Comparing Mixed Fractions

YThe fraction with greater whole number part is greater. For example 3\(\frac{1}{2}\) > 2\(\frac{1}{2}\); 4\(\frac{1}{3}\) > 3\(\frac{1}{3}\).

When the whole number parts are equal, we first convert mixed fractions to improper fractions and then compare the two by using cross multiplication method.

Solved example on Comparing Mixed Fractions:

Arrange the fractions \(\frac{4}{15}\), \(\frac{5}{9}\), \(\frac{7}{18}\) and \(\frac{13}{24}\) in ascending order.

Solution:

Prime factors of 15, 9, 18 and 24 are 15 = 3 × 5; 9 = 3 × 3; 18 = 2 × 3 × 3 and 24 = 2 × 2 × 2 × 3

LCM of 15, 9, 18 and 24 is 360

Now, \(\frac{4}{15}\) = \(\frac{4 × 24}{15 × 24}\),

\(\frac{5}{9}\) = \(\frac{5 × 40}{9 × 40}\),

\(\frac{7}{18}\) = \(\frac{7 × 20}{18 × 20}\) and

\(\frac{13}{24}\) = \(\frac{13 × 15}{24 × 15}\)

By comparing the numerators we get \(\frac{96}{360}\), \(\frac{200}{360}\), \(\frac{140}{360}\), \(\frac{195}{360}\);

96 < 140 < 195 < 200

Hence, ascending order is \(\frac{4}{15}\), \(\frac{7}{18}\), \(\frac{13}{24}\) and \(\frac{5}{9}\).

Questions and Answers on Comparing Mixed Fractions:

1. Arrange the given fractions in descending order.

(i) \(\frac{5}{6}\), \(\frac{5}{8}\), \(\frac{5}{4}\)

(ii) 2\(\frac{1}{16}\), 3\(\frac{1}{4}\), 3\(\frac{1}{2}\)

(iii) \(\frac{5}{4}\), \(\frac{3}{12}\), \(\frac{1}{3}\)

(iv) \(\frac{2}{7}\), \(\frac{9}{14}\), \(\frac{11}{14}\)

Answers:

(i) \(\frac{5}{4}\), \(\frac{5}{6}\), \(\frac{5}{8}\)

(ii) 3\(\frac{1}{2}\), 3\(\frac{1}{4}\), 2\(\frac{1}{16}\)

(iii) \(\frac{5}{4}\), \(\frac{1}{3}\), \(\frac{3}{12}\)

(iv) \(\frac{11}{14}\), \(\frac{9}{14}\), \(\frac{2}{7}\)

Word Problems on Comparing Mixed Fractions:

2. Rachel took 5\(\frac{1}{4}\) m of cloth and Ria took 4\(\frac{2}{3}\) m of cloth. Who took the longer length?

Answer: Rachel

3. Jack lives 2 kilometer away from school and Sam lives 1\(\frac{5}{6}\) km away from the school. Who lives closer to the school and by how much?

Answer: Sam

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