How to subtract fractions with different denominators

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Subtracting fractions with different denominators requires a bit of manipulation to get them on an equal footing. Here’s a detailed explanation on how to tackle them:

The GCF Method (Greatest Common Factor):

  1. Find the Least Common Multiple (LCM): This is the smallest number that is a multiple of both the denominators of your fractions. You can find the LCM by listing out the multiples of the larger denominator and checking them against the smaller denominator until you find a number common to both.

  2. Make Equivalent Fractions: In order to subtract our fractions, they need to have the same denominator (the bottom number). We can achieve this by multiplying both the numerator and denominator of each fraction by the factor needed to get their denominator equal to the LCM we found in step 1.

For example, if we have the fractions 1/3 and 2/5, the LCM would be 15 (3 x 5). To get a denominator of 15 for the first fraction, we multiply it by 5/5 (which equals 1) so it becomes 5/15. Similarly, to get a denominator of 15 for the second fraction, we multiply it by 3/3 (which equals 1) so it becomes 6/15.

  1. Simple Subtraction: Now that both fractions have the same denominator (15 in this example), you can simply subtract the numerators (the top numbers) and keep the denominator the same.

So, in our example: 5/15 – 6/15 = -1/15.

The Cross-Multiplication Method:

  1. Multiply Across: In this method, we multiply the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.

For example, with 1/3 and 2/5, we would get (1 x 5) and (2 x 3). This gives us 5 and 6.

  1. Subtract Numerators, Keep Denominator: Now, subtract the two products you obtained in step 1. In our example, 5 – 6 = -1. The denominator (3 x 5) from both fractions remains the same, so the answer is -1/15.

Simplifying the Answer (Optional):

  • Check if the numerator and denominator have a common divisor (a number that divides both). If they do, you can divide both the numerator and denominator by that number to get a simplified fraction.

In our example, -1 and 15 have a common divisor of 1, so we can simplify -1/15 to -1/15 (already in its simplest form).

Remember: Both the LCM and cross-multiplication methods will give you the same answer. Choose the method you find easier to understand and apply.