Greater than Less Than and Equal Worksheet - Free Printable Online - Free Printable
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Step-by-step solution for: Greater than Less Than and Equal Worksheet - Free Printable Online
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Step-by-step solution for: Greater than Less Than and Equal Worksheet - Free Printable Online
To solve the problems in the image, we need to compare fractions by finding a common denominator and then comparing their numerators. Let's go through each problem step by step.
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- Both fractions already have the same denominator (4).
- Compare the numerators: \( 3 > 1 \).
Answer: \( \frac{3}{4} > \frac{1}{4} \)
---
- Both fractions already have the same denominator (7).
- Compare the numerators: \( 5 < 6 \).
Answer: \( \frac{5}{7} < \frac{6}{7} \)
---
- Both fractions are identical.
- Compare the numerators: \( 8 = 8 \).
Answer: \( \frac{8}{10} = \frac{8}{10} \)
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- Simplify \( \frac{2}{6} \) to \( \frac{1}{3} \).
- Now compare \( \frac{1}{3} \) and \( \frac{2}{3} \).
- Both fractions have the same denominator (3).
- Compare the numerators: \( 1 < 2 \).
Answer: \( \frac{2}{6} < \frac{2}{3} \)
---
- Find a common denominator. The least common multiple (LCM) of 2 and 8 is 8.
- Convert \( \frac{1}{2} \) to a fraction with denominator 8: \( \frac{1}{2} = \frac{4}{8} \).
- Now compare \( \frac{4}{8} \) and \( \frac{5}{8} \).
- Compare the numerators: \( 4 < 5 \).
Answer: \( \frac{1}{2} < \frac{5}{8} \)
---
- Find a common denominator. The LCM of 8 and 3 is 24.
- Convert \( \frac{5}{8} \) to a fraction with denominator 24: \( \frac{5}{8} = \frac{15}{24} \).
- Convert \( \frac{1}{3} \) to a fraction with denominator 24: \( \frac{1}{3} = \frac{8}{24} \).
- Now compare \( \frac{15}{24} \) and \( \frac{8}{24} \).
- Compare the numerators: \( 15 > 8 \).
Answer: \( \frac{5}{8} > \frac{1}{3} \)
---
- Find a common denominator. The LCM of 5 and 25 is 25.
- Convert \( \frac{4}{5} \) to a fraction with denominator 25: \( \frac{4}{5} = \frac{20}{25} \).
- Now compare \( \frac{20}{25} \) and \( \frac{22}{25} \).
- Compare the numerators: \( 20 < 22 \).
Answer: \( \frac{4}{5} < \frac{22}{25} \)
---
- Simplify \( \frac{33}{42} \): Divide both numerator and denominator by 3 to get \( \frac{11}{14} \).
- Find a common denominator. The LCM of 6 and 14 is 42.
- Convert \( \frac{5}{6} \) to a fraction with denominator 42: \( \frac{5}{6} = \frac{35}{42} \).
- Now compare \( \frac{35}{42} \) and \( \frac{33}{42} \).
- Compare the numerators: \( 35 > 33 \).
Answer: \( \frac{5}{6} > \frac{33}{42} \)
---
- Simplify \( \frac{80}{10} \) to \( 8 \) or \( \frac{8}{1} \).
- Find a common denominator. The LCM of 1 and 5 is 5.
- Convert \( \frac{8}{1} \) to a fraction with denominator 5: \( \frac{8}{1} = \frac{40}{5} \).
- Now compare \( \frac{40}{5} \) and \( \frac{4}{5} \).
- Compare the numerators: \( 40 > 4 \).
Answer: \( \frac{80}{10} > \frac{4}{5} \)
---
- Simplify \( \frac{15}{21} \): Divide both numerator and denominator by 3 to get \( \frac{5}{7} \).
- Now compare \( \frac{5}{7} \) and \( \frac{4}{7} \).
- Both fractions have the same denominator (7).
- Compare the numerators: \( 5 > 4 \).
Answer: \( \frac{15}{21} > \frac{4}{7} \)
---
- Simplify \( \frac{4}{16} \): Divide both numerator and denominator by 4 to get \( \frac{1}{4} \).
