Comparing fractions using papers:
Another way of comparing fractions is using papers of similar sizes and shape. Suppose you have eleven-twelve squares of papers. Keep one square as it is and write 1/1 on it using a sketch pen.
Take another square and fold it once to get two congruent parts. Separate the two parts using a pair of scissors. On one of the two parts, write 1/2 on it with sketch pen.
In a similar fashion, get one-thirds, one-fourths, etc. from the additional squares with you.
Now compare different fractions of the squares you have obtained by overlaying them on each other. Note down your observations regarding their comparative sizes. All these fractions have a numerator 1.
You will have noticed: 1/1 > 1/2 > 1/3 > 1/4 > 1/5 etc...
This is like the comparison of regions we have on a fractions wall.
Comparing fractions using a number line:
It is easy to compare fractions with the help of segments of number lines. We will now compare fractions having 2 as numerator and different denominators.
As shown in the figure, draw a number line and choose a unit measure large enough to partition it into smaller equal portions like: 2, 3, 4 etc...
On the first number-line, we will indicate the length of the measure 2/2, on the second number-line we will represent the fraction 2/3, on the third number-line we will illustrate the fraction 2/4 etc... If we draw all the number lines with their points '0' and '1' falling one below the other in a vertical line, we can compare the different lengths representing specific fractions at a glance. You can see that 2/2 > 2/3 > 2/4 > 2/6
It is also possible to draw a single number line with multiple numbering, as shown in the figure below.
However, this model is suitable only for comparing two numbers. For comparisons involving more than two fractions, it is better to have separate number lines, having representation of one fraction on one number line.
Enjoy comparing any two fractions here! The program is interactive. Enter any two fractions you want to compare and you will get to see the portions of two pies corresponding to these fractions. Looking at the sizes of portions of the pies you can decide the larger fraction. The answer for each comparison is also provided with a reason! So, you may check the answers yourself and correct if necessary. Try as many problems as you like, with same numerator and different denominators!
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