Factor Vocab Word 2 Fraction Division Its meaning (As it is used - PDF document

Slide 1 / 315 Slide 2 / 315 6th Grade Fraction and Decimal Computation 2014-10-16 www.njctl.org Slide 3 / 315 Slide 4 / 315 Vocabulary words are identified with a Fraction and Decimal Computation dotted underline. Unit Topics Click on the topic to go to that section · Fraction Division Sometimes when you subtract the fractions, · Long Division Review you find that you can't because the first · Adding Decimals numerator is smaller than the second! When · Subtracting Decimals this happens, you need to regroup from the whole number. · Distributive Property & Product of Decimals (Click on the dotted underline.) · Multiplying Decimals · Dividing Decimals How many thirds are in 1 whole? · Even and Odd Numbers · Divisibility Rules for 3 & 9 How many fifths are in 1 whole? · Greatest Common Factor How many ninths are in 1 whole? · Least Common Multiple · GCF and LCM Word Problems The underline is linked to the glossary at the end of the · Glossary Notebook. It can also be printed for a word wall. Common Core Standards: 6.NS.1, 6.NS.2, 6.NS.3 Slide 5 / 315 Slide 6 / 315 The charts have 4 parts. 1 Factor Vocab Word 2 Fraction Division Its meaning (As it is used A whole number A whole number that can divide into that multiplies with in the another number another number to lesson.) with no remainder. make a third number. 5 .1 R 15 3 5 3 16 3 is a factor of 15 3 is not a 3 x 5 = 15 factor of 16 3 Back to 3 and 5 are 4 Instruction Return to factors of 15 Examples/ Table of Link to return to the Contents Counterexamples instructional page.

Slide 7 / 315 Slide 8 / 315 Modeling Division Applying to Fractions Recall from 5th grade: The previous example used whole numbers and grouped the dividend according to the divisor. When we are dividing, we are breaking apart into equal groups. Teacher Notes The same strategy can be applied when dividing with fractions. Dividend Divisor = Quotient Use the model below to demonstrate: 8 The model below represents: 8 4 = 2 8 The pink rectangle represents . See how many you can fit in the 8 squares. 2 groups of 4 Slide 9 / 315 Slide 10 / 315 Example 1 Evaluate the following problem using the model Use the model below to demonstrate 2 below: 3 2 Answer 3 Slide 11 / 315 Slide 12 / 315 A fraction can be divided by a whole number using the following 2 Evaluate the following problem using the model visual model. below: 3/5 ÷ 4 5 1 2 3 4 Divide into 4 groups Answer 5 3/5 ÷ 4 = 3/20 Click to Reveal

Slide 13 / 315 Slide 14 / 315 The previous expression can be represented by the following 3 Evaluate the following problem using the model word problem: below. How much will each person receive if 4 friends share a 3/5 pound bag of popcorn? 1 2 3 4 Answer Drag the line Each friend will receive 3/20 lb. of popcorn. Slide 15 / 315 Slide 16 / 315 Create a story to represent the problem and use a visual model to 4 Evaluate the following problem using the model show the quotient. below. Answer Drag the line Slide 17 / 315 Slide 18 / 315 Fraction Divided by a Fraction Example The same strategy we utilized for the previous examples can also Use the model below to evaluate: be applied when dividing a fraction by another fraction. In this example our division problem is: We need to determine how many 's there are in

Slide 19 / 315 Slide 20 / 315 5 Evaluate the following problem using the model 6 Evaluate the following problem using the model below: below: Answer Answer Slide 21 / 315 Slide 22 / 315 Patterns Vocabulary Review Do you notice a pattern between the division of fractions and Complex Fraction: A fraction with another fraction in the their solution? numerator, denominator or both Teacher Notes Reciprocal: The inverse of a number/fraction Original 4 Number Reciprocal 2 Slide 23 / 315 Slide 24 / 315 Example If you think about it, we are dividing by a fraction which creates a complex fraction. 1 1 x 3 1 x 3 2 2 2 2 2 1 2 1 x 3 = = You need to eliminate the fraction in the denominator in order = = 2 2 2 3 x 3 2 1 2 to solve the problem. 3 3 2 To do this, multiply the numerator and denominator of the Original Complex Simplify Rewrite Multiply by complex fraction by the reciprocal of the denominator (making Problem Denominator Without 1 Fraction Reciprocal the denominator = 1). There are rules that can be applied to fraction You can then simplify the fraction by rewriting it without the division problems to eliminate steps from this denominator of 1 and solve the new multiplication problem. lengthy procedure. source - http://www.helpwithfractions.com/dividing-fractions.html

