FRACCIONES. EJERCICIOS...

CUESTIONES ... ======================== FRACCIONES o Q[blank_start]UEBRADOS[blank_end]. TÉRMINOS: N[blank_start]UMERADOR[blank_end] y D[blank_start]ENOMINADOR[blank_end]. Una FRACCIÓN indica una p[blank_start]artición[blank_end] en partes i[blank_start]guales[blank_end], y equivale a una d[blank_start]ivisión[blank_end]. El TÉRMINO 1º se nombra con su C[blank_start]ARDINAL[blank_end]. El TÉRMINO 2º se nombra: ... Si es 2: m[blank_start]edio[blank_end]/s. ... Si es 3: t[blank_start]ercio[blank_end]/s. ... De 4 A 10: su o[blank_start]rdinal[blank_end]. ... >10: su c[blank_start]ardinal[blank_end]+[blank_start]avo[blank_end]/s.

MÁS CUESTIONES ... ======================== FRACCIÓN PROPIA: N[blank_start]umerador[blank_end] < D[blank_start]enominador[blank_end]. ... Ejemplos: [blank_start]1[blank_end]/2, 1/3, [blank_start]2[blank_end]/3 ... FRACCIÓN IMPROPIA: Numerador [blank_start]>[blank_end] Denominador. ... Ejemplos: 3/[blank_start]2[blank_end], [blank_start]4[blank_end]/3. 5/3 ... ... Se puede expresar con número m[blank_start]ixto[blank_end]. NÚMERO MIXTO: E[blank_start]ntero[blank_end] + F[blank_start]racción[blank_end] [blank_start]propia[blank_end]. ... Ejemplos: 3\(\frac{1}{4}\) = [blank_start]3[blank_end] + [blank_start]1/4[blank_end] = [blank_start]13/4[blank_end] ... ... ... ... 2\(\frac{3}{5}\) = [blank_start]2[blank_end] + [blank_start]3/5[blank_end] = [blank_start]13/5[blank_end]

FRACCIONES ...

NOMBRAR · FRACCIONES ... ======================= 1/2 = un [blank_start]medio[blank_end] ... ... ... 2/3 = dos [blank_start]tercios[blank_end] 3/4 = tres [blank_start]cuartos[blank_end] ... ... 2/5 = [blank_start]dos[blank_end] [blank_start]quintos[blank_end] 5/6 = cinco [blank_start]sextos[blank_end] ... ... 3/7 = [blank_start]tres[blank_end] [blank_start]séptimos[blank_end] 1/8 = [blank_start]un[blank_end] [blank_start]octavo[blank_end] ... ... ... 7/9 = [blank_start]siete[blank_end] [blank_start]novenos[blank_end] 3/10 = [blank_start]tres[blank_end] [blank_start]décimos[blank_end] ... 9/11 = [blank_start]nueve[blank_end] [blank_start]onceavos[blank_end] 8/15 = [blank_start]ocho[blank_end] [blank_start]quinceavos[blank_end] ... 12/23 = [blank_start]doce[blank_end] [blank_start]veintitresavos[blank_end] 15/97 = [blank_start]quince[blank_end] [blank_start]noventaisieteavos[blank_end]

FRACCIÓN en RECTA NUMÉRICA ... ============================ 0--,--,--,--,--|--,--,--,--,--1--,--,--,--,--|--,--,--,--,--2--,--,--,--,--|--,--,--,--,--3 . . . . .^ . . . ^ . . . . ^.^ . . . . ^ . . . . ^ . . . . . . . . . . . . ^ . . . ^ 1º => [blank_start]1/4[blank_end] ... ... 2º => [blank_start]1/2[blank_end] ... ... 3º => [blank_start]4/5[blank_end] ... 4ª => [blank_start]9/10[blank_end] 5º => [blank_start]6/5[blank_end] ... ... 6º => [blank_start]3/2[blank_end] ... ... 7º => [blank_start]9/4[blank_end] ... 8º => [blank_start]5/2[blank_end]

