,\\%0D%0A15\,\times \,6\,%26=\,90\,\\%0D%0A15\,\times \,7\,%26=\,105\,\\%0D%0A15\,\times \,8\,%26=\,120\,\\%0D%0A15\,\times \,9\,%26=\,135\,\\%0D%0A\end{align%2A}$

Effectuons maintenant les divisions pour l’exercice.

Pour a) $\frac{537215}{15}$ :

$\begin{align%2A}%0D%0A537215\,: \,15\,%26=\,35814\,\quad\,reste\,\,5\,\\%0D%0A\end{align%2A}$

Donc,

$Q\,=\,35814\,\quad\,%3B\,\quad\,R\,=\,5$

Pour b) $\frac{6118615}{15}$ :

$\begin{align%2A}%0D%0A6118615\,: \,15\,%26=\,407907\,\quad\,reste\,\,0\,\\%0D%0A\end{align%2A}$

Donc,

$Q\,=\,407907\,\quad\,%3B\,\quad\,R\,=\,0$

Exercice 25 : compléter la table du 15 puis effectuer les divisions
$\begin{array}{c%7Cc}%0D%0ATable\,de\,25\,%26\,Resultat\,\\%0D%0A\hline%0D%0A25\,\times \,1\,%26\,25\,\\%0D%0A25\,\times \,2\,%26\,50\,\\%0D%0A25\,\times \,3\,%26\,75\,\\%0D%0A25\,\times \,4\,%26\,100\,\\%0D%0A25\,\times \,5\,%26\,125\,\\%0D%0A25\,\times \,6\,%26\,150\,\\%0D%0A25\,\times \,7\,%26\,175\,\\%0D%0A25\,\times \,8\,%26\,200\,\\%0D%0A25\,\times \,9\,%26\,225\,\\%0D%0A\end{array}$

Pour les divisions, nous allons diviser chaque nombre par 25 et trouver le quotient (Q) et le reste (R) :

a. 537225 ÷ 25 :
$\begin{array}{r}%0D%0AQ\,=\,537225\,%C3%B7\,25\,=\,21489\,\\%0D%0AR\,=\,0\,\\%0D%0A\end{array}$

Donc, pour a :
$Q\,=\,21489\,%3B\,\quad\,R\,=\,0$

b. 61186525 ÷ 25 :
$\begin{array}{r}%0D%0AQ\,=\,61186525\,%C3%B7\,25\,=\,2447461\,\\%0D%0AR\,=\,0\,\\%0D%0A\end{array}$

Donc, pour b :
$Q\,=\,2447461\,%3B\,\quad\,R\,=\,0$

Exercice 26 : addition, soustraction, multiplication et division
a. $54\%2C895\,%2B\,89\%2C546\,=\,144\%2C441$

b. $63\%2C604\,%2B\,97\%2C442\,=\,161\%2C046$

c. $36\%2C000\,-\,14\%2C023\,=\,21\%2C977$

d. $95\%2C632\,-\,46\%2C672\,=\,48\%2C960$

e. $562\,\times \,41\,=\,23\%2C042$

f. $498\,\times \,73\,=\,36\%2C354$

g. $6\%2C356\,: \,4\,=\,1\%2C589$

h. $4\%2C623\,: \,5\,=\,924%2C6$

a. $844\%2C211\,%2B\,73\%2C856\,=\,918\%2C067$

b. $257\%2C624\,%2B\,2\%2C507\,=\,260\%2C131$

c. $124\%2C809\,-\,19\%2C910\,=\,104\%2C899$

d. $568\%2C256\,-\,8\%2C967\,=\,559\%2C289$

e. $6\%2C308\,\times \,507\,=\,3\%2C196\%2C956$

f. $8\%2C715\,\times \,324\,=\,2\%2C825\%2C460$

g. $12\%2C769\,: \,25\,=\,510%2C76$

h. $52\%2C824\,: \,50\,=\,1\%2C056%2C48$

Exercice 27 : problèmes à résoudre
a. La grenouille Froggy doit effectuer 54 sauts de 25 cm pour atteindre sa mare. Quelle distance la sépare de cette mare ?

La distance qui sépare Froggy de la mare est donnée par le produit du nombre de sauts et de la distance de chaque saut. Ainsi :
$d\,=\,54\,\times \,25$
Calculons le produit :
$d\,=\,1350\,\,cm$

Donc, la grenouille Froggy doit parcourir une distance de $1350\,\,cm$ .

b. Son amie Rana fait des sauts d’au plus 9 cm. Elle veut atteindre un moustique situé à 157 cm d’elle. Combien de sauts (au minimum) devra-t-elle effectuer pour atteindre le moustique ?

