Subtraction of Rational Numbers

Subtraction of Rational Numbers plays a very important role in various mathematical calculations, here are some steps for subtracting two or more rational numbers:


  1. For subtraction we need to check whether the denominator of the given numbers are same or not

  2. If both the rational numbers have same denominators then we can directly subtract numerators.

  3. Now if the denominators are not same then we just need to equalize the denominator by taking LCM of both the denominator and then we have to subtract the terms.

  4. After taking the LCM of denominators we just need to subtract the numerator terms and simplify the result.


Here are few examples which further help you to understand Subtraction of Ra

Example 1: Subtraction of the rational numbers 3/4 and 2/4.

Solution: In the very first step we will write the rational numbers like 5/4 - 2/4,

Now as we can see the denominators are same, which is equal to 4.

So, in the next step we will directly subtract the numerator and simplify like = (5-2)/4 = 3/4.


Example 2. Subtract the rational numbers 5/2 and 7/6.

Solution: Here the denominators are not same, so first of all we find the common denominator which is 6, the rule for this is we need to multiply the denominator of 1st number to 2nd number and 2nd number to 1st.

Now we divide the common denominator 6 by each denominator and multiply the result by each numerator respectively like:

5×3/6 - 7×1/6

Now we subtract the numerators and obtain the result

15/6 - 7/6 = 8/6 this is our answer.

So friends, from today’s class you will able to subtract two or more rational numbers together. 



Subtract: 3/7 - 3/8?

For the subtraction of these two quantities we just need to equalize the denominator first then we have to subtract them. We don’t need to do any application with the numerator. For equalizing the denominator we need to fallow some specific rules:
We have to multiply both the denominator and numerator with the same Integer so the value of fraction doesn’t change and we have to multiply the integer in a manner so that the value of both the denominator will be same or for simplification you can multiply the first value by denominator of second and second value with the denominator of first. Now, let’s see how to multiply,
3*8/7*8 – 3*7/8*7  the denominator of first number is 7 and we have multiply it on both the numerator and denominator. The denominator of second number is 8 and we have multiplied it on both the numerator and denominator. Now, the result will be,
24/56 -21/56,
Now it’s very easy we just have to subtract the numerator, denominator remains the same, so required answer will be,

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