ORDENAR fracciones de [menor] a [mayor] ... ===================================== \(\frac{1}{2}\) , \(\frac{2}{3}\) , \(\frac{3}{5}\) , \(\frac{3}{4}\) 1·3·5·4 , [blank_start]2[blank_end]·[blank_start]2[blank_end]·[blank_start]5[blank_end]·[blank_start]4[blank_end] , [blank_start]3[blank_end]·[blank_start]2[blank_end]·[blank_start]3[blank_end]·[blank_start]4[blank_end] , [blank_start]3[blank_end]·[blank_start]2[blank_end]·[blank_start]3[blank_end]·[blank_start]5[blank_end] [blank_start]60[blank_end] , [blank_start]80[blank_end] , [blank_start]72[blank_end] , [blank_start]90[blank_end] [blank_start]1/2[blank_end] < [blank_start]3/5[blank_end] < [blank_start]2/3[blank_end] < [blank_start]3/4[blank_end]

MAYOR (>) o MENOR (<) ==================== 1/2 [blank_start]>[blank_end] 2/5 . . . 1/4 [blank_start]<[blank_end] 2/7 2/3 [blank_start]<[blank_end] 3/4 . . . 2/3 [blank_start]>[blank_end] 4/7 3/5 [blank_start]>[blank_end] 4/7 . . . 1/3 [blank_start]<[blank_end] 2/5 2/3 [blank_start]<[blank_end] 5/7 . . . 2/5 [blank_start]<[blank_end] 3/7 1/2 [blank_start]<[blank_end] 4/7 . . . 3/4 [blank_start]>[blank_end] 5/7 2/3 [blank_start]>[blank_end] 3/5 . . . 3/4 [blank_start]<[blank_end] 4/5 1/2 [blank_start]<[blank_end] 3/5 . . . 4/5 [blank_start]>[blank_end] 5/7

MIXTO a FRACCIÓN IMPROPIA ... =========================== 1\(\frac{2}{3}\) = [blank_start]5[blank_end] / [blank_start]3[blank_end] 2\(\frac{3}{4}\) = [blank_start]11[blank_end] / [blank_start]4[blank_end] 3\(\frac{1}{5}\) = [blank_start]16[blank_end] / [blank_start]5[blank_end] FRACCIÓN IMPROPIA a MIXTO ... =========================== \(\frac{3}{2}\) = [blank_start]1[blank_end] + [blank_start]1/2[blank_end] \(\frac{11}{3}\) = [blank_start]3[blank_end] + [blank_start]2/3[blank_end] \(\frac{20}{7}\) = [blank_start]2[blank_end] + [blank_start]6/7[blank_end]

FRACCIÓN a DECIMAL ... ==================== \(\frac{3}{5}\) = 0,[blank_start]6[blank_end] ... ... \(\frac{1}{2}\) = 0,[blank_start]5[blank_end] \(\frac{5}{8}\) = 0,[blank_start]625[blank_end] ... \(\frac{3}{4}\) = 0,[blank_start]75[blank_end] \(\frac{5}{4}\) = [blank_start]1,25[blank_end] ... \(\frac{9}{5}\) = [blank_start]1,8[blank_end] DECIMAL EXACTO a FRACCIÓN ... =========================== 0,4 = 4/10 = [blank_start]2/5[blank_end] ... ... ... ... 0,8 = [blank_start]8/10[blank_end] = [blank_start]4/5[blank_end] 0,65 = [blank_start]65[blank_end]/100 = [blank_start]13/20[blank_end] ... 0,375 = [blank_start]375[blank_end]/1000 = [blank_start]3/8[blank_end] 3,4 = [blank_start]34/10[blank_end] = [blank_start]17/5[blank_end] ... ... 2,75 = [blank_start]275/100[blank_end] = [blank_start]11/4[blank_end]

DECIMAL PERIÓDICO (N) a FRACCIÓN ... ============================== 2,\(\stackrel{\frown}{3}\) => Nx10 – N 23,3... – 2,3... = [blank_start]21[blank_end] => [blank_start]21[blank_end]/(10-1) = [blank_start]21/9[blank_end] = [blank_start]7/3[blank_end] 3,\(\stackrel{\frown}{15}\) => Nx100 – N 315,15... – 3,15... = [blank_start]312[blank_end] => [blank_start]312[blank_end]/(100-1) = [blank_start]312/99[blank_end] = [blank_start]104/33[blank_end] 0,6\(\stackrel{\frown}{1}\) => Nx100 – Nx10 61,1... – 6,1... = [blank_start]55[blank_end] => [blank_start]55[blank_end]/(100-10) = [blank_start]55/90[blank_end] = [blank_start]11/18[blank_end]

