<meta http-equiv="refresh" content="1; url=/nojavascript/"> Addition of Fractions ( Read ) | Arithmetic | CK-12 Foundation

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Modeling Adding and Subtracting Mixed Numbers with like, or common denominators

### Introduction

“Look at this,” Dan exclaimed rushing into student council meeting one afternoon. In his arms he held several boxes.

Dan stopped and put all of the boxes in the middle of the table. He was grinning from ear to ear.

“Look, Katie,  the custodian, found all of these boxes of colored pencils in the store room. She said we can have them for free. We have $2\frac{3}{4}$ boxes of colored pencils here and another $\frac{3}{4}$ of a box,” Dan said smiling.

“Great work! We also ordered a case of colored pencils and there are 25 boxes in a case. Now we will have a lot of colored pencils,” Riley said.

“How many do we have altogether?” Hailey asked.

It is time to learn about fraction addition. In this Concept, you will learn how to add and subtract mixed numbers fractions. When finished, you will see this problem again so be sure to pay close attention!

### Guided Learning

By this time in math class you have been working with fractions for a long time. Yet fractions are often a place of struggle for many students. We often think in terms of whole numbers and not in terms of fractions.

A fraction is a number that names a part of a whole or a part of a group.

If a rectangle is $\frac{1}{3}$ shaded, it means that if the rectangle were divided into three equal parts, one of those parts would be shaded. Most fractions will represents numbers less than 1, meaning that the numerator is less than the denominator.

To represent a number greater than 1, we use an improper fraction or a mixed number.

An improper fraction has a numerator that is larger than its denominator, such as $\frac{5}{3}$ .

This fraction can also be written as the mixed number $1 \frac{2}{3}$ .

A mixed number is a number that has both wholes and parts, so you will see a whole number and a fraction with mixed numbers.

Let's review adding and subtracting fractions with like denominators.

How do we add and subtract fractions?

Well, the first thing to look at is the bottom number of the fractions that you are adding or subtracting. The bottom number or denominator tells you how many parts the whole is divided into. If the denominator is a three, then we know that the whole is divided into three parts. The top number or numerator tells you how many parts you have out of the whole.

If the denominators of the fractions being added are the same, then the wholes are divided the same way so we can simply add or subtract the numerators.

$\frac{1}{8}+ \frac{2}{8} = \frac{3}{8}$

Here you can see that both fractions have denominators of 8, so we can simply add the numerators.

We can also subtract fractions.

$\frac{10}{12}- \frac{3}{12} = \frac{7}{12}$

Once again our denominators are common. So we can simply subtract the numerators.

Let's look at this video to see how to draw a model of adding and subtraction mixed fractions.

Let's work with mixed numbers and fractions . There is an added step when working with this combination. First, you need to add or subtract the whole numbers, then add or subtract the fractions. Using a model or number line, find the answers to these two problems.

Add: $1\frac{1}{5}+2\frac{3}{5}=$

Subtract: $2\frac{7}{8}-\frac{2}{8}=$

#### Example A

Subtract: $2\frac{4}{9}+1\frac{6}{9}$

#### Example B

Add: $4\frac{10}{12}+2\frac{2}{10}$

Example C

Subtract: $3\frac{4}{8}-2\frac{1}{8}$

Now let's go back to the dilemma from the beginning of the Concept.

To solve this problem, we need to find a sum. A sum means addition, so we are going to figure out how many boxes of pens the student council has in all.

First, let’s find the sum of the extras.

The students were given $2 \frac{3}{4}$ boxes of pens and another $\frac{3}{4}$ of a box.

$2 \frac{3}{4} + \frac{3}{4}$

Using the distributive property, we would split the whole numbers from the fractions. So, we have 2 for the whole number and $\frac{3}{4} + \frac{3}{4}$  for the fractions. Adding the fractions, we get $\frac{6}{4} or 1\frac{2}{4}$ . Last, we add the whole numbers together and we get $1\frac{2}{4} + 2 = 3\frac{2}{4}$

Now we can take the sum of the extras and add it to the number of boxes in a case. Be careful that you don’t add it to the number of cases. We are talking about boxes here.

There are 25 boxes in 1 case. $3\frac{2}{4} + 25 = 28\frac{2}{4}$

The students will have a sum of $28 \frac{2}{4} or 28 \frac{1}{2}$ boxes of colored pencils.

Here is one for you to try on your own.

$1\frac{4}{6}+1\frac{5}{6}=\underline{\;\;\;\;\;\;\;\;\;\;}$

### Practice Set

Directions : Add or subtract the following mixed numbers. Be sure that your answer is in simplest form.

1. $2\frac{3}{6}+4\frac{1}{6}=\underline{\;\;\;\;\;\;\;\;\;\;}$
2. $2\frac{2}{5}+3\frac{1}{5}=\underline{\;\;\;\;\;\;\;\;\;\;}$
3. $5\frac{6}{10}+2\frac{1}{10}=\underline{\;\;\;\;\;\;\;\;\;\;}$
4. $3\frac{8}{12}+6\frac{2}{12}=\underline{\;\;\;\;\;\;\;\;\;\;}$
5. $7\frac{9}{16}+2\frac{1}{16}=\underline{\;\;\;\;\;\;\;\;\;\;}$
6. $3\frac{10}{20}+8\frac{3}{20}=\underline{\;\;\;\;\;\;\;\;\;\;}$
7. $6\frac{18}{20}-2\frac{3}{20}=\underline{\;\;\;\;\;\;\;\;\;\;}$
8. $4\frac{20}{21}-2\frac{13}{21}=\underline{\;\;\;\;\;\;\;\;\;\;}$
9. $9\frac{16}{18}-3\frac{10}{18} =\underline{\;\;\;\;\;\;\;\;\;\;}$
10. $6\frac{24}{25}-1\frac{9}{25}=\underline{\;\;\;\;\;\;\;\;\;\;}$

Directions : Add or subtract the following mixed numbers and fractions. Be sure that your answer is in simplest form.

1. $2\frac{1}{2}+3=\underline{\;\;\;\;\;\;\;\;\;\;}$
2. $6\frac{4}{5}-\frac{1}{5}=\underline{\;\;\;\;\;\;\;\;\;\;}$
3. $8\frac{1}{2}+\frac{1}{2}=\underline{\;\;\;\;\;\;\;\;\;\;}$
4. $9\frac{4}{5}-2\frac{1}{5}=\underline{\;\;\;\;\;\;\;\;\;\;}$
5. $6\frac{4}{9}-4\frac{1}{9}=\underline{\;\;\;\;\;\;\;\;\;\;}$
6. $5\frac{1}{4}+2\frac{1}{4}=\underline{\;\;\;\;\;\;\;\;\;\;}$
7. $8\frac{4}{6}+2\frac{2}{6}=\underline{\;\;\;\;\;\;\;\;\;\;}$

Challenge problems

20. $4 - \frac{3}{9}=\underline{\;\;\;\;\;\;\;\;\;\;}$

21. $6-\frac{3}{8}=\underline{\;\;\;\;\;\;\;\;\;\;}$

### Review

• In adding and subtracting fractions, the first thing you look at is that you have common denominators.
• A fraction is a number that names a part of a whole or a part of a group.
• An improper fraction has a numerator that is larger than its denominator.
• A mixed number is a number that has both wholes and parts, so you will see a whole number and a fraction with mixed numbers.
• You can use pictures and number lines to solve the equations.