Greater Than or Less Than? Comparing Fractions | Worksheet ... - Free Printable

The task involves comparing fractions by multiplying or dividing to find a common denominator, then determining whether one fraction is greater than (>), less than (<), or equal to (=) the other. Below is a step-by-step explanation of how to solve each problem.

---

Problem 1:

$$
\frac{3}{4} \quad \text{?} \quad \frac{1}{4}
$$

- Step 1: Compare the numerators directly since the denominators are the same.
- Step 2: Since \(3 > 1\), we have:
$$
\frac{3}{4} > \frac{1}{4}
$$

Answer: \(>\)

---

Problem 2:

$$
\frac{5}{7} \quad \text{?} \quad \frac{6}{7}
$$

- Step 1: Compare the numerators directly since the denominators are the same.
- Step 2: Since \(5 < 6\), we have:
$$
\frac{5}{7} < \frac{6}{7}
$$

Answer: \(<\)

---

Problem 3:

$$
-\frac{2}{10} \quad \text{?} \quad \frac{8}{10}
$$

- Step 1: Compare the numerators directly since the denominators are the same.
- Step 2: Since \(-2 < 8\), we have:
$$
-\frac{2}{10} < \frac{8}{10}
$$

Answer: \(<\)

---

Problem 4:

$$
\frac{3}{6} \quad \text{?} \quad \frac{2}{3}
$$

- Step 1: Simplify \(\frac{3}{6}\) to \(\frac{1}{2}\).
- Step 2: Find a common denominator for \(\frac{1}{2}\) and \(\frac{2}{3}\). The least common denominator (LCD) is 6.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{1}{2} = \frac{3}{6}, \quad \frac{2}{3} = \frac{4}{6}
$$
- Step 4: Compare the numerators:
$$
\frac{3}{6} < \frac{4}{6}
$$
- Step 5: Therefore:
$$
\frac{3}{6} < \frac{2}{3}
$$

Answer: \(<\)

---

Problem 5:

$$
\frac{1}{2} \quad \text{?} \quad \frac{5}{8}
$$

- Step 1: Find a common denominator for \(\frac{1}{2}\) and \(\frac{5}{8}\). The LCD is 8.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{1}{2} = \frac{4}{8}, \quad \frac{5}{8} = \frac{5}{8}
$$
- Step 3: Compare the numerators:
$$
\frac{4}{8} < \frac{5}{8}
$$
- Step 4: Therefore:
$$
\frac{1}{2} < \frac{5}{8}
$$

Answer: \(<\)

---

Problem 6:

$$
\frac{5}{18} \quad \text{?} \quad \frac{1}{3}
$$

- Step 1: Rewrite \(\frac{1}{3}\) with a denominator of 18:
$$
\frac{1}{3} = \frac{6}{18}
$$
- Step 2: Compare the numerators:
$$
\frac{5}{18} < \frac{6}{18}
$$
- Step 3: Therefore:
$$
\frac{5}{18} < \frac{1}{3}
$$

Answer: \(<\)

---

Problem 7:

$$
\frac{4}{5} \quad \text{?} \quad \frac{22}{25}
$$

- Step 1: Find a common denominator for \(\frac{4}{5}\) and \(\frac{22}{25}\). The LCD is 25.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{4}{5} = \frac{20}{25}, \quad \frac{22}{25} = \frac{22}{25}
$$
- Step 3: Compare the numerators:
$$
\frac{20}{25} < \frac{22}{25}
$$
- Step 4: Therefore:
$$
\frac{4}{5} < \frac{22}{25}
$$

Answer: \(<\)

---

Problem 8:

$$
\frac{5}{6} \quad \text{?} \quad \frac{33}{42}
$$

- Step 1: Simplify \(\frac{33}{42}\):
$$
\frac{33}{42} = \frac{11}{14}
$$
- Step 2: Find a common denominator for \(\frac{5}{6}\) and \(\frac{11}{14}\). The LCD is 42.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{5}{6} = \frac{35}{42}, \quad \frac{11}{14} = \frac{33}{42}
$$
- Step 4: Compare the numerators:
$$
\frac{35}{42} > \frac{33}{42}
$$
- Step 5: Therefore:
$$
\frac{5}{6} > \frac{33}{42}
$$

Answer: \(>\)

---

Problem 9:

$$
\frac{80}{100} \quad \text{?} \quad \frac{4}{5}
$$

- Step 1: Simplify \(\frac{80}{100}\):
$$
\frac{80}{100} = \frac{4}{5}
$$
- Step 2: Compare the simplified fractions:
$$
\frac{4}{5} = \frac{4}{5}
$$
- Step 3: Therefore:
$$
\frac{80}{100} = \frac{4}{5}
$$

Answer: \(=\)

