Fractions Nancy Hughes Olathe District Schools

Standards Seventh Grade N M7.1.4.K2d The student adds, subtracts, multiplies, and divides fractions and expresses answers in simplest form. Eighth Grade M8.1.4.A1bThe student models, performs, and explains computation with rational numbers, the irrational number pi, and algebraic expressions in a variety of situations.

Vocabulary Addend Common denominators Denominator Dividend Division Equivalent fraction Fraction Improper fraction Least common denominator Lowest terms Minuend Mixed number Numerator Proper fraction Quotient Simplify Subtrahend Unit fraction

Objectives Develop concepts of fractions and mixed numbers Use models to add, subtract, multiply and divide fractions Add, subtract, multiply, divide fractions and mixed numbers

Adding Fractions – Using Fraction Circles Pull out your fraction circles and sort them by colors. The clear circle is the number 1 or 1 whole.

Do the same with the fraction tiles. Sort them by color. 1

Adding Fractions – Using Fraction Circles or Fraction Tiles Let’s add Which colored circle or tile will you need to add these fractions? Explain. Because the fraction has a denominator of 4, find the fraction piece that has been divided into fourths. Take the ¼ piece and add to it the piece. + = + =

Adding Fractions – Using Fraction Circles or Tiles Use either fraction circles or tiles to model Again, look at the denominator and choose your tiles accordingly. + = + =

Adding Fractions – Using Fraction Circles or Tiles Use either fraction circles or tiles to model ½ Notice we do not have like denominators. This makes it more of a challenge. Begin by taking the ½ and the 1/3 and find tiles or circles that are exactly the same size. Did you find like tiles? Explain. If you found tiles or parts of a circle that have a denominator of 6, you were correct. Notice the ½ matches up with 3/6 and the 1/3 matches up with 2/6. Now we can add!

Adding Fractions – Using fraction circles or tiles Use either fraction circles or tiles to model + = = +

You Try Use your fraction circles or fraction tiles to find + = + =

Quick Review Quick Review #1 #2 #3 #4 #5 Roll 1st Fraction Use two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions, and then add. Roll 1st Fraction 2nd Fraction Sum #1 #2 #3 #4 #5

How to use your calculator to check! Change to a fraction Simplify Mixed Number and Improper Fraction Change to a decimal Fraction bar

Subtracting Fractions Visual approach using fraction tiles or fraction circles

Subtracting Fractions using fraction circles or fraction tiles What is ? Again we will have to find like denominators. Which sets of tiles or circles will work? Explain. If you guessed the 10th’s you were right, 6/10 = 3/5 -

Subtracting Fractions using fraction circles or fraction tiles What is ? If you used fraction circles, your work should be identical to the fraction tiles. = -

You Try – Use fraction tiles or fraction circles to show your answer. What is ? - or ¼ - =

Quick Review Quick Review #1 #2 #3 #4 #5 Roll 1st Fraction Use two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then subtract. Roll 1st Fraction 2nd Fraction Difference #1 #2 #3 #4 #5

Multiplying fractions Multiplying fractions is like finding what one fraction is of another.

Multiplying fractions For example, to find , we begin with an area model. 3/4 1 2 3 7 2/3 4 5 6 8 9 10 11 12

Multiplying Fractions To simplify ,find the prime factorization of 6 and 12. Composite Prime Composite Prime 6 2 12 2 3 6 2 3 6 2 • 3 = 1 12 2 • 2 •3 2

Multiplying fractions What is? ¼

Multiplying Fractions To find the answer to ½ x 3/5, we will use another model. Show 3 out of 5 Show 1 out of 2 Shade the answer

You try! To find the answer to . Model your answer. Show 2 out of 3 Shade the answer

Quick Review Quick Review #1 #2 #3 #4 #5 Roll 1st Fraction Use two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then multiply. Roll 1st Fraction 2nd Fraction Product #1 #2 #3 #4 #5

Dividing Fractions – Fraction Tiles Find Visualize how many ¼’s will go into 5/8. Using fraction tiles, visualize how many ¼’s you can place upon 5/8.

Dividing Fractions – Fraction Tiles Find

You try! Use your fraction circles or tiles. Find

Quick Review Quick Review #1 #2 #3 #4 #5 Roll 1st Fraction Use two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then divide. Roll 1st Fraction 2nd Fraction Quotient #1 #2 #3 #4 #5

Adding Fractions – Using Arithmetic Method 2 3 x5 15 + 2 x4 8 = 23 4 x5 20 + 5 x4 20 20 Method 1 3 x5 15 4 x5 20 2 x4 8 +5 x4 20 23 20 Method 3

You try! Use one of the three methods to find If you do not know the common denominator, find the LCM. Composite Prime 8 4 2 Composite Prime 3 2 3 LCM = 2x2x2x3=24

Subtracting Fractions – Using Arithmetic Method 2 3 x5 15 - 2 x4 8 = 7 4 x5 20 5 x4 20 20 Method 1 3 x5 15 4 x5 20 2 x4 8 -5 x4 20 7 20 Method 3

You try! Use one of the three methods to find If you do not know the common denominator, find the LCM. Composite Prime 12 6 2 3 Composite Prime 4 2 2 3 LCM = 2x2x3=12

Multiplying Fractions – Using Arithmetic Method 1 Method 2 1 ¼ Composite Prime 10 2 5 Composite Prime 40 20 2 5 4

You Try! Use one of the two methods to multiply fractions.

Dividing Fractions Using Arithmetic Divide the following: Before you begin, change the problem to a multiplication problem by using the reciprocal of the fraction after the division sign. Multiply the fractions.

You try! Divide the following: Before you begin, change the problem to a multiplication problem by using the reciprocal of the fraction after the division sign. Multiply the fractions.

Journaling Answer two of the following questions in your journal: Explain how to add fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain. Explain how to subtract fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain. Explain how to multiply fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain. Explain how to divide fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.

Practice Operations with Fractions

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