Kopertina e librit Matematika 10 - 11: Pjesa I

Zgjidhja e ushtrimit 13

Zgjidhja e ushtrimit 13 të mësimit 5.2A në librin Matematika 10 - 11: Pjesa I nga shtëpia botuese Botime Pegi me autorë Steve Fearnley, June Haighton, Steve Lomax, Peter Mullarkey, James Nicholson dhe Matt Nixon.

Pyetja

Llogaritni:

  1. 34+1258−14\dfrac{\dfrac{3}{4} + \dfrac{1}{2}}{\dfrac{5}{8} - \dfrac{1}{4}}
  2. (34−18)(34+18)\Big(\dfrac{3}{4} - \dfrac{1}{8}\Big)\Big(\dfrac{3}{4} + \dfrac{1}{8}\Big)
  3. 112−78234−116\dfrac{1\dfrac{1}{2}-\dfrac{7}{8}}{2\dfrac{3}{4}-1\dfrac{1}{6}}
  4. (235−134)(178+314)\Big(2\dfrac{3}{5}-1\dfrac{3}{4}\Big)\Big(1\dfrac{7}{8}+3\dfrac{1}{4}\Big)

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Zgjidhja

  1. 3+245−28=5438=54×83=5×21×3=103=313\dfrac{\dfrac{3+2}{4}}{\dfrac{5-2}{8}} = \dfrac{\dfrac{5}{4}}{\dfrac{3}{8}} = \dfrac{5}{\cancel{4}} \times \dfrac{\cancel{8}}{3} = \dfrac{5 \times 2}{1 \times 3} = \dfrac{10}{3} = 3\dfrac{1}{3}
  2. 6−18×6+18=58×78=5×78×8=3564\dfrac{6-1}{8} \times \dfrac{6+1}{8} = \dfrac{5}{8} \times \dfrac{7}{8} = \dfrac{5 \times 7}{8 \times 8} = \dfrac{35}{64}
  3. 32−78114−76=12−7833−1412=581912=58×1219=5×32×19=1538\dfrac{\dfrac{3}{2}-\dfrac{7}{8}}{\dfrac{11}{4}-\dfrac{7}{6}} = \dfrac{\dfrac{12-7}{8}}{\dfrac{33-14}{12}} = \dfrac{\dfrac{5}{8}}{\dfrac{19}{12}} = \dfrac{5}{\cancel8} \times \dfrac{\cancel{12}}{19} = \dfrac{5 \times 3}{2 \times 19} = \dfrac{15}{38}
  4. (135−74)(158+134)=52−3520×15+268=1720×418=17×4120×8=697160=457160\Big(\dfrac{13}{5}-\dfrac{7}{4}\Big)\Big(\dfrac{15}{8}+\dfrac{13}{4}\Big)=\dfrac{52-35}{20} \times \dfrac{15+26}{8} = \dfrac{17}{20} \times \dfrac{41}{8} = \dfrac{17 \times 41}{20 \times 8} = \dfrac{697}{160} = 4\dfrac{57}{160}