Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 3.5 Adding or Subtracting Mixed Numbers with Unlike Denominators to secure good marks & knowledge in the exams.
McGraw-Hill Math Grade 8 Answer Key Lesson 3.5 Adding or Subtracting Mixed Numbers with Unlike Denominators
Exercises Add
Question 1.
12\(\frac{1}{2}\) + 3\(\frac{3}{4}\)
Answer:
\(\frac{65}{4}\) or 16\(\frac{1}{4}\),
Explanation:
Given to add 12\(\frac{1}{2}\) + 3\(\frac{3}{4}\) as
both are in mixed fractions we convert into fractions as
12\(\frac{1}{2}\) = \(\frac{12 X 2 + 1}{2}\) = \(\frac{25}{2}\) and 3\(\frac{3}{4}\) = \(\frac{3 X 4 + 3}{4}\) = \(\frac{15}{4}\) both don’t have common denominators first we multiply \(\frac{25}{2}\) by 2 we get
\(\frac{25 X 2}{2 X 2}\) = \(\frac{50}{4}\) now we add numerators as \(\frac{50 + 15}{4}\) = \(\frac{65}{4}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{16 X 4 + 1}{4}\) = 16\(\frac{1}{4}\).
Question 2.
13\(\frac{3}{7}\) + 4\(\frac{3}{11}\)
Answer:
\(\frac{1,363}{77}\) or 17\(\frac{54}{77}\),
Explanation:
Given to add 13\(\frac{3}{7}\) + 4\(\frac{3}{11}\) as
both are in mixed fractions we convert into fractions as
13\(\frac{3}{7}\) = \(\frac{13 X 7 + 3}{7}\) = \(\frac{94}{7}\) and 4\(\frac{3}{11}\) = \(\frac{4 X 11 + 3}{11}\) = \(\frac{47}{11}\) both don’t have common denominators first we multiply \(\frac{94}{7}\) by 11 we get
\(\frac{94 X 11}{7 X 11}\) = \(\frac{1,034}{77}\) and
\(\frac{47}{11}\) by 7 we get
\(\frac{47 X 7}{11 X 7}\) = \(\frac{329}{77}\)
now we add numerators as \(\frac{1,034 + 329}{77}\) = \(\frac{1,363}{77}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{17 X 77 + 54}{77}\) = 17\(\frac{54}{77}\).
Question 3.
5\(\frac{2}{7}\) + 3\(\frac{3}{8}\)
Answer:
\(\frac{485}{56}\) or 8\(\frac{37}{56}\),
Explanation:
Given to add 5\(\frac{2}{7}\) + 3\(\frac{3}{8}\) as
both are in mixed fractions we convert into fractions as
5\(\frac{2}{7}\) = \(\frac{5 X 7 + 2}{7}\) = \(\frac{37}{7}\) and 3\(\frac{3}{8}\) = \(\frac{3 X 8 + 3}{8}\) = \(\frac{27}{8}\) both don’t have common denominators first we multiply \(\frac{37}{7}\) by 8 we get
\(\frac{37 X 8}{7 X 8}\) = \(\frac{296}{56}\) and
\(\frac{27}{8}\) by 7 we get
\(\frac{27 X 7}{8 X 7}\) = \(\frac{189}{56}\)
now we add numerators as \(\frac{296 + 189}{56}\) = \(\frac{485}{56}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{8 X 56 + 37}{56}\) = 8\(\frac{37}{56}\).
Question 4.
3\(\frac{1}{6}\) + 7\(\frac{1}{4}\)
Answer:
\(\frac{125}{12}\) or 10\(\frac{5}{12}\),
Explanation:
Given to add 3\(\frac{1}{6}\) + 7\(\frac{1}{4}\) as
both are in mixed fractions we convert into fractions as
3\(\frac{1}{6}\) = \(\frac{3 X 6 + 1}{6}\) = \(\frac{19}{6}\) and 7\(\frac{1}{4}\) = \(\frac{7 X 4 + 1}{4}\) = \(\frac{29}{4}\) both don’t have common denominators first we multiply \(\frac{19}{6}\) by 4 we get
\(\frac{19 X 4}{6 X 4}\) = \(\frac{76}{24}\) and
\(\frac{29}{4}\) by 6 we get
\(\frac{29 X 6}{4 X 6}\) = \(\frac{174}{24}\)
now we add numerators as \(\frac{76 + 174}{24}\) = \(\frac{250}{24}\) both goes in 2 which is \(\frac{125}{12}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{10 X 12 + 5}{12}\) = 10\(\frac{5}{12}\).
