Question

greater than >, less than < or equal =
directions: 1. multiply or divide to find a common denominator

1. then compare the numerator.
2. write >, <, or = in the circle.

\\( \frac { 3 } { 4 } \bigcirc \frac { 1 } { 4 } \\) \\( \frac { 5 } { 7 } \bigcirc \frac { 6 } { 7 } \\) \\( \frac { 2 } { 10 } \bigcirc \frac { 8 } { 10 } \\)
\\( \frac { 2 } { 6 } \bigcirc \frac { 2 } { 3 } \\) \\( \frac { 1 } { 2 } \bigcirc \frac { 5 } { 8 } \\) \\( \frac { 5 } { 18 } \bigcirc \frac { 1 } { 3 } \\)
\\( \frac { 4 } { 5 } \bigcirc \frac { 22 } { 25 } \\) \\( \frac { 5 } { 6 } \bigcirc \frac { 33 } { 42 } \\) \\( \frac { 80 } { 100 } \bigcirc \frac { 4 } { 5 } \\)
\\( \frac { 15 } { 21 } \bigcirc \frac { 4 } { 7 } \\) \\( \frac { 4 } { 16 } \bigcirc \frac { 12 } { 24 } \\) \\( \frac { 36 } { 81 } \bigcirc \frac { 18 } { 27 } \\)
\\( \frac { 21 } { 35 } \bigcirc \frac { 16 } { 40 } \\) \\( \frac { 28 } { 49 } \bigcirc \frac { 18 } { 21 } \\) \\( \frac { 60 } { 144 } \bigcirc \frac { 12 } { 24 } \\)
\\( \frac { 2 } { 5 } \bigcirc \frac { 4 } { 7 } \\) \\( \frac { 5 } { 9 } \bigcirc \frac { 3 } { 4 } \\) \\( \frac { 4 } { 6 } \bigcirc \frac { 7 } { 8 } \\)
\\( \frac { 9 } { 13 } \bigcirc \frac { 5 } { 8 } \\) \\( \frac { 8 } { 10 } \bigcirc \frac { 6 } { 9 } \\) \\( \frac { 7 } { 11 } \bigcirc \frac { 2 } { 4 } \\)
\\( \frac { 25 } { 10 } \bigcirc \frac { 20 } { 10 } \\) \\( \frac { 46 } { 6 } \bigcirc \frac { 14 } { 4 } \\) \\( \frac { 57 } { 7 } \bigcirc \frac { 62 } { 9 } \\)

Explanation:

Step1: Compare \(\frac{3}{4}\) and \(\frac{1}{4}\)

Since denominators are same (\(4\)), compare numerators. \(3>1\), so \(\frac{3}{4}>\frac{1}{4}\)

Step2: Compare \(\frac{5}{7}\) and \(\frac{6}{7}\)

Denominators are same (\(7\)). \(5 < 6\), so \(\frac{5}{7}<\frac{6}{7}\)

Step3: Compare \(\frac{2}{10}\) and \(\frac{8}{10}\)

Denominators are same (\(10\)). \(2<8\), so \(\frac{2}{10}<\frac{8}{10}\)

Step4: Compare \(\frac{2}{6}\) and \(\frac{2}{3}\)

Find common denominator. \(LCM(6,3)=6\). \(\frac{2}{3}=\frac{4}{6}\). Since \(2 < 4\), \(\frac{2}{6}<\frac{2}{3}\)

Step5: Compare \(\frac{1}{2}\) and \(\frac{5}{8}\)

Find common denominator. \(LCM(2,8) = 8\). \(\frac{1}{2}=\frac{4}{8}\). Since \(4<5\), \(\frac{1}{2}<\frac{5}{8}\)

Step6: Compare \(\frac{5}{18}\) and \(\frac{1}{3}\)

Find common denominator. \(LCM(18,3)=18\). \(\frac{1}{3}=\frac{6}{18}\). Since \(5<6\), \(\frac{5}{18}<\frac{1}{3}\)

Step7: Compare \(\frac{4}{5}\) and \(\frac{22}{25}\)

Find common denominator. \(LCM(5,25)=25\). \(\frac{4}{5}=\frac{20}{25}\). Since \(20<22\), \(\frac{4}{5}<\frac{22}{25}\)

Step8: Compare \(\frac{5}{6}\) and \(\frac{33}{42}\)

Find common denominator. \(LCM(6,42)=42\). \(\frac{5}{6}=\frac{35}{42}\). Since \(35>33\), \(\frac{5}{6}>\frac{33}{42}\)

Step9: Compare \(\frac{80}{100}\) and \(\frac{4}{5}\)

Find common denominator. \(LCM(100,5)=100\). \(\frac{4}{5}=\frac{80}{100}\). So \(\frac{80}{100}=\frac{4}{5}\)

Step10: Compare \(\frac{15}{21}\) and \(\frac{4}{7}\)

Find common denominator. \(LCM(21,7)=21\). \(\frac{4}{7}=\frac{12}{21}\). Since \(15>12\), \(\frac{15}{21}>\frac{4}{7}\)

Step11: Compare \(\frac{4}{16}\) and \(\frac{12}{24}\)

Simplify first. \(\frac{4}{16}=\frac{1}{4}\), \(\frac{12}{24}=\frac{1}{2}\). Find common denominator \(LCM(4,2) = 4\). \(\frac{1}{2}=\frac{2}{4}\). Since \(1<2\), \(\frac{4}{16}<\frac{12}{24}\)

Step12: Compare \(\frac{36}{81}\) and \(\frac{18}{27}\)

