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High School Algebra I: Help and Review25 chapters | 292 lessons

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Lesson Transcript

Instructor:
*Stephanie Matalone*

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

This lesson will teach you how to identify unlike fractions, which are fractions with different numbers in the denominator. We will also explore simplifying fractions and how a group of fractions that started out as unlike may be reduced to like fractions that can be added or subtracted.

So you have a few friends over and grab some food. You have one pizza and three cans of soda to share between the four of you. How do you decide how much to give each friend? Well, you can use **fractions**, which are just whole numbers divided by other whole numbers. Let's start with the pizzas. Take your pizza and divide it by the four people for a fraction of 1/4. Take your three cans of soda and divide them by the four people for a fraction of 3/4. Each person gets 1/4 of the pizza and 3/4 of a soda!

Now, to decide if these fractions are like or unlike we need to identify the numerators and denominators. **Numerators** are the numbers on top of the fraction bar, while **denominators** are the numbers on the bottom of the fraction bar. In our pizza and soda example, the number of people would be the denominator because it is on the bottom of both fractions.

For a group of fractions to be **like**, they have to have the same number in the denominator. In other words, they have to have the same number on the bottom of the fraction bar. In our example, the pizza and soda were both being split between four people. Four was the denominator in both of those fractions. For fractions to be **unlike**, they have to have different numbers in the denominator. In other words, they have to have different numbers on the bottom of the fraction bar.

Back to our pizza example, in order to have unlike fractions you would need to split the pizza between a different number of people than the soda (maybe one of your friends only drinks water). This would change our fractions like so: each person gets 1/4 of the pizza and 3/3 of a soda. 1/4 and 3/4 are like fractions because they both have four in the denominator. On the other hand, 1/4 and 3/3 are unlike fractions because they have different numbers in the denominator. One fraction has 4 in the denominator, while the other has 3. 4 and 3 are different numbers.

Do not forget that fractions can be **simplified** or **reduced** if the numerator and denominator can be divided by the same number. For example, the fraction 2/4 can be simplified or reduced because both the numerator (2) and the denominator (4) can be divided by two. When you do this, the simplified fraction becomes 1/2. 6/8 and 1/4 are unlike fractions but when reduced 3/4 and 1/4 are actually like fractions because they both have a denominator of 4.

Make sure you simplify fractions all the way. For example, 16/40 can be simplified by dividing both 16 and 40 by 2, which will give the fraction 8/20. But, 8 and 20 can also be divided by 2, which gives the fraction 4/10. Are we done yet? No, 4 and 10 can also be divided by 2, which gives the simplest fraction of 2/5. A simpler way to do this is go back to the original fraction of 16/40 and see what is the largest number that 16 and 40 can both be divided by. They both can be divided by 8, which will bring you right to the simplest fraction of 2/5 instead of going through all those steps.

Why is this important? The only time you can add and subtract fractions are when they are like. Unlike fractions cannot be added or subtracted. Unlike fractions, on the other hand, can still be multiplied and divided.

Let's look at some more examples. These three fractions are unlike: 2/3, 11/9, and 7/2. These three fractions are unlike because they do not have the same number in the denominator and cannot be simplified to have the same number in the denominator. This means that these three fractions could not be added or subtracted.

Another example is these three fractions: 1/5, 7/25, and 3/10. Again, the denominators are not the same and the fractions cannot be simplified to make the denominators the same. At first, it might look like all the denominators could be changed to five but the numerators are preventing that simplification from happening. So, can the three fractions, 1/5, 7/25, and 3/10, be added or subtracted? No. They would have to have the same denominator to be able to do so.

**Fractions** are whole numbers divided by other whole numbers. **Numerators** are the top numbers in a fraction and **denominators** are the bottom numbers in fractions. So, in order to decide if fractions are like or unlike we can then look at the denominators. If the denominators are the same, then they are **like**. If the denominators are different, we can then decide that the fractions are **unlike**. This will mean that these fractions cannot be added or subtracted from each other. Remember that reduction or simplification of an unlike fraction may turn it into one that is like.

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High School Algebra I: Help and Review25 chapters | 292 lessons

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