Question 5.
4\(\frac{3}{11}\) + 3\(\frac{1}{3}\)
Answer:
\(\frac{251}{33}\) or 7\(\frac{20}{33}\),
Explanation:
Given to add 4\(\frac{3}{11}\) + 3\(\frac{1}{3}\) as
both are in mixed fractions we convert into fractions as
4\(\frac{3}{11}\) = \(\frac{4 X 11 + 3}{11}\) = \(\frac{47}{11}\) and 3\(\frac{1}{3}\) = \(\frac{3 X 3 + 1}{3}\) = \(\frac{10}{3}\) both don’t have common denominators first we multiply \(\frac{47}{11}\) by 3 we get
\(\frac{47 X 3}{11 X 3}\) = \(\frac{141}{33}\) and
\(\frac{10}{3}\) by 11 we get
\(\frac{10 X 11}{3 X 11}\) = \(\frac{110}{33}\)
now we add numerators as \(\frac{141 + 110}{33}\) = \(\frac{251}{33}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{7 X 33 + 20}{33}\) = 7\(\frac{20}{33}\).
Question 6.
11\(\frac{1}{2}\) + 5\(\frac{2}{5}\)
Answer:
\(\frac{169}{10}\) or 16\(\frac{9}{10}\),
Explanation:
Given to add 11\(\frac{1}{2}\) + 5\(\frac{2}{5}\) as
both are in mixed fractions we convert into fractions as
11\(\frac{1}{2}\) = \(\frac{11 X 2 + 1}{10}\) = \(\frac{23}{2}\) and 5\(\frac{2}{5}\) = \(\frac{5 X 5 + 2}{5}\) = \(\frac{27}{5}\) both don’t have common denominators first we multiply \(\frac{23}{2}\) by 5 we get
\(\frac{23 X 5}{2 X 5}\) = \(\frac{115}{10}\) and
\(\frac{27}{5}\) by 2 we get
\(\frac{27 X 2}{5 X 2}\) = \(\frac{54}{10}\)
now we add numerators as \(\frac{115 + 54}{10}\) = \(\frac{169}{10}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{16 X 10 + 9}{10}\) = 16\(\frac{9}{10}\).
Question 7.
4\(\frac{7}{9}\) + 5\(\frac{2}{7}\)
Answer:
\(\frac{634}{63}\) or 10\(\frac{4}{63}\),
Explanation:
Given to add 4\(\frac{7}{9}\) + 5\(\frac{2}{7}\) as
both are in mixed fractions we convert into fractions as
4\(\frac{7}{9}\) = \(\frac{4 X 9 + 7}{9}\) = \(\frac{43}{9}\) and 5\(\frac{2}{7}\) = \(\frac{5 X 7 + 2}{7}\) = \(\frac{37}{7}\) both don’t have common denominators first we multiply \(\frac{43}{9}\) by 7 we get
\(\frac{43 X 7}{9 X 7}\) = \(\frac{301}{63}\) and
\(\frac{37}{7}\) by 9 we get
\(\frac{37 X 9}{7 X 9}\) = \(\frac{333}{63}\)
now we add numerators as \(\frac{301 + 333}{63}\) = \(\frac{634}{63}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{10 X 63 + 4}{63}\) = 10\(\frac{4}{63}\).
Question 8.
13\(\frac{3}{5}\) + 15\(\frac{7}{11}\)
Answer:
\(\frac{1,608}{55}\) or 29\(\frac{13}{55}\),
Explanation:
Given to add 13\(\frac{3}{5}\) + 15\(\frac{7}{11}\) as
both are in mixed fractions we convert into fractions as
13\(\frac{3}{5}\) = \(\frac{13 X 5 + 3}{5}\) = \(\frac{68}{5}\) and 15\(\frac{7}{11}\) = \(\frac{15 X 11 + 7}{11}\) = \(\frac{172}{11}\) both don’t have common denominators first we multiply \(\frac{68}{5}\) by 11 we get
\(\frac{68 X 11}{5 X 11}\) = \(\frac{748}{55}\) and
\(\frac{172}{11}\) by 5 we get
\(\frac{172 X 5}{11 X 5}\) = \(\frac{860}{55}\)
now we add numerators as \(\frac{748 + 860}{55}\) = \(\frac{1,608}{55}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{29 X 55 + 13}{55}\) = 29\(\frac{13}{55}\).