- Simplify \( \frac{12}{24} \): Divide both numerator and denominator by 12 to get \( \frac{1}{2} \).
- Find a common denominator. The LCM of 4 and 2 is 4.
- Convert \( \frac{1}{2} \) to a fraction with denominator 4: \( \frac{1}{2} = \frac{2}{4} \).
- Now compare \( \frac{1}{4} \) and \( \frac{2}{4} \).
- Compare the numerators: \( 1 < 2 \).
Answer: \( \frac{4}{16} < \frac{12}{24} \)
---
- Simplify \( \frac{36}{81} \): Divide both numerator and denominator by 9 to get \( \frac{4}{9} \).
- Simplify \( \frac{18}{27} \): Divide both numerator and denominator by 9 to get \( \frac{2}{3} \).
- Find a common denominator. The LCM of 9 and 3 is 9.
- Convert \( \frac{2}{3} \) to a fraction with denominator 9: \( \frac{2}{3} = \frac{6}{9} \).
- Now compare \( \frac{4}{9} \) and \( \frac{6}{9} \).
- Compare the numerators: \( 4 < 6 \).
Answer: \( \frac{36}{81} < \frac{18}{27} \)
---
- Simplify \( \frac{21}{35} \): Divide both numerator and denominator by 7 to get \( \frac{3}{5} \).
- Simplify \( \frac{16}{40} \): Divide both numerator and denominator by 8 to get \( \frac{2}{5} \).
- Both fractions now have the same denominator (5).
- Compare the numerators: \( 3 > 2 \).
Answer: \( \frac{21}{35} > \frac{16}{40} \)
---
- Simplify \( \frac{28}{49} \): Divide both numerator and denominator by 7 to get \( \frac{4}{7} \).
- Simplify \( \frac{18}{21} \): Divide both numerator and denominator by 3 to get \( \frac{6}{7} \).
- Both fractions now have the same denominator (7).
- Compare the numerators: \( 4 < 6 \).
Answer: \( \frac{28}{49} < \frac{18}{21} \)
---
- Simplify \( \frac{60}{120} \): Divide both numerator and denominator by 60 to get \( \frac{1}{2} \).
- Simplify \( \frac{12}{24} \): Divide both numerator and denominator by 12 to get \( \frac{1}{2} \).
- Both fractions are identical.
Answer: \( \frac{60}{120} = \frac{12}{24} \)
---
- Simplify \( \frac{144}{216} \): Divide both numerator and denominator by 72 to get \( \frac{2}{3} \).
- Simplify \( \frac{14}{24} \): Divide both numerator and denominator by 2 to get \( \frac{7}{12} \).
- Find a common denominator. The LCM of 3 and 12 is 12.
- Convert \( \frac{2}{3} \) to a fraction with denominator 12: \( \frac{2}{3} = \frac{8}{12} \).
- Now compare \( \frac{8}{12} \) and \( \frac{7}{12} \).
- Compare the numerators: \( 8 > 7 \).
Answer: \( \frac{144}{216} > \frac{14}{24} \)
---
- Find a common denominator. The LCM of 5 and 7 is 35.
- Convert \( \frac{2}{5} \) to a fraction with denominator 35: \( \frac{2}{5} = \frac{14}{35} \).
- Convert \( \frac{4}{7} \) to a fraction with denominator 35: \( \frac{4}{7} = \frac{20}{35} \).
- Now compare \( \frac{14}{35} \) and \( \frac{20}{35} \).
- Compare the numerators: \( 14 < 20 \).
Answer: \( \frac{2}{5} < \frac{4}{7} \)
---
- Find a common denominator. The LCM of 9 and 4 is 36.
- Convert \( \frac{5}{9} \) to a fraction with denominator 36: \( \frac{5}{9} = \frac{20}{36} \).
- Convert \( \frac{3}{4} \) to a fraction with denominator 36: \( \frac{3}{4} = \frac{27}{36} \).
- Now compare \( \frac{20}{36} \) and \( \frac{27}{36} \).
- Compare the numerators: \( 20 < 27 \).
