4th Grade Math

Operations with Fractions

Unit 4

Lesson One: Adding and Subtracting Fractions with Like Denominators

Like Denominators- Fractions with like denominators are fractions that have the same denominator. An example of fractions with like denominators are 3/8 and 7/8. When fractions have like denominators, it makes it way easier to add and subtract them with each other.

Adding Fractions: Like I said it is much easier to add fractions when they have like denominators. All you have to do is add the numerators and put it in simplest form if possible.

Let's use the equation on the left as an example. All you have to do here is add the numerators. Add 5 + 1 which gives you 6. Then, just put it back over the denominator. 6/7 is already in simplest form.

Fractions can also be added with unlike denominators!

Subtracting Fractions: It is also easier to subtract fractions when they have the same denominator. Again, you just have to subtract the numerators and put the fraction in simplest form if possible.

Use the example on the right. All you have to do is subtract 3 - 1 which gives you 2. Then, you just put it over the denominator. 2/5 is already in simplest form.

This is an example of a mixed fraction!

You can also add and subtract mixed numbers with like denominators. When you add mixed numbers, you add the whole numbers first, then the fractions.

For example, let's add the mixed fractions 1 3/4 + 4 1/4. First you have to add the whole numbers, 1 + 4 which is 5. Next, you have to add the fractions 3/4 + 1/4 which is 4/4. This is another whole. We add this to 5 so we do 5 + 1 which is 6.

1 3/4 + 4 1/4 = 6

Lesson Two: Decomposing Fractions

Fractions can also be "decomposed" or divided up. This means they can be broken down to see what they're made of. They show you what can be added up to make the fraction.

For example, the fraction 3/6 can be decomposed into three parts. These three parts can be added up to make 3/6. What three fractions can make 3/6?

The answer is 1/6 + 1/6 + 1/6. This is one way 3/6 can be decomposed.

Fractions can be decomposed more than one way.

For example, let's look at the fraction 5/8.

This can be decomposed in more than one way. You can decompose this into 2/8 + 3/8. You can also decompose this into 1/8 + 4/8. They both add up to make 5/8.

Lesson Three: Multiplying Fractions

Fractions can be multiplied by whole numbers pretty easily. All that you have to do is multiply the numerator. Remember that every whole number is over 1 (for example 4 is 4/1).

Let's do an example together. Let's multiply 3/5 x 4. What we are doing is multiplying 3/5 by 4/1. Do this on a sheet of paper! When you multipy 3/5 x 4/1 you do 3 x 4 and 5 x 1. This give you 12/5.

You can make this into the mixed number, 5 2/5.

Multiplying Fractions on a Number Line

You can use a number line to figure out how to multiply a fraction.

Say you are multiply 1/3 x 4. You can jump 1/3 on the number line 4 times and you will eventually land on 1 1/3.

Factors and Multiples of Fractions

Just like there are factors of whole numbers, there are also factors of fractions.

For example, let's take the fraction 3/6. We know that 1/6 is one of the factors. What is the other factor? What multiplies with 1/6 to make 3/6?

The answer is 3. 3 and 1/6 are factors of 3/6.

Fractions also have multiples!

For example, let's take the fraction 1/6. The numbers created when you multiply it are multiples of 1/6. If you multiply 1/6 by 5, you get 5/6. Therefore, 5/6 is a multiple of 1/6.