Question 9.
22\(\frac{5}{6}\) + 27\(\frac{5}{13}\)
Answer:
\(\frac{3,917}{78}\) or 50\(\frac{17}{78}\),
Explanation:
Given to add 22\(\frac{5}{6}\) + 27\(\frac{5}{13}\) as
both are in mixed fractions we convert into fractions as
22\(\frac{5}{6}\) = \(\frac{22 X 6 + 5}{6}\) = \(\frac{137}{6}\) and 27\(\frac{5}{13}\) = \(\frac{27 X 13 + 5}{13}\) = \(\frac{356}{13}\) both don’t have common denominators first we multiply \(\frac{137}{6}\) by 13 we get
\(\frac{137 X 13}{6 X 13}\) = \(\frac{1,781}{78}\) and
\(\frac{356}{13}\) by 6 we get
\(\frac{356 X 6}{13 X 6}\) = \(\frac{2,136}{78}\)
now we add numerators as \(\frac{1,781 + 2,136}{78}\) = \(\frac{3,917}{78}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{50 X 78 + 17}{78}\) = 50\(\frac{17}{78}\).
Question 10.
1\(\frac{1}{11}\) + 7\(\frac{2}{5}\)
Answer:
\(\frac{467}{55}\) or 8\(\frac{27}{55}\),
Explanation:
Given to add 1\(\frac{1}{11}\) + 7\(\frac{2}{5}\) as
both are in mixed fractions we convert into fractions as
1\(\frac{1}{11}\) = \(\frac{1 X 11 + 1}{11}\) = \(\frac{12}{11}\) and 7\(\frac{2}{5}\) = \(\frac{7 X 5 + 2}{5}\) = \(\frac{37}{5}\) both don’t have common denominators first we multiply \(\frac{12}{11}\) by 5 we get
\(\frac{12 X 5}{11 X 5}\) = \(\frac{60}{55}\) and
\(\frac{37}{5}\) by 11 we get
\(\frac{37 X 11}{5 X 11}\) = \(\frac{407}{55}\)
now we add numerators as \(\frac{60 + 407}{55}\) = \(\frac{467}{55}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{8 X 55 + 27}{55}\) = 8\(\frac{27}{55}\).
Question 11.
44\(\frac{1}{2}\) + 14\(\frac{2}{9}\)
Answer:
\(\frac{1,053}{18}\) or \(\frac{117}{2}\) or
58\(\frac{1}{2}\),
Explanation:
Given to add 44\(\frac{1}{2}\) + 14\(\frac{2}{9}\) as
both are in mixed fractions we convert into fractions as
44\(\frac{1}{2}\) = \(\frac{44 X 2 + 1}{2}\) = \(\frac{89}{2}\) and 14\(\frac{2}{9}\) = \(\frac{14 X 9 + 2}{13}\) = \(\frac{128}{9}\) both don’t have common denominators first we multiply \(\frac{89}{2}\) by 9 we get
\(\frac{89 X 9}{2 X 9}\) = \(\frac{801}{18}\) and
\(\frac{128}{9}\) by 2 we get
\(\frac{128 X 2}{9 X 2}\) = \(\frac{252}{18}\)
now we add numerators as \(\frac{801 + 252}{18}\) = \(\frac{1,053}{18}\) both goes by 3 we divide by 3 we get
\(\frac{351}{6}\) still goes by 3 we get \(\frac{117}{2}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{58 X 2 + 1}{2}\) = 58\(\frac{1}{2}\).
Question 12.
9\(\frac{5}{7}\) + 10\(\frac{1}{3}\)
Answer:
\(\frac{421}{21}\) or 20\(\frac{1}{21}\),
Explanation:
Given to add 9\(\frac{5}{7}\) + 10\(\frac{1}{3}\) as
both are in mixed fractions we convert into fractions as
9\(\frac{5}{7}\) = \(\frac{9 X 7 + 5}{7}\) = \(\frac{68}{7}\) and 10\(\frac{1}{3}\) = \(\frac{10 X 3 + 1}{3}\) = \(\frac{31}{3}\) both don’t have common denominators first we multiply \(\frac{68}{7}\) by 3 we get
\(\frac{68 X 3}{7 X 3}\) = \(\frac{204}{21}\) and
\(\frac{31}{3}\) by 7 we get
\(\frac{31 X 7}{3 X 7}\) = \(\frac{217}{21}\)
now we add numerators as \(\frac{204 + 217}{21}\) = \(\frac{421}{21}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{20 X 21 + 1}{21}\) = 20\(\frac{1}{21}\).