Answer: \( \frac{5}{9} < \frac{3}{4} \)
---
- Simplify \( \frac{2}{4} \) to \( \frac{1}{2} \).
- Find a common denominator. The LCM of 11 and 2 is 22.
- Convert \( \frac{7}{11} \) to a fraction with denominator 22: \( \frac{7}{11} = \frac{14}{22} \).
- Convert \( \frac{1}{2} \) to a fraction with denominator 22: \( \frac{1}{2} = \frac{11}{22} \).
- Now compare \( \frac{14}{22} \) and \( \frac{11}{22} \).
- Compare the numerators: \( 14 > 11 \).
Answer: \( \frac{7}{11} > \frac{2}{4} \)
---
- Find a common denominator. The LCM of 13 and 8 is 104.
- Convert \( \frac{9}{13} \) to a fraction with denominator 104: \( \frac{9}{13} = \frac{72}{104} \).
- Convert \( \frac{5}{8} \) to a fraction with denominator 104: \( \frac{5}{8} = \frac{65}{104} \).
- Now compare \( \frac{72}{104} \) and \( \frac{65}{104} \).
- Compare the numerators: \( 72 > 65 \).
Answer: \( \frac{9}{13} > \frac{5}{8} \)
---
- Simplify \( \frac{8}{10} \) to \( \frac{4}{5} \).
- Simplify \( \frac{6}{9} \) to \( \frac{2}{3} \).
- Find a common denominator. The LCM of 5 and 3 is 15.
- Convert \( \frac{4}{5} \) to a fraction with denominator 15: \( \frac{4}{5} = \frac{12}{15} \).
- Convert \( \frac{2}{3} \) to a fraction with denominator 15: \( \frac{2}{3} = \frac{10}{15} \).
- Now compare \( \frac{12}{15} \) and \( \frac{10}{15} \).
- Compare the numerators: \( 12 > 10 \).
Answer: \( \frac{8}{10} > \frac{6}{9} \)
---
- Simplify \( \frac{57}{7} \) and \( \frac{62}{9} \) as they are already in simplest form.
- Find a common denominator. The LCM of 7 and 9 is 63.
- Convert \( \frac{57}{7} \) to a fraction with denominator 63: \( \frac{57}{7} = \frac{513}{63} \).
- Convert \( \frac{62}{9} \) to a fraction with denominator 63: \( \frac{62}{9} = \frac{434}{63} \).
- Now compare \( \frac{513}{63} \) and \( \frac{434}{63} \).
- Compare the numerators: \( 513 > 434 \).
Answer: \( \frac{57}{7} > \frac{62}{9} \)
---
- Both fractions have the same denominator (10).
- Compare the numerators: \( 25 > 20 \).
Answer: \( \frac{25}{10} > \frac{20}{10} \)
---
- Simplify \( \frac{46}{6} \): Divide both numerator and denominator by 2 to get \( \frac{23}{3} \).
- Simplify \( \frac{14}{4} \): Divide both numerator and denominator by 2 to get \( \frac{7}{2} \).
- Find a common denominator. The LCM of 3 and 2 is 6.
- Convert \( \frac{23}{3} \) to a fraction with denominator 6: \( \frac{23}{3} = \frac{46}{6} \).
- Convert \( \frac{7}{2} \) to a fraction with denominator 6: \( \frac{7}{2} = \frac{21}{6} \).
- Now compare \( \frac{46}{6} \) and \( \frac{21}{6} \).
- Compare the numerators: \( 46 > 21 \).
Answer: \( \frac{46}{6} > \frac{14}{4} \)
---
- Both fractions have the same denominator (4).
- Compare the numerators: \( 3 > 1 \).