---

Problem 10:

$$
\frac{15}{21} \quad \text{?} \quad \frac{4}{7}
$$

- Step 1: Simplify \(\frac{15}{21}\):
$$
\frac{15}{21} = \frac{5}{7}
$$
- Step 2: Compare \(\frac{5}{7}\) and \(\frac{4}{7}\):
$$
\frac{5}{7} > \frac{4}{7}
$$
- Step 3: Therefore:
$$
\frac{15}{21} > \frac{4}{7}
$$

Answer: \(>\)

---

Problem 11:

$$
\frac{4}{12} \quad \text{?} \quad \frac{4}{24}
$$

- Step 1: Simplify \(\frac{4}{12}\) and \(\frac{4}{24}\):
$$
\frac{4}{12} = \frac{1}{3}, \quad \frac{4}{24} = \frac{1}{6}
$$
- Step 2: Find a common denominator for \(\frac{1}{3}\) and \(\frac{1}{6}\). The LCD is 6.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{1}{3} = \frac{2}{6}, \quad \frac{1}{6} = \frac{1}{6}
$$
- Step 4: Compare the numerators:
$$
\frac{2}{6} > \frac{1}{6}
$$
- Step 5: Therefore:
$$
\frac{4}{12} > \frac{4}{24}
$$

Answer: \(>\)

---

Problem 12:

$$
-\frac{36}{81} \quad \text{?} \quad \frac{18}{27}
$$

- Step 1: Simplify \(\frac{36}{81}\) and \(\frac{18}{27}\):
$$
\frac{36}{81} = \frac{4}{9}, \quad \frac{18}{27} = \frac{2}{3}
$$
- Step 2: Rewrite \(\frac{2}{3}\) with a denominator of 9:
$$
\frac{2}{3} = \frac{6}{9}
$$
- Step 3: Compare \(-\frac{4}{9}\) and \(\frac{6}{9}\):
$$
-\frac{4}{9} < \frac{6}{9}
$$
- Step 4: Therefore:
$$
-\frac{36}{81} < \frac{18}{27}
$$

Answer: \(<\)

---

Problem 13:

$$
\frac{21}{35} \quad \text{?} \quad \frac{16}{40}
$$

- Step 1: Simplify \(\frac{21}{35}\) and \(\frac{16}{40}\):
$$
\frac{21}{35} = \frac{3}{5}, \quad \frac{16}{40} = \frac{2}{5}
$$
- Step 2: Compare \(\frac{3}{5}\) and \(\frac{2}{5}\):
$$
\frac{3}{5} > \frac{2}{5}
$$
- Step 3: Therefore:
$$
\frac{21}{35} > \frac{16}{40}
$$

Answer: \(>\)

---

Problem 14:

$$
\frac{28}{49} \quad \text{?} \quad \frac{18}{21}
$$

- Step 1: Simplify \(\frac{28}{49}\) and \(\frac{18}{21}\):
$$
\frac{28}{49} = \frac{4}{7}, \quad \frac{18}{21} = \frac{6}{7}
$$
- Step 2: Compare \(\frac{4}{7}\) and \(\frac{6}{7}\):
$$
\frac{4}{7} < \frac{6}{7}
$$
- Step 3: Therefore:
$$
\frac{28}{49} < \frac{18}{21}
$$

Answer: \(<\)

---

Problem 15:

$$
-\frac{60}{144} \quad \text{?} \quad \frac{12}{24}
$$

- Step 1: Simplify \(\frac{60}{144}\) and \(\frac{12}{24}\):
$$
\frac{60}{144} = \frac{5}{12}, \quad \frac{12}{24} = \frac{1}{2}
$$
- Step 2: Rewrite \(\frac{1}{2}\) with a denominator of 12:
$$
\frac{1}{2} = \frac{6}{12}
$$
- Step 3: Compare \(-\frac{5}{12}\) and \(\frac{6}{12}\):
$$
-\frac{5}{12} < \frac{6}{12}
$$
- Step 4: Therefore:
$$
-\frac{60}{144} < \frac{12}{24}
$$

Answer: \(<\)

---

Problem 16:

$$
\frac{2}{5} \quad \text{?} \quad \frac{4}{7}
$$

- Step 1: Find a common denominator for \(\frac{2}{5}\) and \(\frac{4}{7}\). The LCD is 35.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{2}{5} = \frac{14}{35}, \quad \frac{4}{7} = \frac{20}{35}
$$
- Step 3: Compare the numerators:
$$
\frac{14}{35} < \frac{20}{35}
$$
- Step 4: Therefore:
$$
\frac{2}{5} < \frac{4}{7}
$$

Answer: \(<\)

