Nombres en Ecriture Fractionnaire

Fiche relue en 2016.

exercice 1

Calculer les expressions suivantes (penser à simplifier si possible) :

$\begin{array}{lllll} A=\dfrac{7}{3}+\dfrac{4}{3}&\hspace{25pt}&B=\dfrac{5}{7}+\dfrac{8}{7}&\hspace{25pt}&C=\dfrac{3}{4}+\dfrac{7}{4}\\ \\D=\dfrac{4}{5}+\dfrac{3}{10}&\hspace{75pt}&E=\dfrac{7}{15}+\dfrac{10}{5}&\hspace{75pt}&F=\dfrac{11}{9}+\dfrac{4}{9}\\ \\G=\dfrac{9}{7}-\dfrac{5}{7}&&H=\dfrac{27}{11}-\dfrac{13}{11}&&I=\dfrac{13}{5}-\dfrac{7}{5}\\ \\J=\dfrac{9}{4}-\dfrac{3}{4}&&K=\dfrac{19}{15}-\dfrac{14}{15}&&L=\dfrac{26}{35}-\dfrac{12}{35}\\ \\M=\dfrac{1}{3}-\dfrac{2}{9}&&N=\dfrac{4}{3}-\dfrac{7}{12}&&O=\dfrac{28}{15}-\dfrac{2}{5}\\ \\P=\dfrac{25}{4}-\dfrac{3}{2}+\dfrac{7}{4}&&Q=\dfrac{5}{3}-\dfrac{2}{9}-\dfrac{1}{3}&&R=\dfrac{7}{28}-\dfrac{1}{7}+\dfrac{5}{7}\\ \end{array}$

exercice 2

Calculer les produits suivants :

$\begin{array}{lllll} \\A=\dfrac{4}{7}\times\dfrac{3}{5}&\hspace{50pt}&B=\dfrac{7}{11}\times\dfrac{4}{3}&\hspace{50pt}&C=\dfrac{5}{4}\times\dfrac{13}{2}\\ \\D=\dfrac{1}{2}\times\dfrac{3}{5}&&E=15\times\dfrac{2}{7}&&F=\dfrac{5}{3}\times20\\ \end{array}$

exercice 3

Calculer les produits suivants (penser à simplifier) :

$\begin{array}{lllll} \\A=\dfrac{4}{7}\times\dfrac{21}{5}&\hspace{50pt}&B=\dfrac{5}{4}\times\dfrac{2}{7}&\hspace{50pt}&C=\dfrac{3}{35}\times\dfrac{28}{21}\\ \\D=\dfrac{3}{7}\times\dfrac{56}{9}&&E=\dfrac{10}{13}\times\dfrac{39}{15}&&F=\dfrac{10}{19}\times\dfrac{38}{35}\\ \end{array}$

exercice 4

Sarah mange $\dfrac{3}{7}$ d'une tarte le midi et les $\dfrac{3}{4}$ du reste le soir.
Quelle fraction de la tarte a été mangée le soir ?

exercice 5

Calculer les expressions suivantes :

$\begin{array}{lll} A=\dfrac{34}{7}-\dfrac{3}{14}\times\dfrac{2}{3}&\hspace{50pt}&B=\dfrac{21}{4}-\dfrac{7}{4}+\dfrac{8}{18}\times\dfrac{9}{16}\\ \\C=\dfrac{1}{7}-\dfrac{4}{49}+\dfrac{5}{7}\times\dfrac{30}{25}&\hspace{50pt}&D=\left(\dfrac{4}{5}-\dfrac{1}{25}+\dfrac{3}{5}\right)\times\dfrac{35}{18}\\ \end{array}$

