Lesson 7, Topic 3
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# Arranging Fractions in Order of Size

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### Fractions with Same Denominators:

The four shapes below are of the same size and they are divided in different ways.

You can see that;

4/5 is greater than 3/5

3/5 is greater than 2/5

When a set of fractions have equal denominators, and the denominators of the fractions are equal (i.e. the same), the one with the largest numerator is the largest fraction and the one with the smallest numerator is the least.

⇒ the order of size is

1/5, 2/5, 3/5, 4/5 in ascending order.

4/5, 3/5, 2/5, 1/5 in descending order.

### Fraction with Different Denominators:

The three shapes of the same size shown below. It is obvious from these shapes that:

1/2 is larger than 1/4, and 1/4 is larger than 2/9

1/2, 1/4, 2/9 in descending order

### Example 1:

Which is greater 4/5 or 2/3

Solution:

Find the LCM of the denominators i.e. LCM of 3 and 5 is 15.

Write each fraction with the same denominator (i.e. is) by using equivalent fractions.

$$\frac {2}{3}= \frac {2}{3} \: \times \: \frac {5}{5}= \frac {10}{15}$$

$$\frac {4}{5} = \frac {4}{5} \: \times \: \frac {3}{3}= \frac {12}{15}$$

This means 2/3 = 10/5 and 4/5 = 12/15

Comparing the size of the numerators of the equivalent fraction, 4/5 is greater than 2/3.

### Example 2:

Arrange the following factors in ascending order:  $$\frac {2}{3}, \frac {3}{8}, \frac {1}{4}= \frac {5}{6}$$

Solution:

Find the LCM of the denominator 3, 8, 4 and 5 is 24

Therefore, the equivalent fractions are:

$$\frac {2}{3} = \frac {2}{3} \: \times \: \frac {8}{8}= \frac {16}{24}$$

$$\frac {3}{8} = \frac {3}{8} \: \times \: \frac {3}{3}= \frac {9}{24}$$

$$\frac {1}{4} = \frac {1}{4} \: \times \: \frac {6}{6}= \frac {6}{24}$$

$$\frac {5}{6} = \frac {5}{6} \: \times \: \frac {4}{4}= \frac {20}{24}$$

By comparing the sizes of the numerators of the equivalent fractions in ascending order, we have

$$\frac {6}{24}, \frac {9}{24}, \frac {16}{24}, \frac {20}{24}$$

Here, the given fractions in descending order gives:

$$\frac {1}{4}, \frac {3}{8}, \frac {2}{3}, \frac {5}{6}$$

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