Example of subtracting fractions with unlike denominators | Fractions | Pre-Algebra | Khan Academy

TL;DR

The video explains how to subtract fractions with different denominators by finding the least common multiple and multiplying the numerators and denominators accordingly.

Transcript

Let's figure out 7/12 minus 6/13. And in order to be able to do this, we need to find a common denominator. We notice that they're not common right over here. Here, the denominator is 12. Here, it is 13. And the common denominator is going to be the least common multiple of 12 and 13. And 12 and 13 share no common factors other than 1, so their lea... Read More

Key Insights

• 🎭 Common denominators are necessary to perform addition or subtraction operations with fractions.
• 🧑‍🏭 To find the least common multiple of two numbers, identify their prime factors and multiply the highest power of each prime factor.
• ✖️ Multiplying the numerator and denominator by the same number does not change the value of the fraction.

Questions & Answers

Q: How do we find the least common multiple of two numbers?

To find the least common multiple of two numbers, identify their prime factors and multiply the highest power of each prime factor. In this case, since 12 and 13 have no common factors other than 1, the least common multiple is simply the product of the two numbers, which is 12 times 13.

Q: Why do we multiply both the numerator and denominator by the same number when finding a common denominator?

Multiplying both the numerator and denominator by the same number does not change the value of the fraction because it is equivalent to multiplying it by 1. This ensures that the fraction remains the same, but with the denominator necessary for performing operations with other fractions.

Q: How did the numerator and denominator change when finding the common denominators in the video?

When finding the common denominators, the numerator and denominator were multiplied by the necessary factor. For example, when multiplying the denominator of 7/12 by 13, the numerator was also multiplied by 13 to maintain the equivalent value of the fraction.

Q: Can the resulting fraction be simplified further?

In this case, the resulting fraction, 19/156, cannot be simplified further as 19 is not divisible by any factor of 156, and they have no common factors other than 1.

Summary & Key Takeaways

• In order to subtract fractions with different denominators, the first step is to find the least common multiple of the denominators.

• Once the least common multiple is determined, the numerator and denominator of each fraction are multiplied by the necessary factor to make them equivalent.

• After obtaining fractions with the same denominators, the subtraction can be performed by subtracting the numerators and keeping the common denominator.