แบบฝึกหัด 4.5 ข ข้อ 4 [ม.1 เล่ม 1 บทที่ 4 ทศนิยมและเศษส่วน : สสวท. 2560]

1) \(\mathsf{(\frac{5}{7} + \frac{11}{14}) \,-\, (-\frac{13}{21})}\)

 
= \(\mathsf{(\frac{5}{7} \times \frac{6}{6}) + (\frac{11}{14} \times \frac{3}{3}) + (\frac{13}{21} \times \frac{2}{2})}\)
 
= \(\mathsf{\frac{30}{42} + \frac{33}{42} + \frac{26}{42}}\)
 
= \(\mathsf{\frac{30 \,+\, 33 \,+\, 26}{42}}\)
 
= \(\mathsf{\frac{89}{42}}\)
 
= \(\mathsf{2\frac{5}{42}}\)

 
2) \(\mathsf{[(-6\frac{1}{3}) + 9] \,-\, 1\frac{2}{3}}\)

 
= \(\mathsf{[(-\frac{19}{3}) + (9 \times \frac{3}{3})] \,-\, \frac{5}{3}}\)
 
= \(\mathsf{[(-\frac{19}{3}) + \frac{27}{3}] \,-\, \frac{5}{3}}\)
 
= \(\mathsf{\frac{[(-19) \,+\, 27] \,-\, 5}{3}}\)
 
= \(\mathsf{\frac{8 \,-\, 5}{3}}\)
 
= \(\mathsf{\frac{3}{3}}\)
 
= 1

 
3) \(\mathsf{1\frac{2}{9} \,-\, (\frac{1}{7} + 2\frac{1}{3})}\)

 
= \(\mathsf{\frac{11}{9} \,-\, [(\frac{1}{7} \times \frac{3}{3}) + (\frac{7}{3} \times \frac{7}{7})]}\)
 
= \(\mathsf{\frac{11}{9} \,-\, (\frac{3}{21} + \frac{49}{21})}\)
 
= \(\mathsf{\frac{11}{9} \,-\, \frac{3 \,+\, 49}{21}}\)
 
= \(\mathsf{\frac{11}{9} \,-\, \frac{52}{21}}\)
 
= \(\mathsf{(\frac{11}{9} \times \frac{7}{7}) \,-\, (\frac{52}{21} \times \frac{3}{3})}\)
 
= \(\mathsf{\frac{77}{63} \,-\, \frac{156}{63}}\)
 
= \(\mathsf{-\frac{79}{63}}\)
 
= \(\mathsf{-1\frac{16}{63}}\)

 
4) \(\mathsf{-\frac{4}{5} \,-\, [(-1\frac{1}{2}) \,-\, \frac{3}{4}]}\)

 
= \(\mathsf{-\frac{4}{5} \,-\, [(-\frac{3}{2} \times \frac{2}{2}) + (-\frac{3}{4})]}\)
 
= \(\mathsf{-\frac{4}{5} \,-\, [(-\frac{6}{4}) + (-\frac{3}{4})]}\)
 
= \(\mathsf{-\frac{4}{5} \,-\, (-\frac{9}{4})}\)
 
= \(\mathsf{-\frac{4}{5} + \frac{9}{4}}\)
 
= \(\mathsf{[(-\frac{4}{5}) \times \frac{4}{4}] + (\frac{9}{4} \times \frac{5}{5})}\)
 
= \(\mathsf{-\frac{16}{20} + \frac{45}{20}}\)
 
= \(\mathsf{\frac{29}{20}}\)
 
= \(\mathsf{1\frac{9}{20}}\)

 
5) \(\mathsf{[3 \,-\, (-\frac{5}{9})] \,-\, (\frac{4}{9} \,-\, 1\frac{1}{3})}\)

 
= \(\mathsf{[(3 \times \frac{9}{9}) + \frac{5}{9}] \,-\, [\frac{4}{9} \,-\, (\frac{4}{3} \times \frac{3}{3})]}\)
 
= \(\mathsf{(\frac{27}{9} + \frac{5}{9}) \,-\, (\frac{4}{9} \,-\, \frac{12}{9})}\)
 
= \(\mathsf{\frac{32}{9} \,-\, (-\frac{8}{9})}\)
 
= \(\mathsf{\frac{32}{9} + \frac{8}{9}}\)
 
= \(\mathsf{\frac{40}{9}}\)
 
= \(\mathsf{4\frac{4}{9}}\)

 
6) \(\mathsf{(3\frac{1}{4} \,-\, 3\frac{1}{2}) \,-\, [1\frac{1}{6} \,-\, (-2)]}\)

 
= \(\mathsf{[\frac{13}{4} \,-\, (\frac{7}{2} \times \frac{2}{2})] \,-\, [\frac{7}{6} + (2 \times \frac{6}{6})]}\)
 
= \(\mathsf{(\frac{13}{4} \,-\, \frac{14}{4}) \,-\, (\frac{7}{6} + \frac{12}{6})}\)
 
= \(\mathsf{-\frac{1}{4} \,-\, \frac{19}{6}}\)
 
= \(\mathsf{-\frac{1}{4} + (-\frac{19}{6})}\)
 
= \(\mathsf{(-\frac{1}{4} \times \frac{3}{3}) + (-\frac{19}{6} \times \frac{2}{2})}\)
 
= \(\mathsf{-\frac{3}{12} + (-\frac{38}{12})}\)
 
= \(\mathsf{-\frac{41}{12}}\)
 
= \(\mathsf{-3\frac{5}{12}}\)