How to Subtract Fractions with Different Denominators: Step-by-Step Guide with Example

Subtracting with different denominator

To subtract fractions with different denominators, you need to find a common denominator for both fractions

To subtract fractions with different denominators, you need to find a common denominator for both fractions. Here are the steps to follow:

1. Identify the denominators of the fractions you want to subtract. Let’s say you have fractions with denominators a and b.

2. Find the least common multiple (LCM) of these two denominators. If you are not familiar with finding the LCM, you can use the prime factorization method or the listing method to determine the smallest number that is divisible by both denominators.

3. Rewrite each fraction so that they have the same denominator, equal to the LCM found in step 2. To do this, multiply the numerator and denominator of each fraction by a suitable value that makes the denominator equal to the LCM.

4. Once you have both fractions with the same denominator, you can subtract their numerators. The denominator remains the same.

5. Simplify the resulting fraction, if necessary, by dividing the numerator and denominator by their greatest common divisor (GCD).

Let’s work through an example:

Let’s subtract 2/5 from 3/8:

Step 1: Denominators are 5 and 8.

Step 2: The LCM of 5 and 8 is 40 (you can verify this by listing the multiples or finding the prime factorization).

Step 3: Rewrite the fractions with the common denominator of 40:

2/5 = (2 * 8) / (5 * 8) = 16/40
3/8 = (3 * 5) / (8 * 5) = 15/40

Step 4: Subtract the numerators while keeping the denominator the same:

15/40 – 16/40 = (15 – 16) / 40 = -1/40

Step 5: The resulting fraction, -1/40, cannot be simplified further.

So, 3/8 minus 2/5 equals -1/40.

Remember to always double-check your work and simplify your fractions whenever possible.

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