FRACCIÓN de CANTIDAD ... ====================== 1/2 de 34 = 34 : 2 x 1 = [blank_start]17[blank_end] 3/4 de 76 = [blank_start]76[blank_end] : [blank_start]4[blank_end] x [blank_start]3[blank_end] = [blank_start]19[blank_end] x [blank_start]3[blank_end] = [blank_start]57[blank_end] 2/5 de 80 = [blank_start]80[blank_end] : [blank_start]5[blank_end] x [blank_start]2[blank_end] = [blank_start]32[blank_end] 5/8 de 1.000 = 1.000 : [blank_start]8[blank_end] x [blank_start]5[blank_end] = [blank_start]625[blank_end]

FRACCIÓN de CANTIDAD ... ======================= 2/3 de 21 = [blank_start]14[blank_end] . . . 2/5 de 30 = [blank_start]12[blank_end] 1/2 de 32 = [blank_start]16[blank_end] . . . 5/6 de 24 = [blank_start]20[blank_end] 3/5 de 45 = [blank_start]27[blank_end] . . . 3/7 de 49 = [blank_start]21[blank_end] 1/6 de 42 = [blank_start]7[blank_end] . . . . 1/4 de 60 = [blank_start]15[blank_end] 5/7 de 42 = [blank_start]30[blank_end] . . . 4/5 de 40 = [blank_start]32[blank_end] 3/4 de 100=[blank_start]75[blank_end] . . . 1/3 de 27 = [blank_start]9[blank_end]

SUMA de FRACCIONES .... ===================== \(\frac{2}{3}\) + \(\frac{3}{5}\) = \(\frac{2·5+3·3}{3·5}\) = ([blank_start]10[blank_end]+[blank_start]9[blank_end]) / [blank_start]15[blank_end] = [blank_start]19/15[blank_end] \(\frac{1}{5}\) + \(\frac{3}{4}\) + \(\frac{2}{3}\) = ([blank_start]1[blank_end]·[blank_start]4[blank_end]·[blank_start]3[blank_end]+[blank_start]3[blank_end]·[blank_start]5[blank_end]·[blank_start]3[blank_end]+[blank_start]2[blank_end]·[blank_start]5[blank_end]·[blank_start]4[blank_end]) / [blank_start]5[blank_end]·[blank_start]4[blank_end]·[blank_start]3[blank_end] = ([blank_start]12[blank_end]+[blank_start]45[blank_end]+[blank_start]40[blank_end]) / [blank_start]60[blank_end] = [blank_start]97/60[blank_end] RESTA de FRACCIONES ... ===================== \(\frac{2}{3}\) – \(\frac{3}{5}\) = \(\frac{2·5–3·3}{3·5}\) = ([blank_start]10[blank_end]–[blank_start]9[blank_end]) / [blank_start]15[blank_end] = [blank_start]1/15[blank_end] \(\frac{1}{5}\) – \(\frac{3}{4}\) + \(\frac{2}{3}\) = ([blank_start]1[blank_end]·[blank_start]4[blank_end]·[blank_start]3[blank_end]–[blank_start]3[blank_end]·[blank_start]5[blank_end]·[blank_start]3[blank_end]+[blank_start]2[blank_end]·[blank_start]5[blank_end]·[blank_start]4[blank_end]) / [blank_start]5[blank_end]·[blank_start]4[blank_end]·[blank_start]3[blank_end] = ([blank_start]12[blank_end]–[blank_start]45[blank_end]+[blank_start]40[blank_end]) / [blank_start]60[blank_end] = [blank_start]7/60[blank_end]

MULTIPLICAR y DIVIDIR ... ===================== \(\frac{2}{5}\) x \(\frac{3}{4}\) = \(\frac{2·3}{5·4}\) = [blank_start]6[blank_end] / [blank_start]20[blank_end] = [blank_start]3/10[blank_end] \(\frac{2}{5}\) : \(\frac{3}{4}\) = \(\frac{2}{5}\) x \(\frac{4}{3}\) = [blank_start]2[blank_end] · [blank_start]4[blank_end] / [blank_start]5[blank_end] · [blank_start]3[blank_end] = [blank_start]8/15[blank_end]