Voir la correction

exercice 1

$\begin{array}{lllll} A=\dfrac{7}{3}+\dfrac{4}{3}&\hspace{50pt}&B=\dfrac{5}{7}+\dfrac{8}{7}&\hspace{50pt}&C=\dfrac{3}{4}+\dfrac{7}{4}\\ \\A=\dfrac{7+4}{3}&&B=\dfrac{5+8}{7}&&C=\dfrac{3+7}{4}\\ \\A=\dfrac{11}{3}&&B=\dfrac{13}{7}&&C=\dfrac{10}{4}\\ \\&&&&C=\dfrac{2\times5}{2\times 2}\\ \\&&&&C=\dfrac{5}{2}\\\ \end{array}$

$\begin{array}{lllll} D=\dfrac{4}{5}+\dfrac{3}{10}&\hspace{50pt}&E=\dfrac{7}{15}+\dfrac{10}{5}&\hspace{50pt}&F=\dfrac{11}{9}+\dfrac{4}{9}\\ \\D=\dfrac{4\times2}{5\times2}+\dfrac{3}{10}&&E=\dfrac{7}{15}+\dfrac{10\times3}{5\times3}&&F=\dfrac{11+4}{9}\\ \\D=\dfrac{8}{10}+\dfrac{3}{10}&&E=\dfrac{7}{15}+\dfrac{30}{15}&&F=\dfrac{15}{9}\\ \\D=\dfrac{8+3}{10}&&E=\dfrac{7+30}{15}&&F=\dfrac{5\times3}{3\times3}\\ \\D=\dfrac{11}{10}&&E=\dfrac{37}{15}&&F=\dfrac{5}{3}\\ \end{array}$

$\begin{array}{lllll} G=\dfrac{9}{7}-\dfrac{5}{7}&\hspace{50pt}&H=\dfrac{27}{11}-\dfrac{13}{11}&\hspace{50pt}&I=\dfrac{13}{5}-\dfrac{7}{5}\\ \\G=\dfrac{9-5}{7}&&H=\dfrac{27-13}{11}&&I=\dfrac{13-7}{5}\\ \\G=\dfrac{4}{7}&&H=\dfrac{14}{11}&&I=\dfrac{6}{5}\\ \end{array}$

$\begin{array}{lllll} J=\dfrac{9}{4}-\dfrac{3}{4}&\hspace{50pt}&K=\dfrac{19}{15}-\dfrac{14}{15}&\hspace{50pt}&L=\dfrac{26}{35}-\dfrac{12}{35}\\ \\J=\dfrac{9-3}{4}&&K=\dfrac{19-14}{15}&&L=\dfrac{26-12}{35}\\ \\J=\dfrac{6}{4}&&K=\dfrac{5}{15}&&L=\dfrac{14}{35}\\ \\J=\dfrac{2\times3}{2\times2}&&K=\dfrac{5\times1}{5\times3}&&L=\dfrac{2\times7}{5\times7}\\ \\J=\dfrac{3}{2}&&K=\dfrac{1}{3}&&L=\dfrac{2}{5}\\ \end{array}$

$\begin{array}{lllll} M=\dfrac{1}{3}-\dfrac{2}{9}&\hspace{50pt}&N=\dfrac{4}{3}-\dfrac{7}{12}&\hspace{50pt}&O=\dfrac{28}{15}-\dfrac{2}{5}\\ \\M=\dfrac{1\times3}{3\times3}-\dfrac{2}{9}&&N=\dfrac{4\times4}{3\times4}-\dfrac{7}{12}&&O=\dfrac{28}{15}-\dfrac{2\times3}{5\times3}\\ \\M=\dfrac{3}{9}-\dfrac{2}{9}&&N=\dfrac{16}{12}-\dfrac{7}{12}&&O=\dfrac{28}{15}-\dfrac{6}{15}\\ \\M=\dfrac{3-2}{9}&&N=\dfrac{16-7}{12}&&O=\dfrac{28-6}{15}\\ \\M=\dfrac{1}{9}&&N=\dfrac{9}{12}&&O=\dfrac{22}{15}\\ \\&&N=\dfrac{3\times3}{3\times4}&&\\ \\&&N=\dfrac{3}{4}&&\\ \end{array}$