Question 13.
4\(\frac{3}{7}\) + 4\(\frac{4}{9}\)
Answer:
\(\frac{559}{63}\) or 8\(\frac{55}{63}\),
Explanation:
Given to add 4\(\frac{3}{7}\) + 4\(\frac{4}{9}\) as
both are in mixed fractions we convert into fractions as
4\(\frac{3}{7}\) = \(\frac{4 X 7 + 3}{7}\) = \(\frac{31}{7}\) and 4\(\frac{4}{9}\) = \(\frac{4 X 9 + 4}{9}\) = \(\frac{40}{9}\) both don’t have common denominators first we multiply \(\frac{31}{7}\) by 9 we get
\(\frac{31 X 9}{7 X 9}\) = \(\frac{279}{63}\) and
\(\frac{40}{9}\) by 7 we get
\(\frac{40 X 7}{9 X 7}\) = \(\frac{280}{63}\)
now we add numerators as \(\frac{279 + 280}{63}\) = \(\frac{559}{63}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{8 X 63 + 55}{63}\) = 8\(\frac{55}{63}\).
Question 14.
5\(\frac{5}{8}\) + 3\(\frac{3}{7}\)
Answer:
\(\frac{507}{56}\) or 9\(\frac{3}{56}\),
Explanation:
Given to add 5\(\frac{5}{8}\) + 3\(\frac{3}{7}\) as
both are in mixed fractions we convert into fractions as
5\(\frac{5}{8}\) = \(\frac{5 X 8 + 5}{8}\) = \(\frac{45}{8}\) and 3\(\frac{3}{7}\) = \(\frac{3 X 7 + 3}{7}\) = \(\frac{24}{7}\) both don’t have common denominators first we multiply \(\frac{45}{8}\) by 7 we get
\(\frac{45 X 7}{8 X 7}\) = \(\frac{315}{56}\) and
\(\frac{24}{7}\) by 8 we get
\(\frac{24 X 8}{7 X 8}\) = \(\frac{192}{56}\)
now we add numerators as \(\frac{315 + 192}{56}\) = \(\frac{507}{56}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{9 X 56 + 3}{56}\) = 9\(\frac{3}{56}\).
Question 15.
46\(\frac{4}{7}\) + 44\(\frac{1}{2}\)
Answer:
\(\frac{1,275}{14}\) or 91\(\frac{1}{14}\),
Explanation:
Given to add 46\(\frac{4}{7}\) + 44\(\frac{1}{2}\) as
both are in mixed fractions we convert into fractions as
46\(\frac{4}{7}\) = \(\frac{46 X 7 + 4}{7}\) = \(\frac{326}{7}\) and 44\(\frac{1}{2}\) = \(\frac{44 X 2 + 1}{2}\) = \(\frac{89}{2}\) both don’t have common denominators first we multiply \(\frac{326}{7}\) by 2 we get
\(\frac{326 X 2}{7 X 2}\) = \(\frac{652}{14}\) and
\(\frac{89}{2}\) by 7 we get
\(\frac{89 X 7}{2 X 7}\) = \(\frac{623}{14}\)
now we add numerators as \(\frac{652 + 623}{14}\) = \(\frac{1,275}{14}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{91 X 14 + 1}{14}\) = 91\(\frac{1}{14}\).
Question 16.
4\(\frac{5}{8}\) + 3\(\frac{7}{9}\)
Answer:
\(\frac{605}{72}\) or 8\(\frac{29}{72}\),
Explanation:
Given to add 4\(\frac{5}{8}\) + 3\(\frac{7}{9}\) as
both are in mixed fractions we convert into fractions as
4\(\frac{5}{8}\) = \(\frac{4 X 8 + 5}{8}\) = \(\frac{37}{8}\) and 3\(\frac{7}{9}\) = \(\frac{3 X 9 + 7}{9}\) = \(\frac{34}{9}\) both don’t have common denominators first we multiply \(\frac{37}{8}\) by 9 we get
\(\frac{37 X 9}{8 X 9}\) = \(\frac{333}{72}\) and
\(\frac{34}{9}\) by 8 we get
\(\frac{34 X 8}{9 X 8}\) = \(\frac{272}{72}\)
now we add numerators as \(\frac{333 + 272}{72}\) = \(\frac{605}{72}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{8 X 72 + 29}{72}\) = 8\(\frac{29}{72}\).
