Comparing Fractions Worksheets - Math Monks - Free Printable

To solve the problem of comparing and ordering fractions, we need to compare each set of fractions and arrange them in the specified order (either ascending or descending). Let's go through each row step by step.

Row 1:

#### Column 1:
Fractions: \( \frac{3}{4}, \frac{1}{4}, \frac{2}{4} \)
- These fractions have the same denominator (4), so we compare the numerators directly.
- Numerators: \( 3 > 2 > 1 \)
- Ordered: \( \frac{3}{4} > \frac{2}{4} > \frac{1}{4} \)

#### Column 2:
Fractions: \( \frac{7}{8}, \frac{6}{8}, \frac{9}{8} \)
- These fractions also have the same denominator (8), so we compare the numerators directly.
- Numerators: \( 9 > 7 > 6 \)
- Ordered: \( \frac{9}{8} > \frac{7}{8} > \frac{6}{8} \)

#### Column 3:
Fractions: \( \frac{2}{15}, \frac{8}{15}, \frac{10}{15} \)
- These fractions have the same denominator (15), so we compare the numerators directly.
- Numerators: \( 10 > 8 > 2 \)
- Ordered: \( \frac{10}{15} > \frac{8}{15} > \frac{2}{15} \)

Row 2:

#### Column 1:
Fractions: \( \frac{6}{9}, \frac{6}{4}, \frac{6}{7} \)
- These fractions have the same numerator (6), so we compare the denominators. The larger the denominator, the smaller the fraction.
- Denominators: \( 9 > 7 > 4 \)
- Ordered: \( \frac{6}{9} < \frac{6}{7} < \frac{6}{4} \)

#### Column 2:
Fractions: \( \frac{3}{5}, \frac{5}{6}, \frac{2}{9} \)
- These fractions have different numerators and denominators. To compare them, we can find a common denominator or convert them to decimals.
- Converting to decimals:
- \( \frac{3}{5} = 0.6 \)
- \( \frac{5}{6} \approx 0.833 \)
- \( \frac{2}{9} \approx 0.222 \)
- Ordered: \( \frac{2}{9} < \frac{3}{5} < \frac{5}{6} \)

#### Column 3:
Fractions: \( \frac{4}{9}, \frac{4}{3}, \frac{4}{5} \)
- These fractions have the same numerator (4), so we compare the denominators. The larger the denominator, the smaller the fraction.
- Denominators: \( 9 > 5 > 3 \)
- Ordered: \( \frac{4}{9} < \frac{4}{5} < \frac{4}{3} \)

Row 3:

#### Column 1:
Fractions: \( \frac{14}{7}, \frac{14}{3}, \frac{14}{9} \)
- These fractions have the same numerator (14), so we compare the denominators. The larger the denominator, the smaller the fraction.
- Denominators: \( 9 > 7 > 3 \)
- Ordered: \( \frac{14}{9} < \frac{14}{7} < \frac{14}{3} \)

#### Column 2:
Fractions: \( \frac{8}{9}, \frac{1}{3}, 6\frac{1}{2} \)
- Convert mixed number to improper fraction: \( 6\frac{1}{2} = \frac{13}{2} \)
- Compare:
- \( \frac{8}{9} \approx 0.889 \)
- \( \frac{1}{3} \approx 0.333 \)
- \( \frac{13}{2} = 6.5 \)
- Ordered: \( 6\frac{1}{2} > \frac{8}{9} > \frac{1}{3} \)

#### Column 3:
Fractions: \( 1\frac{1}{5}, 2\frac{1}{4}, \frac{3}{7} \)
- Convert mixed numbers to improper fractions:
- \( 1\frac{1}{5} = \frac{6}{5} \)
- \( 2\frac{1}{4} = \frac{9}{4} \)
- Compare:
- \( \frac{6}{5} = 1.2 \)
- \( \frac{9}{4} = 2.25 \)
- \( \frac{3}{7} \approx 0.429 \)
- Ordered: \( \frac{3}{7} < 1\frac{1}{5} < 2\frac{1}{4} \)

Final Answer:

\[
\boxed{
\begin{array}{ccc}
\frac{3}{4} > \frac{2}{4} > \frac{1}{4} & \frac{9}{8} > \frac{7}{8} > \frac{6}{8} & \frac{10}{15} > \frac{8}{15} > \frac{2}{15} \\
\frac{6}{9} < \frac{6}{7} < \frac{6}{4} & \frac{2}{9} < \frac{3}{5} < \frac{5}{6} & \frac{4}{9} < \frac{4}{5} < \frac{4}{3} \\
\frac{14}{9} < \frac{14}{7} < \frac{14}{3} & 6\frac{1}{2} > \frac{8}{9} > \frac{1}{3} & \frac{3}{7} < 1\frac{1}{5} < 2\frac{1}{4}
\end{array}
}
\]