OTRAS CUESTIONES ... =================== 3/4 de hora = 3/4 x [blank_start]60[blank_end] min = [blank_start]60[blank_end] : [blank_start]4[blank_end] x [blank_start]3[blank_end] = [blank_start]15[blank_end] x [blank_start]3[blank_end] = [blank_start]45[blank_end] minutos. 1/5 de litro = 1/5 de [blank_start]100[blank_end] cl = [blank_start]1/5[blank_end] x [blank_start]100[blank_end] = [blank_start]100[blank_end] : [blank_start]5[blank_end] x [blank_start]1[blank_end] = [blank_start]20[blank_end] cl Cuarto y mitad de kg = \(\frac{1}{4}\) + \(\frac{1}{2}\)x\(\frac{1}{4}\) = [blank_start]1/4[blank_end]+[blank_start]1/8[blank_end] = ([blank_start]8+4[blank_end])/([blank_start]4x8[blank_end]) = [blank_start]12/32[blank_end] = [blank_start]3/8[blank_end] En gramos: [blank_start]3/8[blank_end] x 1.000 g = 1.000 : [blank_start]8[blank_end] x [blank_start]3[blank_end] = [blank_start]375[blank_end] g

PROBLEMAS con FRACCIONES ... =========================== Una huerta tiene plantados 1/4 de tomates, 2/5 de pimientos y el resto, 280 m², de patatas. ¿Qué fracción hay plantada de patatas? ¿Cuál es la superficie total de la huerta? [blank_start]1/4[blank_end] + [blank_start]2/5[blank_end] = [blank_start]13/20[blank_end] [blank_start]1[blank_end] – [blank_start]13/20[blank_end] = [blank_start]7/20[blank_end] de patatas. [blank_start]7/20[blank_end] = 280 => [blank_start]280[blank_end] : [blank_start]7[blank_end] x [blank_start]20[blank_end] = [blank_start]800[blank_end] m² superficie de la [blank_start]huerta[blank_end]. Un paso equivale a 3/5 de metro. ¿Qué distancia recorre con 1.000 pasos? ¿Cuántos pasos debe dar para recorrer una distancia de kilómetro y medio? 1.000 x [blank_start]3/5[blank_end] = [blank_start]600[blank_end] [blank_start]metros[blank_end]. kilómetro y medio => 1.000 + [blank_start]1/2[blank_end] x 1.000 = [blank_start]1.500[blank_end] [blank_start]metros[blank_end] 1.500 : [blank_start]3/5[blank_end] => 1.500 x [blank_start]5/3[blank_end] = [blank_start]2.500[blank_end] [blank_start]pasos[blank_end].

¿Qué FRACCIÓN de HORA representan? ... ================================== ... ... 5 minutos => 5/60 [:5] = [blank_start]1/12[blank_end] ... 10 minutos => 10/60 [:10] =[blank_start]1/6[blank_end] ... 15 minutos => 15/60 [:15] =[blank_start]1/4[blank_end] ... 20 minutos => 20/60 [:20] =[blank_start]1/3[blank_end] ... 30 minutos => 30/60 [:30] =[blank_start]1/2[blank_end] ... 40 minutos => 40/60 [:20] =[blank_start]2/3[blank_end] ... 45 minutos => 45/60 [:15] =[blank_start]3/4[blank_end] ... 50 minutos => 50/60 [:10] =[blank_start]5/6[blank_end]

FRACCIONES: SUMA y RESTA [N/15] … ============================== 1/3 + 1/5 = [blank_start]8[blank_end]/15 1/3 - 1/5 = [blank_start]2[blank_end]/15 2/3 + 1/5 = [blank_start]13[blank_end]/15 2/3 - 1/5 = [blank_start]7[blank_end]/15 2/3 + 3/5 = [blank_start]19[blank_end]/15 2/3 - 3/5 = [blank_start]1[blank_end]/15 2/5 + 1/3 = [blank_start]11[blank_end]/15 2/5 - 1/3 = [blank_start]1[blank_end]/15 3/5 + 1/3 = [blank_start]14[blank_end]/15 3/5 - 1/3 = [blank_start]4[blank_end]/15 4/5 + 1/3 = [blank_start]17[blank_end]/15 4/5 - 1/3 = [blank_start]7[blank_end]/15 4/5 + 2/3 = [blank_start]22[blank_end]/15 4/5 - 2/3 = [blank_start]2[blank_end]/15 5/3 + 2/5 = [blank_start]31[blank_end]/15 5/3 - 2/5 = [blank_start]19[blank_end]/15 5/3 + 3/5 = [blank_start]34[blank_end]/15 5/3 - 3/5 = [blank_start]16[blank_end]/15