Answer: \( \frac{3}{4} > \frac{1}{4} \)
---
\[
\boxed{
\begin{array}{c}
\frac{3}{4} > \frac{1}{4}, \quad \frac{5}{7} < \frac{6}{7}, \quad \frac{8}{10} = \frac{8}{10}, \\
\frac{2}{6} < \frac{2}{3}, \quad \frac{1}{2} < \frac{5}{8}, \quad \frac{5}{8} > \frac{1}{3}, \\
\frac{4}{5} < \frac{22}{25}, \quad \frac{5}{6} > \frac{33}{42}, \quad \frac{80}{10} > \frac{4}{5}, \\
\frac{15}{21} > \frac{4}{7}, \quad \frac{4}{16} < \frac{12}{24}, \quad \frac{36}{81} < \frac{18}{27}, \\
\frac{21}{35} > \frac{16}{40}, \quad \frac{28}{49} < \frac{18}{21}, \quad \frac{60}{120} = \frac{12}{24}, \\
\frac{144}{216} > \frac{14}{24}, \quad \frac{2}{5} < \frac{4}{7}, \quad \frac{5}{9} < \frac{3}{4}, \\
\frac{7}{11} > \frac{2}{4}, \quad \frac{9}{13} > \frac{5}{8}, \quad \frac{8}{10} > \frac{6}{9}, \\
\frac{57}{7} > \frac{62}{9}, \quad \frac{25}{10} > \frac{20}{10}, \quad \frac{46}{6} > \frac{14}{4}, \\
\frac{3}{4} > \frac{1}{4}.
\end{array}
}
\]
---
Problem 1: \( \frac{3}{4} \) vs \( \frac{1}{4} \)
- Both fractions already have the same denominator (4).
- Compare the numerators: \( 3 > 1 \).
Answer: \( \frac{3}{4} > \frac{1}{4} \)
---
Problem 2: \( \frac{5}{7} \) vs \( \frac{6}{7} \)
- Both fractions already have the same denominator (7).
- Compare the numerators: \( 5 < 6 \).
Answer: \( \frac{5}{7} < \frac{6}{7} \)
---
Problem 3: \( \frac{8}{10} \) vs \( \frac{8}{10} \)
- Both fractions are identical.
- Compare the numerators: \( 8 = 8 \).
Answer: \( \frac{8}{10} = \frac{8}{10} \)
---
Problem 4: \( \frac{2}{6} \) vs \( \frac{2}{3} \)
- Simplify \( \frac{2}{6} \) to \( \frac{1}{3} \).
- Now compare \( \frac{1}{3} \) and \( \frac{2}{3} \).
- Both fractions have the same denominator (3).
- Compare the numerators: \( 1 < 2 \).
Answer: \( \frac{2}{6} < \frac{2}{3} \)
---
Problem 5: \( \frac{1}{2} \) vs \( \frac{5}{8} \)
- Find a common denominator. The least common multiple (LCM) of 2 and 8 is 8.
- Convert \( \frac{1}{2} \) to a fraction with denominator 8: \( \frac{1}{2} = \frac{4}{8} \).
- Now compare \( \frac{4}{8} \) and \( \frac{5}{8} \).
- Compare the numerators: \( 4 < 5 \).
Answer: \( \frac{1}{2} < \frac{5}{8} \)
---
Problem 6: \( \frac{5}{8} \) vs \( \frac{1}{3} \)
- Find a common denominator. The LCM of 8 and 3 is 24.
- Convert \( \frac{5}{8} \) to a fraction with denominator 24: \( \frac{5}{8} = \frac{15}{24} \).
- Convert \( \frac{1}{3} \) to a fraction with denominator 24: \( \frac{1}{3} = \frac{8}{24} \).
- Now compare \( \frac{15}{24} \) and \( \frac{8}{24} \).
- Compare the numerators: \( 15 > 8 \).
Answer: \( \frac{5}{8} > \frac{1}{3} \)
---
Problem 7: \( \frac{4}{5} \) vs \( \frac{22}{25} \)
- Find a common denominator. The LCM of 5 and 25 is 25.
- Convert \( \frac{4}{5} \) to a fraction with denominator 25: \( \frac{4}{5} = \frac{20}{25} \).
- Now compare \( \frac{20}{25} \) and \( \frac{22}{25} \).
- Compare the numerators: \( 20 < 22 \).
Answer: \( \frac{4}{5} < \frac{22}{25} \)
---
Problem 8: \( \frac{5}{6} \) vs \( \frac{33}{42} \)
- Simplify \( \frac{33}{42} \): Divide both numerator and denominator by 3 to get \( \frac{11}{14} \).