Exercises Subtract
Question 1.
11\(\frac{5}{9}\) – 4\(\frac{9}{13}\)
Answer:
\(\frac{803}{117}\) or 6\(\frac{101}{13}\),
Explanation:
Given to subtract 11\(\frac{5}{9}\) – 4\(\frac{9}{13}\) as
both are in mixed fractions we convert into fractions as
11\(\frac{5}{9}\) = \(\frac{11 X 9 + 5}{9}\) = \(\frac{104}{9}\) and 4\(\frac{9}{13}\) = \(\frac{4 X 13 + 9}{13}\) = \(\frac{61}{13}\) both don’t have common denominators first we multiply \(\frac{104}{9}\) by 13 we get
\(\frac{104 X 13}{9 X 13}\) = \(\frac{1,352}{117}\) and
\(\frac{61}{13}\) by 9 we get
\(\frac{61 X 9}{13 X 9}\) = \(\frac{549}{117}\)
now we subtract numerators as \(\frac{1,352 – 549}{117}\) = \(\frac{803}{117}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{6 X 117 + 101}{117}\) = 6\(\frac{101}{117}\).
Question 2.
13\(\frac{1}{6}\) – 10\(\frac{2}{15}\)
Answer:
\(\frac{91}{30}\) or 3\(\frac{1}{30}\),
Explanation:
Given to subtract 13\(\frac{1}{6}\) – 10\(\frac{2}{15}\) as
both are in mixed fractions we convert into fractions as
13\(\frac{1}{6}\) = \(\frac{13 X 6 + 1}{6}\) = \(\frac{79}{6}\) and 10\(\frac{2}{15}\) = \(\frac{10 X 15 + 2}{15}\) = \(\frac{152}{15}\) both don’t have common denominators first we multiply \(\frac{79}{6}\) by 15 we get
\(\frac{79 X 15}{6 X 15}\) = \(\frac{1,185}{90}\) and
\(\frac{152}{15}\) by 6 we get
\(\frac{152 X 6}{15 X 6}\) = \(\frac{912}{90}\)
now we subtract numerators as \(\frac{1,185 – 912}{90}\) = \(\frac{273}{90}\) both goes by 3 we get \(\frac{91}{30}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{3 X 30 + 1}{30}\) = 3\(\frac{1}{30}\).
Question 3.
15\(\frac{2}{3}\) – 14\(\frac{1}{6}\)
Answer:
\(\frac{3}{2}\) or 1\(\frac{1}{2}\),
Explanation:
Given to subtract 15\(\frac{2}{3}\) – 14\(\frac{1}{6}\) as
both are in mixed fractions we convert into fractions as
15\(\frac{2}{3}\) = \(\frac{15 X 3 + 2}{3}\) = \(\frac{47}{3}\) and 14\(\frac{1}{6}\) = \(\frac{14 X 6 + 1}{6}\) = \(\frac{85}{6}\) both don’t have common denominators first we multiply \(\frac{47}{3}\) by 2 we get
\(\frac{47 X 2}{3 X 2}\) = \(\frac{94}{6}\)
now we subtract numerators as \(\frac{94 – 85}{6}\) = \(\frac{9}{6}\) both goes by 3 we get \(\frac{3}{2}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{1 X 2 + 1}{2}\) = 1\(\frac{1}{2}\).
Question 4.
20\(\frac{3}{4}\) – 11\(\frac{4}{9}\)
Answer:
\(\frac{335}{36}\) or 9\(\frac{11}{36}\),
Explanation:
Given to subtract 20\(\frac{3}{4}\) – 11\(\frac{4}{9}\) as
both are in mixed fractions we convert into fractions as
20\(\frac{3}{4}\) = \(\frac{20 X 4 + 3}{4}\) = \(\frac{83}{4}\) and 11\(\frac{4}{9}\) = \(\frac{11 X 9 + 4}{9}\) = \(\frac{103}{9}\) both don’t have common denominators first we multiply \(\frac{83}{4}\) by 9 we get
\(\frac{83 X 9}{4 X 9}\) = \(\frac{747}{36}\) and
\(\frac{103}{9}\) by 4 we get \(\frac{103 X 4}{9 X 4}\)=
\(\frac{412}{36}\) now we subtract numerators as \(\frac{747 – 412}{36}\) = \(\frac{335}{36}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{9 X 36 + 11}{36}\) = 9\(\frac{11}{36}\).
