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.


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


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

Comparing Mixed Fractions

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

4th Grade Math Activities

From Comparing Mixed Fractions to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Estimating Sum and Difference | Reasonable Estimate | Procedure | Math

    May 22, 24 06:21 PM

    The procedure of estimating sum and difference are in the following examples. Example 1: Estimate the sum 5290 + 17986 by estimating the numbers to their nearest (i) hundreds (ii) thousands.

    Read More

  2. Round off to Nearest 1000 |Rounding Numbers to Nearest Thousand| Rules

    May 22, 24 06:14 PM

    Round off to Nearest 1000
    While rounding off to the nearest thousand, if the digit in the hundreds place is between 0 – 4 i.e., < 5, then the hundreds place is replaced by ‘0’. If the digit in the hundreds place is = to or > 5…

    Read More

  3. Round off to Nearest 100 | Rounding Numbers To Nearest Hundred | Rules

    May 22, 24 05:17 PM

    Round off to Nearest 100
    While rounding off to the nearest hundred, if the digit in the tens place is between 0 – 4 i.e. < 5, then the tens place is replaced by ‘0’. If the digit in the units place is equal to or >5, then the…

    Read More

  4. Round off to Nearest 10 |How To Round off to Nearest 10?|Rounding Rule

    May 22, 24 03:49 PM

    Rounding to the Nearest 10
    Round off to nearest 10 is discussed here. Rounding can be done for every place-value of number. To round off a number to the nearest tens, we round off to the nearest multiple of ten. A large number…

    Read More

  5. Rounding Numbers | How do you Round Numbers?|Nearest Hundred, Thousand

    May 22, 24 02:33 PM

    rounding off numbers
    Rounding numbers is required when we deal with large numbers, for example, suppose the population of a district is 5834237, it is difficult to remember the seven digits and their order

    Read More