- Find a common denominator. The LCM of 6 and 14 is 42.
- Convert \( \frac{5}{6} \) to a fraction with denominator 42: \( \frac{5}{6} = \frac{35}{42} \).
- Now compare \( \frac{35}{42} \) and \( \frac{33}{42} \).
- Compare the numerators: \( 35 > 33 \).
Answer: \( \frac{5}{6} > \frac{33}{42} \)
---
Problem 9: \( \frac{80}{10} \) vs \( \frac{4}{5} \)
- Simplify \( \frac{80}{10} \) to \( 8 \) or \( \frac{8}{1} \).
- Find a common denominator. The LCM of 1 and 5 is 5.
- Convert \( \frac{8}{1} \) to a fraction with denominator 5: \( \frac{8}{1} = \frac{40}{5} \).
- Now compare \( \frac{40}{5} \) and \( \frac{4}{5} \).
- Compare the numerators: \( 40 > 4 \).
Answer: \( \frac{80}{10} > \frac{4}{5} \)
---
Problem 10: \( \frac{15}{21} \) vs \( \frac{4}{7} \)
- Simplify \( \frac{15}{21} \): Divide both numerator and denominator by 3 to get \( \frac{5}{7} \).
- Now compare \( \frac{5}{7} \) and \( \frac{4}{7} \).
- Both fractions have the same denominator (7).
- Compare the numerators: \( 5 > 4 \).
Answer: \( \frac{15}{21} > \frac{4}{7} \)
---
Problem 11: \( \frac{4}{16} \) vs \( \frac{12}{24} \)
- Simplify \( \frac{4}{16} \): Divide both numerator and denominator by 4 to get \( \frac{1}{4} \).
- Simplify \( \frac{12}{24} \): Divide both numerator and denominator by 12 to get \( \frac{1}{2} \).
- Find a common denominator. The LCM of 4 and 2 is 4.
- Convert \( \frac{1}{2} \) to a fraction with denominator 4: \( \frac{1}{2} = \frac{2}{4} \).
- Now compare \( \frac{1}{4} \) and \( \frac{2}{4} \).
- Compare the numerators: \( 1 < 2 \).
Answer: \( \frac{4}{16} < \frac{12}{24} \)
---
Problem 12: \( \frac{36}{81} \) vs \( \frac{18}{27} \)
- Simplify \( \frac{36}{81} \): Divide both numerator and denominator by 9 to get \( \frac{4}{9} \).
- Simplify \( \frac{18}{27} \): Divide both numerator and denominator by 9 to get \( \frac{2}{3} \).
- Find a common denominator. The LCM of 9 and 3 is 9.
- Convert \( \frac{2}{3} \) to a fraction with denominator 9: \( \frac{2}{3} = \frac{6}{9} \).
- Now compare \( \frac{4}{9} \) and \( \frac{6}{9} \).
- Compare the numerators: \( 4 < 6 \).
Answer: \( \frac{36}{81} < \frac{18}{27} \)
---
Problem 13: \( \frac{21}{35} \) vs \( \frac{16}{40} \)
- Simplify \( \frac{21}{35} \): Divide both numerator and denominator by 7 to get \( \frac{3}{5} \).
- Simplify \( \frac{16}{40} \): Divide both numerator and denominator by 8 to get \( \frac{2}{5} \).
- Both fractions now have the same denominator (5).
- Compare the numerators: \( 3 > 2 \).
Answer: \( \frac{21}{35} > \frac{16}{40} \)
---
Problem 14: \( \frac{28}{49} \) vs \( \frac{18}{21} \)
- Simplify \( \frac{28}{49} \): Divide both numerator and denominator by 7 to get \( \frac{4}{7} \).
- Simplify \( \frac{18}{21} \): Divide both numerator and denominator by 3 to get \( \frac{6}{7} \).
- Both fractions now have the same denominator (7).
- Compare the numerators: \( 4 < 6 \).