Le nombre minimum de sauts est donné par :
$n\,=\,\lceil\,\frac{157}{9}\,\rceil$
où $\lceil\,x\,\rceil$ représente le plafond de (c’est-à-dire le plus petit entier supérieur ou égal à ).
Calculons cette valeur :
$\frac{157}{9}\,\approx\,17.4444$
$n\,=\,\lceil\,17.4444\,\rceil\,=\,18$

Donc, Rana devra effectuer au minimum sauts pour atteindre le moustique.

Exercice 28 : problème de l’ascenceur

[a.] On nous donne les poids des six personnes : 82 kg, 95 kg, 86 kg, 71 kg, 67 kg et 59 kg.

Le poids total est :
$82\,%2B\,95\,%2B\,86\,%2B\,71\,%2B\,67\,%2B\,59\,=\,460\,\%2C\,kg$

La charge maximale de l’ascenseur est de 450 kg pour 6 personnes. Donc, ces six personnes ne peuvent pas monter ensemble dans cet ascenseur car leur poids total (460 kg) dépasse la charge maximale.

[b.] On nous donne les poids de cinq autres personnes : 74 kg, 88 kg, 63 kg, 79 kg et 62 kg.

Le poids total est :
$74\,%2B\,88\,%2B\,63\,%2B\,79\,%2B\,62\,=\,366\,\%2C\,kg$

Pour ne pas dépasser la charge maximale de 450 kg avec six personnes :
$450\,-\,366\,=\,84\,\%2C\,kg$

Donc, la sixième personne ne doit pas dépasser 84 kg pour que le poids total soit inférieur ou égal à 450 kg.

[c.] La charge maximale de l’ascenseur est de 450 kg pour 6 personnes. Le poids moyen d’une personne est donc :
$\frac{450}{6}\,=\,75\,\%2C\,kg$

[d.] On nous demande si sept personnes de 64 kg chacune peuvent monter ensemble dans cet ascenseur.

Le poids total de sept personnes de 64 kg est :
$7\,\times \,64\,=\,448\,\%2C\,kg$

Cependant, la charge maximale est de 450 kg, mais pour seulement 6 personnes. Même si le poids total ne dépasse pas 450 kg, le nombre maximal de personnes admis est de 6. Donc, sept personnes de 64 kg ne peuvent pas monter ensemble dans cet ascenseur.

Exercice 29 : compléter ces demi-droites graduées
Pour corriger ces demi-droites graduées, déterminons d’abord l’intervalle entre chaque gradation.

a.
L’intervalle entre 0 et 10 est de 10 unités et il y a 5 segments, donc chaque segment représente $\frac{10}{5}\,=\,2$ unités.

\begin{align*}
\text{1ère graduation: } 0 + 2 \times 1 = 2 \\
\text{2ème graduation: } 0 + 2 \times 2 = 4 \\
\text{3ème graduation: } 0 + 2 \times 3 = 6 \\
\text{4ème graduation: } 0 + 2 \times 4 = 8
\end{align*}

La graduation complète est: $0%2C\,2%2C\,4%2C\,6%2C\,8%2C\,10$ .

b.
L’intervalle entre 0 et 300 est de 300 unités et il y a 3 segments, donc chaque segment représente $\frac{300}{3}\,=\,100$ unités.

\begin{align*}
\text{1ère graduation: } 0 + 100 \times 1 = 100 \\
\text{2ème graduation: } 0 + 100 \times 2 = 200
\end{align*}

La graduation complète est: $0%2C\,100%2C\,200%2C\,300$ .

c.
L’intervalle entre 340 et 350 est de 10 unités et il y a 5 segments, donc chaque segment représente $\frac{10}{5}\,=\,2$ unités.

\begin{align*}
\text{1ère graduation: } 340 + 2 \times 1 = 342 \\
\text{2ème graduation: } 340 + 2 \times 2 = 344 \\
\text{3ème graduation: } 340 + 2 \times 3 = 346 \\
\text{4ème graduation: } 340 + 2 \times 4 = 348
\end{align*}

La graduation complète est: $340%2C\,342%2C\,344%2C\,346%2C\,348%2C\,350$ .

d.
L’intervalle entre 1000 et 1010 est de 10 unités et il y a 5 segments, donc chaque segment représente $\frac{10}{5}\,=\,2$ unités.

\begin{align*}
\text{1ère graduation: } 1000 + 2 \times 1 = 1002 \\
\text{2ème graduation: } 1000 + 2 \times 2 = 1004 \\
\text{3ème graduation: } 1000 + 2 \times 3 = 1006 \\
\text{4ème graduation: } 1000 + 2 \times 4 = 1008
\end{align*}

La graduation complète est: $1000%2C\,1002%2C\,1004%2C\,1006%2C\,1008%2C\,1010$ .