Simplify. \(\frac{36}{81}=\frac{4}{9}\), \(\frac{18}{27}=\frac{2}{3}=\frac{6}{9}\). Since \(4<6\), \(\frac{36}{81}<\frac{18}{27}\)

Step13: Compare \(\frac{21}{35}\) and \(\frac{16}{40}\)

Simplify. \(\frac{21}{35}=\frac{3}{5}\), \(\frac{16}{40}=\frac{2}{5}\). Since \(3>2\), \(\frac{21}{35}>\frac{16}{40}\)

Step14: Compare \(\frac{28}{49}\) and \(\frac{18}{21}\)

Simplify. \(\frac{28}{49}=\frac{4}{7}\), \(\frac{18}{21}=\frac{6}{7}\). Since \(4<6\), \(\frac{28}{49}<\frac{18}{21}\)

Step15: Compare \(\frac{60}{144}\) and \(\frac{12}{24}\)

Simplify. \(\frac{60}{144}=\frac{5}{12}\), \(\frac{12}{24}=\frac{1}{2}=\frac{6}{12}\). Since \(5<6\), \(\frac{60}{144}<\frac{12}{24}\)

Step16: Compare \(\frac{2}{5}\) and \(\frac{4}{7}\)

Find common denominator. \(LCM(5,7)=35\). \(\frac{2}{5}=\frac{14}{35}\), \(\frac{4}{7}=\frac{20}{35}\). Since \(14<20\), \(\frac{2}{5}<\frac{4}{7}\)

Step17: Compare \(\frac{5}{9}\) and \(\frac{3}{4}\)

Find common denominator. \(LCM(9,4)=36\). \(\frac{5}{9}=\frac{20}{36}\), \(\frac{3}{4}=\frac{27}{36}\). Since \(20<27\), \(\frac{5}{9}<\frac{3}{4}\)

Step18: Compare \(\frac{4}{6}\) and \(\frac{7}{8}\)

Find common denominator. \(LCM(6,8)=24\). \(\frac{4}{6}=\frac{16}{24}\), \(\frac{7}{8}=\frac{21}{24}\). Since \(16<21\), \(\frac{4}{6}<\frac{7}{8}\)

Step19: Compare \(\frac{9}{13}\) and \(\frac{5}{8}\)

Find common denominator. \(LCM(13,8)=104\). \(\frac{9}{13}=\frac{72}{104}\), \(\frac{5}{8}=\frac{65}{104}\). Since \(72>65\), \(\frac{9}{13}>\frac{5}{8}\)

Step20: Compare \(\frac{8}{10}\) and \(\frac{6}{9}\)

Simplify. \(\frac{8}{10}=\frac{4}{5}\), \(\frac{6}{9}=\frac{2}{3}\). Find common denominator \(LCM(5,3)=15\). \(\frac{4}{5}=\frac{12}{15}\), \(\frac{2}{3}=\frac{10}{15}\). Since \(12>10\), \(\frac{8}{10}>\frac{6}{9}\)

Step21: Compare \(\frac{7}{11}\) and \(\frac{2}{4}\)

Simplify \(\frac{2}{4}=\frac{1}{2}\). Find common denominator. \(LCM(11,2)=22\). \(\frac{7}{11}=\frac{14}{22}\), \(\frac{1}{2}=\frac{11}{22}\). Since \(14>11\), \(\frac{7}{11}>\frac{2}{4}\)

Step22: Compare \(\frac{25}{10}\) and \(\frac{20}{10}\)

Since denominators are same (\(10\)). \(25>20\), so \(\frac{25}{10}>\frac{20}{10}\)

Step23: Compare \(\frac{46}{6}\) and \(\frac{14}{4}\)

Simplify. \(\frac{46}{6}=\frac{23}{3}\), \(\frac{14}{4}=\frac{7}{2}\). Find common denominator. \(LCM(3,2)=6\). \(\frac{23}{3}=\frac{46}{6}\), \(\frac{7}{2}=\frac{21}{6}\). Since \(46>21\), \(\frac{46}{6}>\frac{14}{4}\)

Step24: Compare \(\frac{57}{7}\) and \(\frac{62}{9}\)

Find common denominator. \(LCM(7,9)=63\). \(\frac{57}{7}=\frac{513}{63}\), \(\frac{62}{9}=\frac{434}{63}\). Since \(513>434\), \(\frac{57}{7}>\frac{62}{9}\)

Answer:

\(\frac{3}{4}>\frac{1}{4}\), \(\frac{5}{7}<\frac{6}{7}\), \(\frac{2}{10}<\frac{8}{10}\), \(\frac{2}{6}<\frac{2}{3}\), \(\frac{1}{2}<\frac{5}{8}\), \(\frac{5}{18}<\frac{1}{3}\), \(\frac{4}{5}<\frac{22}{25}\), \(\frac{5}{6}>\frac{33}{42}\), \(\frac{80}{100}=\frac{4}{5}\), \(\frac{15}{21}>\frac{4}{7}\), \(\frac{4}{16}<\frac{12}{24}\), \(\frac{36}{81}<\frac{18}{27}\), \(\frac{21}{35}>\frac{16}{40}\), \(\frac{28}{49}<\frac{18}{21}\), \(\frac{60}{144}<\frac{12}{24}\), \(\frac{2}{5}<\frac{4}{7}\), \(\frac{5}{9}<\frac{3}{4}\), \(\frac{4}{6}<\frac{7}{8}\), \(\frac{9}{13}>\frac{5}{8}\), \(\frac{8}{10}>\frac{6}{9}\), \(\frac{7}{11}>\frac{2}{4}\), \(\frac{25}{10}>\frac{20}{10}\), \(\frac{46}{6}>\frac{14}{4}\), \(\frac{57}{7}>\frac{62}{9}\)