Question 5.
13\(\frac{5}{6}\) – 3\(\frac{5}{7}\)
Answer:
\(\frac{425}{42}\) or 10\(\frac{5}{42}\),
Explanation:
Given to subtract 13\(\frac{5}{6}\) – 3\(\frac{5}{7}\) as
both are in mixed fractions we convert into fractions as
13\(\frac{5}{6}\) = \(\frac{13 X 6 + 5}{6}\) = \(\frac{83}{6}\) and 3\(\frac{5}{7}\) = \(\frac{3 X 7 + 5}{7}\) = \(\frac{26}{7}\) both don’t have common denominators first we multiply \(\frac{83}{6}\) by 7 we get
\(\frac{83 X 7}{6 X 7}\) = \(\frac{581}{42}\) and
\(\frac{26}{7}\) by 6 we get \(\frac{26 X 6}{7 X 6}\)=
\(\frac{156}{42}\) now we subtract numerators as \(\frac{581 – 156}{42}\) = \(\frac{425}{42}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{10 X 42 + 5}{42}\) = 10\(\frac{5}{42}\).
Question 6.
23\(\frac{4}{5}\) – 19\(\frac{5}{11}\)
Answer:
\(\frac{239}{55}\) or 4\(\frac{19}{55}\),
Explanation:
Given to subtract 23\(\frac{4}{5}\) – 19\(\frac{5}{11}\) as
both are in mixed fractions we convert into fractions as
23\(\frac{4}{5}\) = \(\frac{23 X 5 + 4}{5}\) = \(\frac{119}{5}\) and 19\(\frac{5}{11}\) = \(\frac{19 X 11 + 5}{11}\) = \(\frac{214}{11}\) both don’t have common denominators first we multiply \(\frac{119}{5}\) by 11 we get
\(\frac{119 X 11}{5 X 11}\) = \(\frac{1,309}{55}\) and
\(\frac{214}{11}\) by 5 we get \(\frac{214 X 5}{11 X 5}\)=
\(\frac{1,070}{55}\) now we subtract numerators as \(\frac{1,309 – 1,070}{55}\) = \(\frac{239}{55}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{4 X 55 + 19}{55}\) = 4\(\frac{19}{55}\).
Question 7.
13\(\frac{4}{11}\) – 3\(\frac{1}{2}\)
Answer:
\(\frac{217}{22}\) or 9\(\frac{19}{22}\),
Explanation:
Given to subtract 13\(\frac{4}{11}\) – 3\(\frac{1}{2}\) as
both are in mixed fractions we convert into fractions as
13\(\frac{4}{11}\) = \(\frac{13 X 11 + 4}{11}\) = \(\frac{147}{11}\) and 3\(\frac{1}{2}\) = \(\frac{3 X 2 + 1}{2}\) = \(\frac{7}{2}\) both don’t have common denominators first we multiply \(\frac{147}{11}\) by 2 we get \(\frac{147 X 2}{11 X 2}\) = \(\frac{294}{22}\) and
\(\frac{7}{2}\) by 11 we get \(\frac{7 X 11}{2 X 11}\)=
\(\frac{77}{22}\) now we subtract numerators as \(\frac{294 – 77}{222}\) = \(\frac{217}{22}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{9 X 22 + 19}{22}\) = 9\(\frac{19}{22}\).
Question 8.
11\(\frac{2}{3}\) – 10\(\frac{7}{9}\)
Answer:
\(\frac{8}{9}\),
Explanation:
Given to subtract 11\(\frac{2}{3}\) – 10\(\frac{7}{9}\) as
both are in mixed fractions we convert into fractions as
11\(\frac{2}{3}\) = \(\frac{11 X 3 + 2}{3}\) = \(\frac{35}{3}\) and 10\(\frac{7}{9}\) = \(\frac{10 X 9 + 7}{9}\) = \(\frac{97}{9}\) both don’t have common denominators first we multiply \(\frac{35}{3}\) by 3 we get \(\frac{35 X 3}{3 X 3}\) = \(\frac{105}{9}\) and
\(\frac{97}{9}\), now we subtract numerators as \(\frac{105 – 97}{9}\) = \(\frac{8}{9}\).