$\begin{array}{lllll} P=\dfrac{25}{4}-\dfrac{3}{2}+\dfrac{7}{4}&\hspace{50pt}&Q=\dfrac{5}{3}-\dfrac{2}{9}-\dfrac{1}{3}&\hspace{50pt}&R=\dfrac{7}{28}-\dfrac{1}{7}+\dfrac{5}{7}\\ \\P=\dfrac{25}{4}-\dfrac{3\times2}{2\times2}+\dfrac{7}{4}&&Q=\dfrac{5\times3}{3\times3}-\dfrac{2}{9}-\dfrac{1\times3}{3\times3}&&R=\dfrac{7}{28}-\dfrac{1\times4}{7\times4}+\dfrac{5\times4}{7\times4}\\ \\P=\dfrac{25}{4}-\dfrac{6}{4}+\dfrac{7}{4}&&Q=\dfrac{15}{9}-\dfrac{2}{9}-\dfrac{3}{9}&&R=\dfrac{7}{28}-\dfrac{4}{28}+\dfrac{20}{28}\\ \\P=\dfrac{25-6+7}{4}&&Q=\dfrac{15-2-3}{9}&&R=\dfrac{7-4+20}{28}\\ \\P=\dfrac{26}{4}&&Q=\dfrac{10}{9}&&R=\dfrac{23}{28}\\ \\P=\dfrac{2\times13}{2\times2}&&&&\\ \\P=\dfrac{13}{2}&&&&\\ \end{array}$

exercice 2

$\begin{array}{lllll} A=\dfrac{4}{7}\times\dfrac{3}{5}&\hspace{50pt}&B=\dfrac{7}{11}\times\dfrac{4}{3}&\hspace{50pt}&C=\dfrac{5}{4}\times\dfrac{13}{2}\\ \\A=\dfrac{4\times3}{7\times5}&&B=\dfrac{7\times4}{11\times3}&&C=\dfrac{5\times13}{4\times2}\\ \\A=\dfrac{12}{35}&&B=\dfrac{28}{33}&&C=\dfrac{65}{8}\\ \end{array}$

$\begin{array}{lllll} D=\dfrac{1}{2}\times\dfrac{3}{5}&\hspace{50pt}&E=15\times\dfrac{2}{7}&\hspace{50pt}&F=\dfrac{5}{3}\times20\\ \\D=\dfrac{1\times3}{2\times5}&&E=\dfrac{2\times15}{7}&&F=\dfrac{5\times20}{3}\\ \\D=\dfrac{3}{10}&&E=\dfrac{30}{7}&&F=\dfrac{100}{3}\\ \end{array}$

exercice 3

$\begin{array}{lllll} A=\dfrac{4}{7}\times\dfrac{21}{5}&\hspace{50pt}&B=\dfrac{5}{4}\times\dfrac{2}{7}&\hspace{50pt}&C=\dfrac{3}{35}\times\dfrac{28}{21}\\ \\A=\dfrac{4\times21}{7\times5}&&B=\dfrac{5\times2}{4\times7}&&C=\dfrac{3\times28}{35\times21}\\ \\A=\dfrac{4\times7\times3}{7\times5}&&B=\dfrac{5\times2}{2\times2\times7}&&C=\dfrac{3\times7\times4}{7\times5\times7\times3}\\ \\A=\dfrac{4\times3}{5}&&B=\dfrac{5}{2\times7}&&C=\dfrac{4}{5\times7}\\ \\A=\dfrac{12}{5}&&B=\dfrac{5}{14}&&C=\dfrac{4}{35}\\ \end{array}$

