Adding Mixed

NumbersBy: Christin Spurlock

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Before We Begin…

Hello! My name is fractolover, as in fraction solver. I love everything about fractions. My goal at the end of this lesson is to make sure you understand what the parts of a fraction are and can add mixed numbers correctly. Now look to your right and let me show you how the screen buttons work.

By clicking this picture, you will be taken to the home page, which is the beginning of the lesson.

By clicking this arrow, you will go backwards and will be taken to the previous page.

By clicking this arrow, you will continue to move forward and go to the next page.

By clicking this arrow, you will be taken to the last page of this lesson.

Table of Contents

I have a full lesson prepared for you on two ways that you can add mixed numbers. Check out the table of contents, so that you may have an overview of what is to come. When you are finished click the to continue.

Definitions

1st Way to Add Mixed Fractions

Guided Practice

2nd Way to Add Mixed Fractions

Guided Practice

Quiz

DefinitionsMixed Fractions: A fraction that consist of a whole number and fraction.

Whole Number: The bigger number that sits to the left of a fraction.

Numerator: The number that sits at the top in a fraction.

Denominator: The number that sits at the bottom in a fraction.

Lowest Common Denominator (Also known as the LCD): The lowest number that can be the denominator of all the fractions you are trying to add.

Improper Fraction: A fraction where the numerator is equal to or larger than the denominator.

Take a look at these definitions.

1st Way to Add Mix Fractions

1st Step: Add the Whole Numbers Together.

3 5/8 + 4 3/4 … 3 + 4 = 7

Let’s get started adding mix fractions! We will use this equation.

3 5/8 + 4 3/4

2nd Step: Find the lowest Common Denominator (LCD)

HOW TO FIND THE LCD>>> 3 5/8 + 4 3/4

1. Write a few multiples of each denominator 8 = 8, 16, 24, 32 4 = 4, 8, 12, 16

2. What are the lowest multiples each denominator has in common? 8 = 8, 16, 24, 32 4 = 4, 8, 12, 16

3. Your LCD is 8

Mixed Number

Whole Number

Denominator

1st Way to Add Mix Fractions

3rd Step: Multiply each fraction by the number it takes the denominator to equal your LCD.

3 5/8 + 4 3/4 = LCD 8 (8x1=8 and 4x2=8)• 5/8 x 1/1 = 5/8•3/4 x 2/2 = 6/8

More steps to go, but I am glad to see you are understanding.

3 5/8 + 4 3/4

4th Step: Add the fractions by adding the numerators only. 5/8 + 6/8 = 11/8

Improper Fraction

Numerator

1st Way to Add Mix Fractions

5th Step: Remove improper fractions (11/8) by subtracting the denominator from the numerator (keeping your denominator the same) and adding one to the whole number.

1. Subtract the denominator from the numerator… 11/8= 11 – 8 = 3

2. Keep the denominator the same… 11/8= 11 – 8 = 3/8

3. Add one to the whole number… 7 + 1 = 8

YOUR ANSWER!!!! 8 3/8

Last step…keep up the good work!

3 5/8 + 4 3/4 Numerator

Guided PracticeLet’s put your knowledge to work and practice solving one!

Directions: Solve this equation using the steps you just learned for adding mix fractions. (Use your scratch sheet)

6 5/6 + 2 2/3Step 1: Add the whole numbers together.

Step 2: Find the LCD.

Step 3: Multiply each fraction by the number it takes the denominators to equal the LCD.

Step 4: Add the fractions by adding the numerators only.

Step 5: Remove the improper fraction by subtracting the denominator from the numerator (keeping denominator the same) and adding one to the whole number.

6 5/6 + 2 2/3…

6 + 2 = 8

6 5/6 + 2 2/3…

6=6,12,18,24

3=3,6,9,12

LCD= 6

6 5/6 + 2 2/3…

6= 6 x 13= 3 x 2

1/6 x 1/1 = 1/6

5/3 x 2/2 = 10/6

6 5/6 + 2 2/3…

1/6 + 10/6 = 11/6 6 5/6 + 2 2/3…

1. 11 – 6 = 5

2. 11 – 6 = 5/6

3. 8 + 1 = 9THE ANSWER… 6 5/6 + 2 2/3 = 9 5/6

Click here for the answer to step 2.

Click here for the answer to step 3.

Click here for the answer to step 1. Click

here for the answer to step 5.

Click here for the answer to step 4.

Click here for the final answer.

Guided Practice

Let’s test your knowledge of the definitions you have learned.

Directions: Match the letter with the definition and answer the question below. A. Lowest Common DenominatorB. Improper fractionC. DenominatorD. Mixed FractionE. NumeratorF. Whole Number

1. A fraction that consist of a whole number and

fraction. D2. The bigger number that sits to the left of a fraction.

