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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Although whole numbers and fractions do not look the same, it is still possible to add these two types of numbers together. In this lesson, you will learn how to add whole numbers and fractions.

A **whole number** is a number without a fractional part; in other words, a number that represents a whole.

A **fraction** is a number that represents a part of a whole. The **numerator** is the top number of a fraction that tells how many pieces you have, and the **denominator** is the bottom number of a fraction that tells how many *total* pieces the whole is broken into.

Sometimes it is necessary to add numbers that are not in the same format. Let's take a look how to do that. Your baby brother ate 2/3 of a piece of pizza, and you ate 3 pieces. How many pieces did you eat all together?

The question is asking you to add 2/3, a fraction, and 3, a whole number. Look at the image to visualize how much pizza you both ate.

If you have a whole number and a proper fraction, you can simply combine the two elements. A **proper fraction** is a fraction that is less than one and the numerator is smaller than the denominator.

For our pizza example, the fraction 2/3 is proper because it is less than one and the numerator (2) is smaller than the denominator (3). We can simply combine 3 and 2/3 to make 3 2/3. You and your baby brother ate 3 2/3 pieces of pizza.

You can only use this method with proper fractions. Adding whole numbers and improper fractions requires different steps.

An **improper fraction** is a fraction that represents more than one whole, and the numerator is larger than the denominator. For example, you ate 3 pieces of pizza, and your big sister ate 4/3 pieces of pizza. How much did you eat together?

You ate 3 pieces, a whole number, and your sister ate 4/3 pieces, an improper fraction. 4/3 represents more than 1 whole, and the numerator (4) is larger than the denominator (3).

Follow these steps to add whole numbers and improper fractions:

- Turn the whole number into a fraction
- Give the fractions a common denominator
- Add the fractions

Let's looks at each of these steps:

You can make a whole number into a fraction by putting it over a denominator of 1. For the example problem, you ate 3 pieces of pizza, so the whole number is 3. We can turn it into a fraction by using the 3 as the numerator and a 1 as the denominator. The whole is in 1 piece, and you have 3 of them.

Now, we have two fractions. You ate 3/1 pieces of pizza, and your big sister ate 4/3 pieces of pizza. The next step is to give the fractions a **common denominator**, a multiple that both denominators share.

Our denominators are 3 and 1, so the smallest common denominator is 3, which is a multiple of both numbers. We need to make both denominators 3. 4/3 already has a 3 as the denominator, so we can leave it alone.

To give 3/1 a denominator of 3, you multiply both the numerator and denominator by 3

Now that we have two fractions, 4/3 and 9/3, we can add them together and the answer is 13/3 as an improper fraction and 4 1/3 as a mixed number. You and your big sister ate 4 1/3 pieces of pizza.

You can add a **whole number** and a **proper fraction** by simply combining the two elements. To add a whole number and an **improper fraction**, you must convert the whole number to an improper fraction, find a common denominator, then add the fractions.

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Additional Activities

Use a piece of paper to cut out two 4 inch by 4 inch squares. One 4 inch by 4 inch square is equal to one (a whole number). Use a pen or marker to draw one horizontal and one vertical line inside the squares, creating four equal squares. Next, cut out four 1 inch by 1 inch squares. Each square is equal to one-quarter (1/4). Repeat this process until there are twelve 1 inch by 1 inch squares. Using the 4 inch by 4 inch squares as a guide, create the following fractions using the 1 inch by 1 inch squares:

1/4

2/4

4/4 (note that four quarters equals 1 whole)

5/4

7/4

Using the 4 inch by 4 inch squares as a guide, practice adding fractions by combining the following combinations of 1 inch by 1 inch squares that represents fractions with common denominators:

1/4 + 2/4 (3/4 of the 4 inch by 4 inch square are filled after this addition)

1/4 + 3/4 (Notice that the square is completed so 4/4 = 1)

Now, let's look at the addition of improper fractions:

5/4 + 1/4 = 6/4 (There is one complete square (4/4) and two one-quarter squares represented. This equals 1 1/2.)

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Math for Kids23 chapters | 325 lessons

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