$\begin{array}{lllll} D=\dfrac{3}{7}\times\dfrac{56}{9}&\hspace{50pt}&E=\dfrac{10}{13}\times\dfrac{39}{15}&\hspace{50pt}&F=\dfrac{10}{19}\times\dfrac{38}{35}\\ \\D=\dfrac{3\times56}{7\times9}&&E=\dfrac{10\times39}{13\times15}&&F=\dfrac{10\times38}{19\times35}\\ \\D=\dfrac{3\times8\times7}{7\times3\times3}&&E=\dfrac{5\times2\times13\times3}{13\times5\times3}&&F=\dfrac{2\times5\times19\times2}{19\times7\times5}\\ \\D=\dfrac{8}{3}&&E=\dfrac{2}{1}&&F=\dfrac{2\times2}{7}\\ &&E=2&&F=\dfrac{4}{7}\\ \end{array}$

exercice 4

Le soir, il reste $1 - \dfrac{3}{7} = \dfrac{7}{7} - \dfrac{3}{7} = \dfrac{7 - 3}{7} = \dfrac{4}{7}$ de la tarte.
Fraction de la tarte mangée le soir :

$\dfrac{4}{7}\times\dfrac{3}{4} = \dfrac{4 \times 3}{7 \times 4} = \dfrac{3}{7}$
Le soir, Sarah a mangé les $\dfrac{3}{7}$ de la tarte.

exercice 5

$\begin{array}{lll} A=\dfrac{34}{7}-\dfrac{3}{14}\times\dfrac{2}{3}&\hspace{50pt}&B=\dfrac{21}{4}-\dfrac{7}{4}+\dfrac{8}{18}\times\dfrac{9}{16}\\ \\A=\dfrac{34}{7}-\dfrac{3\times2}{14\times3}&&B=\dfrac{21}{4}-\dfrac{7}{4}+\dfrac{8\times9}{18\times16}\\ \\A=\dfrac{34}{7}-\dfrac{3\times2}{7\times2\times3}&&B=\dfrac{21}{4}-\dfrac{7}{4}+\dfrac{4\times2\times9}{9\times2\times4\times4}\\ \\A=\dfrac{34}{7}-\dfrac{1}{7}&&B=\dfrac{21}{4}-\dfrac{7}{4}+\dfrac{1}{4}\\ \\A=\dfrac{34-1}{7}&&B=\dfrac{21-7+1}{4}\\ \\A=\dfrac{33}{7}&&B=\dfrac{15}{4}\\ \end{array}$

$\begin{array}{lll} C=\dfrac{1}{7}-\dfrac{4}{49}+\dfrac{5}{7}\times\dfrac{30}{25}&\hspace{50pt}&D=\left(\dfrac{4}{5}-\dfrac{1}{25}+\dfrac{3}{5}\right)\times\dfrac{35}{18}\\ \\C=\dfrac{1}{7}-\dfrac{4}{49}+\dfrac{5\times30}{7\times25}&&D=\left(\dfrac{4\times5}{5\times5}-\dfrac{1}{25}+\dfrac{3\times5}{5\times5}\right)\times\dfrac{35}{18}\\ \\C=\dfrac{1}{7}-\dfrac{4}{49}+\dfrac{5\times6\times5}{7\times5\times5}&&D=\left(\dfrac{20}{25}-\dfrac{1}{25}+\dfrac{15}{25}\right)\times\dfrac{35}{18}\\ \\C=\dfrac{1}{7}-\dfrac{4}{49}+\dfrac{6}{7}&&D=\left(\dfrac{20-1+15}{25}\right)\times\dfrac{35}{18}\\ \\C=\dfrac{1\times7}{7\times7}-\dfrac{4}{49}+\dfrac{6\times7}{7\times7}&&D=\dfrac{34}{25}\times\dfrac{35}{18}\\ \\C=\dfrac{7}{49}-\dfrac{4}{49}+\dfrac{42}{49}&&D=\dfrac{34\times35}{25\times18}\\ \\C=\dfrac{7-4+42}{49}&&D=\dfrac{17\times2\times7\times5}{5\times5\times9\times2}\\ \\C=\dfrac{45}{49}&&D=\dfrac{17\times7}{5\times9}\\ \\&&D=\dfrac{119}{45}\\ \end{array}$

Publié par Tom_Pascal le 07-12-2022

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