---

Problem 17:

$$
\frac{5}{9} \quad \text{?} \quad \frac{3}{4}
$$

- Step 1: Find a common denominator for \(\frac{5}{9}\) and \(\frac{3}{4}\). The LCD is 36.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{5}{9} = \frac{20}{36}, \quad \frac{3}{4} = \frac{27}{36}
$$
- Step 3: Compare the numerators:
$$
\frac{20}{36} < \frac{27}{36}
$$
- Step 4: Therefore:
$$
\frac{5}{9} < \frac{3}{4}
$$

Answer: \(<\)

---

Problem 18:

$$
-\frac{4}{6} \quad \text{?} \quad \frac{7}{8}
$$

- Step 1: Simplify \(\frac{4}{6}\):
$$
\frac{4}{6} = \frac{2}{3}
$$
- Step 2: Compare \(-\frac{2}{3}\) and \(\frac{7}{8}\):
$$
-\frac{2}{3} < \frac{7}{8}
$$
- Step 3: Therefore:
$$
-\frac{4}{6} < \frac{7}{8}
$$

Answer: \(<\)

---

Problem 19:

$$
-\frac{9}{13} \quad \text{?} \quad \frac{5}{8}
$$

- Step 1: Compare \(-\frac{9}{13}\) and \(\frac{5}{8}\):
$$
-\frac{9}{13} < \frac{5}{8}
$$
- Step 2: Therefore:
$$
-\frac{9}{13} < \frac{5}{8}
$$

Answer: \(<\)

---

Problem 20:

$$
\frac{8}{10} \quad \text{?} \quad \frac{6}{9}
$$

- Step 1: Simplify \(\frac{8}{10}\) and \(\frac{6}{9}\):
$$
\frac{8}{10} = \frac{4}{5}, \quad \frac{6}{9} = \frac{2}{3}
$$
- Step 2: Find a common denominator for \(\frac{4}{5}\) and \(\frac{2}{3}\). The LCD is 15.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{4}{5} = \frac{12}{15}, \quad \frac{2}{3} = \frac{10}{15}
$$
- Step 4: Compare the numerators:
$$
\frac{12}{15} > \frac{10}{15}
$$
- Step 5: Therefore:
$$
\frac{8}{10} > \frac{6}{9}
$$

Answer: \(>\)

---

Problem 21:

$$
\frac{7}{11} \quad \text{?} \quad \frac{2}{4}
$$

- Step 1: Simplify \(\frac{2}{4}\):
$$
\frac{2}{4} = \frac{1}{2}
$$
- Step 2: Find a common denominator for \(\frac{7}{11}\) and \(\frac{1}{2}\). The LCD is 22.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{7}{11} = \frac{14}{22}, \quad \frac{1}{2} = \frac{11}{22}
$$
- Step 4: Compare the numerators:
$$
\frac{14}{22} > \frac{11}{22}
$$
- Step 5: Therefore:
$$
\frac{7}{11} > \frac{2}{4}
$$

Answer: \(>\)

---

Problem 22:

$$
\frac{25}{10} \quad \text{?} \quad \frac{20}{10}
$$

- Step 1: Compare the numerators directly since the denominators are the same.
- Step 2: Since \(25 > 20\), we have:
$$
\frac{25}{10} > \frac{20}{10}
$$

Answer: \(>\)

---

Problem 23:

$$
\frac{46}{6} \quad \text{?} \quad \frac{14}{4}
$$

- Step 1: Simplify \(\frac{46}{6}\) and \(\frac{14}{4}\):
$$
\frac{46}{6} = \frac{23}{3}, \quad \frac{14}{4} = \frac{7}{2}
$$
- Step 2: Find a common denominator for \(\frac{23}{3}\) and \(\frac{7}{2}\). The LCD is 6.
- Step 3: Rewrite the fractions with the common denominator:
$$
\frac{23}{3} = \frac{46}{6}, \quad \frac{7}{2} = \frac{21}{6}
$$
- Step 4: Compare the numerators:
$$
\frac{46}{6} > \frac{21}{6}
$$
- Step 5: Therefore:
$$
\frac{46}{6} > \frac{14}{4}
$$

Answer: \(>\)

---

Problem 24:

$$
\frac{57}{7} \quad \text{?} \quad \frac{62}{9}
$$

- Step 1: Find a common denominator for \(\frac{57}{7}\) and \(\frac{62}{9}\). The LCD is 63.
- Step 2: Rewrite the fractions with the common denominator:
$$
\frac{57}{7} = \frac{513}{63}, \quad \frac{62}{9} = \frac{434}{63}
$$
- Step 3: Compare the numerators:
$$
\frac{513}{63} > \frac{434}{63}
$$
- Step 4: Therefore:
$$
\frac{57}{7} > \frac{62}{9}
$$

Answer: \(>\)

---

Final Answer:

$$
\boxed{
\begin{aligned}
&> &<&<&<&<&=&>&>&<&<&<&<&<&<&<&<&<&<&<&<&<&<&>
\end{aligned}
}
$$