Answer: \( \frac{28}{49} < \frac{18}{21} \)
---
Problem 15: \( \frac{60}{120} \) vs \( \frac{12}{24} \)
- Simplify \( \frac{60}{120} \): Divide both numerator and denominator by 60 to get \( \frac{1}{2} \).
- Simplify \( \frac{12}{24} \): Divide both numerator and denominator by 12 to get \( \frac{1}{2} \).
- Both fractions are identical.
Answer: \( \frac{60}{120} = \frac{12}{24} \)
---
Problem 16: \( \frac{144}{216} \) vs \( \frac{14}{24} \)
- Simplify \( \frac{144}{216} \): Divide both numerator and denominator by 72 to get \( \frac{2}{3} \).
- Simplify \( \frac{14}{24} \): Divide both numerator and denominator by 2 to get \( \frac{7}{12} \).
- Find a common denominator. The LCM of 3 and 12 is 12.
- Convert \( \frac{2}{3} \) to a fraction with denominator 12: \( \frac{2}{3} = \frac{8}{12} \).
- Now compare \( \frac{8}{12} \) and \( \frac{7}{12} \).
- Compare the numerators: \( 8 > 7 \).
Answer: \( \frac{144}{216} > \frac{14}{24} \)
---
Problem 17: \( \frac{2}{5} \) vs \( \frac{4}{7} \)
- Find a common denominator. The LCM of 5 and 7 is 35.
- Convert \( \frac{2}{5} \) to a fraction with denominator 35: \( \frac{2}{5} = \frac{14}{35} \).
- Convert \( \frac{4}{7} \) to a fraction with denominator 35: \( \frac{4}{7} = \frac{20}{35} \).
- Now compare \( \frac{14}{35} \) and \( \frac{20}{35} \).
- Compare the numerators: \( 14 < 20 \).
Answer: \( \frac{2}{5} < \frac{4}{7} \)
---
Problem 18: \( \frac{5}{9} \) vs \( \frac{3}{4} \)
- Find a common denominator. The LCM of 9 and 4 is 36.
- Convert \( \frac{5}{9} \) to a fraction with denominator 36: \( \frac{5}{9} = \frac{20}{36} \).
- Convert \( \frac{3}{4} \) to a fraction with denominator 36: \( \frac{3}{4} = \frac{27}{36} \).
- Now compare \( \frac{20}{36} \) and \( \frac{27}{36} \).
- Compare the numerators: \( 20 < 27 \).
Answer: \( \frac{5}{9} < \frac{3}{4} \)
---
Problem 19: \( \frac{7}{11} \) vs \( \frac{2}{4} \)
- Simplify \( \frac{2}{4} \) to \( \frac{1}{2} \).
- Find a common denominator. The LCM of 11 and 2 is 22.
- Convert \( \frac{7}{11} \) to a fraction with denominator 22: \( \frac{7}{11} = \frac{14}{22} \).
- Convert \( \frac{1}{2} \) to a fraction with denominator 22: \( \frac{1}{2} = \frac{11}{22} \).
- Now compare \( \frac{14}{22} \) and \( \frac{11}{22} \).
- Compare the numerators: \( 14 > 11 \).
Answer: \( \frac{7}{11} > \frac{2}{4} \)
---
Problem 20: \( \frac{9}{13} \) vs \( \frac{5}{8} \)
- Find a common denominator. The LCM of 13 and 8 is 104.
- Convert \( \frac{9}{13} \) to a fraction with denominator 104: \( \frac{9}{13} = \frac{72}{104} \).
- Convert \( \frac{5}{8} \) to a fraction with denominator 104: \( \frac{5}{8} = \frac{65}{104} \).
- Now compare \( \frac{72}{104} \) and \( \frac{65}{104} \).
- Compare the numerators: \( 72 > 65 \).
Answer: \( \frac{9}{13} > \frac{5}{8} \)
---
Problem 21: \( \frac{8}{10} \) vs \( \frac{6}{9} \)
- Simplify \( \frac{8}{10} \) to \( \frac{4}{5} \).
- Simplify \( \frac{6}{9} \) to \( \frac{2}{3} \).
- Find a common denominator. The LCM of 5 and 3 is 15.