Question 9.
77\(\frac{1}{3}\) – 41\(\frac{5}{17}\)
Answer:
\(\frac{1,838}{51}\) or 36\(\frac{2}{51}\),
Explanation:
Given to subtract 77\(\frac{1}{3}\) – 41\(\frac{5}{17}\) as
both are in mixed fractions we convert into fractions as
77\(\frac{1}{3}\) = \(\frac{77 X 3 + 1}{3}\) = \(\frac{232}{3}\) and 41\(\frac{5}{17}\) = \(\frac{41 X 17 + 5}{17}\) = \(\frac{702}{17}\) both don’t have common denominators first we multiply \(\frac{232}{3}\) by 17 we get
\(\frac{232 X 17}{3 X 17}\) = \(\frac{3,944}{51}\) and
\(\frac{702}{17}\) by 3 we get \(\frac{702 X 3}{17 X 3}\)=
\(\frac{2,106}{51}\) now we subtract numerators as \(\frac{3,944 – 2,106}{51}\) = \(\frac{1,838}{51}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{36 X 51 + 2}{51}\) = 36\(\frac{2}{51}\).
Question 10.
9\(\frac{5}{7}\) – 3\(\frac{3}{14}\)
Answer:
\(\frac{91}{14}\) or 6\(\frac{7}{14}\),
Explanation:
Given to subtract 9\(\frac{5}{7}\) – 3\(\frac{3}{14}\) as
both are in mixed fractions we convert into fractions as
9\(\frac{5}{7}\) = \(\frac{9 X 7 + 5}{7}\) = \(\frac{68}{7}\) and 3\(\frac{3}{14}\) = \(\frac{3 X 14 + 3}{14}\) = \(\frac{45}{14}\) both don’t have common denominators first we multiply \(\frac{68}{7}\) by 2 we get \(\frac{68 X 2}{7 X 2}\) = \(\frac{136}{14}\) now we subtract numerators as \(\frac{136 – 45}{14}\) = \(\frac{91}{14}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{6 X 14 + 7}{14}\) = 6\(\frac{7}{14}\).
Question 11.
31\(\frac{7}{8}\) – 12\(\frac{2}{5}\)
Answer:
\(\frac{779}{40}\) or 19\(\frac{19}{40}\),
Explanation:
Given to subtract 31\(\frac{7}{8}\) – 12\(\frac{2}{5}\) as
both are in mixed fractions we convert into fractions as
31\(\frac{7}{8}\) = \(\frac{31 X 8 + 7}{8}\) = \(\frac{255}{8}\) and 12\(\frac{2}{5}\) = \(\frac{12 X 5 + 2}{5}\) = \(\frac{62}{5}\) both don’t have common denominators first we multiply \(\frac{255}{8}\) by 5 we get \(\frac{255 X 5}{8 X 5}\) = \(\frac{1,275}{40}\) and \(\frac{62}{5}\) by 8 we get \(\frac{62 X 8}{5 X 8}\)= \(\frac{496}{40}\) now we subtract numerators as \(\frac{1,275 – 496}{40}\) = \(\frac{779}{40}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{19 X 40 + 19}{40}\) = 19\(\frac{19}{40}\).
Question 12.
45\(\frac{1}{3}\) – 32\(\frac{3}{7}\)
Answer:
\(\frac{271}{21}\) or 12\(\frac{19}{21}\),
Explanation:
Given to subtract 45\(\frac{1}{3}\) – 32\(\frac{3}{7}\) as
both are in mixed fractions we convert into fractions as
\(\frac{45 X 3 + 1}{3}\) = \(\frac{136}{3}\) and 32\(\frac{3}{7}\) = \(\frac{32 X 7 + 3}{7}\) = \(\frac{227}{7}\) both don’t have common denominators first we multiply \(\frac{136}{3}\) by 7 we get \(\frac{136 X 7}{3 X 7}\) = \(\frac{952}{21}\) and \(\frac{227}{7}\) by 3 we get \(\frac{227 X 3}{7 X 3}\)= \(\frac{681}{21}\) now we subtract numerators as \(\frac{952 – 681}{21}\) = \(\frac{271}{21}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{12 X 21 + 19}{21}\) = 12\(\frac{19}{21}\).