F3. The number that sits at the top in a fraction.

E4. The number that sits at the bottom in a fraction. C5. The lowest number that can be the denominator of all

the fractions you are trying to add. A6. A fraction where the numerator is equal to or larger

than the denominator. B7. What is the acronym for Lowest Common

Denominator? LCD

Click for answer

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Click for answerClick for answer

2nd Way to Add Mix FractionsThere is another way to that you can add mix fractions. Let me show you now. We will use this equation.

12 7/9 + 7 1/3 1st Step: Convert the mix fractions to improper fractions

HOW TO MAKE A MIX NUMBER AN IMPROPER FRACTION>>>

1. Multiply the denominator and whole number 12 7/9 : 9 x 12 =81 71/3 : 3 x 7 =21

2. Add that number to the numerator 12 7/9 : 81 + 7 = 88 71/3 : 21 + 1 = 22

3. Make the number you calculate the numerator and the denominator remains the same. 12 7/9 : = 88/9 71/3 : =22/3

2nd Way to Add Mix FractionsWe have more steps to go, but keep up the good work.

12 7/9 + 7 1/3 2nd Step: Find the LCD of the denominator

88/9 + 22/3… 9 = 9, 18, 27, 36 3 = 3, 6, 9, 12

The LCD is 9

3rd Step: Make the denominators the same by multiplying the fraction by the number it takes the denominator to equal the LCD88/9 + 22/3… (9 x 1 = 9 and 3 x 3 = 9)

88/9 x 1/1 = 88/9 22/3 x 3/3 = 66/9

2nd Way to Add Mix FractionsYour are doing a great job learning. Here are the last steps.

12 7/9 + 7 1/3 4th Step: Add the two fractions by adding the numerators. 88/9 + 66/9 = 154/9

5th Step: Convert the improper fraction back into a mixed number by dividing.

1. Divide: 109 ÷ 9 = 17 with a Remainder of 1

2. Make the 17 the whole number, the remainder of 1 the numerator, and keep the denominator the same.

109 ÷ 9 = 17 with a Remainder of 1

17 with a remainder of 1 = 17 1/9

HOW TO MAKE AN IMPROPER FRACTION A MIX NUMBER>>>

YOUR ANSWER!!!! 17 1/9

Guided PracticeLet’s put your knowledge to work and practice solving one!

Directions: Solve this equation using the steps you just learned for adding mix fractions. (Use your scratch sheet)

11 3/10 + 3 4/5Step 1: Convert the mix fractions to improper fractions..

Step 2: Find the LCD.

Step 3: Make the denominators the same by multiplying the fraction by the number it takes the denominator to equal the LCD.

Step 4: Add the two fractions by adding the numerators.

Step 5: Convert the improper fraction back into a mixed number by dividing.

11 3/10 + 3 4/5…• 11 3/10 =

10 x 11 = 110110 + 3 = 113113/10

• 3 4/5 =

5 x 3 = 1515+ 4 = 1919/5

THE ANSWER… 11 3/10 + 3 4/5 = 15 1/10

Click here for the answer to step 1.

Click here for the final answer.

11 3/10 + 3 4/5…

113/10 + 19/5

10= 10, 20, 30, 405 = 5, 10, 15, 20

LCD = 10

11 3/10 + 3 4/5…

113/10 + 19/510 x 1 = 105 x 2 = 10

113/10 x 1/1 = 113/10 19/5 x 2/2 = 38/10

11 3/10 + 3 4/5…

151/10 …

151 = 15 with a remainder of 1

• 15 = whole number

• Remainder = numerator

• Demoninator= stays the same

• 15 1/10

Click here for the answer to step 2.

Click here for the answer to step 3.

11 3/10 + 3 4/5…

113/10 + 38/10 =

151/10

Click here for the answer to step 4.

Click here for the answer to step 5.

Guided PracticeLet’s test your knowledge of the parts of a fraction.

Directions: Name the parts of the fraction and answer the question below.

7 4/9 What do you call this kind of fraction? 63/5

Improper fraction! Great Job!!!

Mixed Number

DenominatorNumerator

Whole Number

Click here for the answerClick here for the

answer

Click here for the answer

Click here for the answer

Click here for the answer

Quiz TimeIt has been great helping you add mix fractions! Now take a quick quiz.

Directions: Use the steps you have learned to add these mix fractions. Use your scratch sheet to show your work. This will be graded.

Use the 1st way to add mix fractions to solve…

1. 9 5/6 + 2 7/12

Use the 2nd way to add mix fractions to solve…

2. 8 3/5 + 11 7/10

12 5/12

20 3/10

Click here for the answer

Click here for the answer

Sources

Wiki How to Add Mix Fractions: http://www.wikihow.com/Add-Mixed-Numbers