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## Three Tips On Ordering and Comparing Fractions

Compare and rank fractions

Not all fractions have the same value. A fraction can be smaller than other fractions and it can be larger than some other fractions. Therefore, children need to know how to compare fractions. The comparison can be divided into three sections. So kids need to know three tricks to learn this skill.

Tip number 1:

The first trick to comparing fractions is to see if they have the same numerators. If the numerators are the same, the fraction with the larger denominator is the smaller. For example; consider the following fractions:

3/5, 3/4, 3/8 and 3/7

As all the above fractions have the same numerator (3), so we need to compare their denominators to compare them. The largest denominator makes the fraction the smallest, so 3/8 is the smallest of all and 3/4 is the largest. Let’s rewrite all the fractions in an order from smallest to largest as shown below:

3/8, 3/7, 3/5 and 3/4

The above order (smallest to largest) is also called ascending order.

Tip number 2:

The second round is as easy as the first. This trick consists in comparing fractions, when they have the same denominators. When the denominators are the same, the fraction with the smallest numerator is the smallest and the fraction with the largest numerator is the largest. For example;

Suppose we want to compare 3/9, 1/9, 7/9 and 2/9; write them in ascending order.

Look at the given fractions, they all have the same denominator (9). So, 1/9 is the smallest because it has the smallest numerator and 7/9 is the largest with the largest numerator. Below they are written in ascending order.

1/9, 2/9, 3/9 and 7/9

Tip number 3:

The two tips above explain comparing fractions with the same numerators or denominators. But more often children are asked to compare and order fractions with different numerators and denominators.

In such a case, they must make the denominator of all fractions the same. To do this, they need to know the lowest common factor (lcm) of all the denominators, also known as the lowest common denominator (lcd).

Consider the following example about comparing fractions:

Write the following fractions in descending order (largest to smallest)

2/3, 1/4, 5/6, 3/4 and 1/2

Solution: Look, most fractions have different denominators. Write all the denominators as shown below and write the first six multiples of each.

2 = 2, 4, 6, 8, 10, 12 3 = 3, 6, 9, 12, 15, 18 4 = 4, 8, 12, 16, 20, 24 6 = 6, 12, 18, 24, 30 , 36

Now look at the factors of all the numbers and find the least common to all of them, which is 12 in this case. Therefore, the lcm or lcd is 12. The next step is to rewrite all the fractions into equivalent fractions with denominator equal to 12. This step is shown below:

2/3, we have to multiply its denominator (3) by 4 to change it to 12. But to keep the same fraction value, remember to multiply the numerator (2) with the same number 4. Let’s do it;

(2×4)/(3×4) = 8/12

Similarly, write all fractions with a denominator of 12 as shown below:

1/4 = (1 x 3)/(4 x 3) = 3/12 5/6 = (5 x 2)/(6 x 2) = 10/12 3/4 = (3 x 3)/(4 x 3) = 9/12 1/2 = (1 x 6)/(2 x 6) = 6/12

Now all fractions have been written as equivalent fractions with the same denominator 12 and it is easy to compare them. Write all equivalent fractions in descending order (largest to smallest)

10/12, 9/12, 8/12, 6/12 and 3/12

But it is not the fractions that are asked to be compared. So this is not our answer, but now it is very easy to write the original fractions in the required order by looking at the order above. We know that 10/12 equals 5/6 and 3/12 equals 1/4 so write the original fractions in order

5/6, 3/4, 2/3, 1/2 and 1/4

Finally, it can be said that to compare and order fractions, children should keep the above three tips in mind. Of course, knowing the least common multiple (lcm) is the key to comparing two or more fractions with different denominators.

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