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# Subtracting Fractions

Fractions are written in the form of $\frac{p}{q}$. The number p which is above the bar, is called "numerator" and number q which below the bar, is known as "denominator". For example: $\frac{18}{71}$, $\frac{4}{5}$, $\frac{20}{7}$ etc.

While subtracting fractions, there may arise following two cases:

Case 1: When both the fractions have same denominator.
Follow the following given steps in this case:
(1): Write same number in denominator.
(2): Write both numerator numbers with minus sign between them.
(3): Subtract numbers in numerator and write the result in numerator.

For Example: Subtract $\frac{12}{5}$ from $\frac{16}{5}$.

Solution: $\frac{16}{5}-\frac{12}{5}$

= $\frac{16-12}{5}$

= $\frac{4}{5}$

Case 2: When both the fractions have different denominator.
In this case, following steps should be followed:
(1): Find the LCM (least common multiple) of both the denominator numbers.
(2): Write LCM in denominator.
(3): Divide LCM by denominator number of first fraction and then multiply the result with numerator of that fraction.
(4): Repeat this process with other number too.
(5): Write both numbers with a minus sign between them.
(6): Subtract them and write the result in numerator.

Following figure illustrates subtraction $\frac{1}{3}-\frac{1}{5}$:

Example: Subtract $\frac{1}{15}$ from $\frac{2}{3}$.

Solution: $\frac{2}{3}-\frac{1}{15}$

Here LCM of 15 and 3 is 15

= $\frac{10-1}{15}$

= $\frac{9}{15}$

= $\frac{3}{5}$

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