- Convert \( \frac{4}{5} \) to a fraction with denominator 15: \( \frac{4}{5} = \frac{12}{15} \).
- Convert \( \frac{2}{3} \) to a fraction with denominator 15: \( \frac{2}{3} = \frac{10}{15} \).
- Now compare \( \frac{12}{15} \) and \( \frac{10}{15} \).
- Compare the numerators: \( 12 > 10 \).
Answer: \( \frac{8}{10} > \frac{6}{9} \)
---
Problem 22: \( \frac{57}{7} \) vs \( \frac{62}{9} \)
- Simplify \( \frac{57}{7} \) and \( \frac{62}{9} \) as they are already in simplest form.
- Find a common denominator. The LCM of 7 and 9 is 63.
- Convert \( \frac{57}{7} \) to a fraction with denominator 63: \( \frac{57}{7} = \frac{513}{63} \).
- Convert \( \frac{62}{9} \) to a fraction with denominator 63: \( \frac{62}{9} = \frac{434}{63} \).
- Now compare \( \frac{513}{63} \) and \( \frac{434}{63} \).
- Compare the numerators: \( 513 > 434 \).
Answer: \( \frac{57}{7} > \frac{62}{9} \)
---
Problem 23: \( \frac{25}{10} \) vs \( \frac{20}{10} \)
- Both fractions have the same denominator (10).
- Compare the numerators: \( 25 > 20 \).
Answer: \( \frac{25}{10} > \frac{20}{10} \)
---
Problem 24: \( \frac{46}{6} \) vs \( \frac{14}{4} \)
- Simplify \( \frac{46}{6} \): Divide both numerator and denominator by 2 to get \( \frac{23}{3} \).
- Simplify \( \frac{14}{4} \): Divide both numerator and denominator by 2 to get \( \frac{7}{2} \).
- Find a common denominator. The LCM of 3 and 2 is 6.
- Convert \( \frac{23}{3} \) to a fraction with denominator 6: \( \frac{23}{3} = \frac{46}{6} \).
- Convert \( \frac{7}{2} \) to a fraction with denominator 6: \( \frac{7}{2} = \frac{21}{6} \).
- Now compare \( \frac{46}{6} \) and \( \frac{21}{6} \).
- Compare the numerators: \( 46 > 21 \).
Answer: \( \frac{46}{6} > \frac{14}{4} \)
---
Problem 25: \( \frac{3}{4} \) vs \( \frac{1}{4} \)
- Both fractions have the same denominator (4).
- Compare the numerators: \( 3 > 1 \).
Answer: \( \frac{3}{4} > \frac{1}{4} \)
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Final Answers:
\[
\boxed{
\begin{array}{c}
\frac{3}{4} > \frac{1}{4}, \quad \frac{5}{7} < \frac{6}{7}, \quad \frac{8}{10} = \frac{8}{10}, \\
\frac{2}{6} < \frac{2}{3}, \quad \frac{1}{2} < \frac{5}{8}, \quad \frac{5}{8} > \frac{1}{3}, \\
\frac{4}{5} < \frac{22}{25}, \quad \frac{5}{6} > \frac{33}{42}, \quad \frac{80}{10} > \frac{4}{5}, \\
\frac{15}{21} > \frac{4}{7}, \quad \frac{4}{16} < \frac{12}{24}, \quad \frac{36}{81} < \frac{18}{27}, \\
\frac{21}{35} > \frac{16}{40}, \quad \frac{28}{49} < \frac{18}{21}, \quad \frac{60}{120} = \frac{12}{24}, \\
\frac{144}{216} > \frac{14}{24}, \quad \frac{2}{5} < \frac{4}{7}, \quad \frac{5}{9} < \frac{3}{4}, \\
\frac{7}{11} > \frac{2}{4}, \quad \frac{9}{13} > \frac{5}{8}, \quad \frac{8}{10} > \frac{6}{9}, \\
\frac{57}{7} > \frac{62}{9}, \quad \frac{25}{10} > \frac{20}{10}, \quad \frac{46}{6} > \frac{14}{4}, \\
\frac{3}{4} > \frac{1}{4}.
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of fractions greater than less than.