Slide 25 / 315 Slide 26 / 315 Dividing Fractions Algorithm Some people use the saying "Keep Change Flip" to help them remember the algorithm. Step 1: Leave the first fraction the same. Step 2: Multiply the first fraction by the reciprocal of the second fraction. Change Changed Keep Flip Flipped Kept Step 3: Simplify your answer. 3 7 3 8 3 x 8 = 24 = = x 5 8 5 7 5 x 7 35 1 1 1 x 2 = 1 x 2 = 2 = 5 2 5 1 5 x 1 5 Slide 27 / 315 Slide 28 / 315 Example Checking Your Answer To check your answer, use your knowledge of fact families. Evaluate: 3 ÷ 7 24 Change = Changed 5 8 35 Keep Flip Flipped Kept 7 24 3 = x 8 5 35 x = = = 3 7 24 is of 5 8 35 Slide 29 / 315 Slide 30 / 315 7 8 8 2 2 7 4 = 5 x 8 3 = 8 5 10 4 10 4 7 True Answer True Answer False False

Slide 31 / 315 Slide 32 / 315 10 9 4 8 = 10 5 Answer Answer 1 A 39 B 40 40 C 42 Slide 33 / 315 Slide 34 / 315 Sometimes you can cross simplify 11 prior to multiplying. without cross with cross simplifying simplifying Answer 5 1 2 3 Slide 35 / 315 Slide 36 / 315 12 Can this problem be cross simplified? 13 Can this problem be cross simplified? Yes Yes No No Answer Answer

Slide 37 / 315 Slide 38 / 315 14 Can this problem be cross simplified? 15 Can this problem be cross simplified? Yes Yes No No Answer Answer Slide 39 / 315 Slide 40 / 315 16 17 Answer Answer Slide 41 / 315 Slide 42 / 315 18 19 Answer Answer

Slide 43 / 315 Slide 44 / 315 A mixed number can be divided by a mixed number using the Since our LCD is 6, every 6 lines is considered a whole. following visual model. 1 1/2 is equivalent to 9 sections on the number line. 1 1/2 First find the least common denominator (LCD) which is 6. 9 10 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7 8 2 2/3 If every 6 lines represents a whole, then how many lines should we draw to make sure both mixed numbers fit? 2 2/3 is equivalent to 16 sections on the number line. Click 18 So 1 1/2 ÷ 2 2/3 = 9/16 to Reveal Slide 45 / 315 Slide 46 / 315 Dividing Mixed Numbers Algorithm What if the problem were written as ? Step 1: Rewrite the Mixed Number(s) as an improper fraction(s). 2 2/3 (write whole numbers / 1) 9 10 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7 8 Step 2: Follow the same steps for dividing fractions 1 1/2 1 1/2 How many times does 1 1/2 divide into 2 2/3? 1 6 3 = 4 6 1 6 x 2 = 12 = = 2 2 1 1 3 3 Slide 47 / 315 Slide 48 / 315 Example 20 1 2 2 1 Evaluate: = 2 3 Answer 2 1 1 5 7 3 5 x 2 = 10 = = 3 2 3 2 3 7 21

Slide 49 / 315 Slide 50 / 315 21 22 1 2 5 1 2 5 4 = = 2 5 2 Answer Answer Slide 51 / 315 Slide 52 / 315 Application Problems - Examples 23 Winnie needs pieces of string for a craft project. How many 1/6 yd 1 2 3 3 = pieces of string can she cut from a piece that is 2/3 yd long? 2 8 2 1 3 ÷ 6 Answer 2 6 12 4 x = = 4 pieces 1 3 3 1 or 2 2 6 4 x = 1 = 4 pieces 3 1 1 Slide 53 / 315 Slide 54 / 315 One student brings 1/2 yd of ribbon. If 3 students receive an Kristen is making a ladder and wants to cut ladder rungs from a 6 ft board. Each rung needs to be 3/4 ft long. How many ladder rungs equal length of the ribbon, how much ribbons will each student receive? can she cut? 3 1 6 ÷ ÷ 3 4 2 6 3 2 x 1 1 1 1 ÷ 6 yards of ribbon = 4 3 4 24 6 8 1 x = = = 8 rungs 3 3 1

Slide 55 / 315 Slide 56 / 315 A box weighing 9 1/3 lb contains toy robots weighing 1 1/6 lb 24 Robert bought 3/4 pound of grapes and apiece. How many toy robots are in the box? divided them into 6 equal portions. What 9 1 1 1 is the weight of each portion? ÷ 3 6 A 8 pounds B 4 1/2 pounds 7 28 ÷ C 2/5 pounds Answer 6 3 1/8 pound D 4 2 28 6 8 x = = 8 robots 3 7 1 1 1 Slide 57 / 315 Slide 58 / 315 25 A car travels 83 7/10 miles on 2 1/4 26 One tablespoon is equal to 1/16 cup. It is gallons of fuel. Which is the best estimate also equal to 1/2 ounce. A recipe uses 3/4 of the number miles the car travels on cup of flour. How many tablespoons of one gallon of fuel? flour does the recipe use? A 84 miles A 48 tablespoons Answer Answer 62 miles B 24 tablespoons B 42 miles C 12 tablespoons C 38 miles D D 6 tablespoons Slide 59 / 315 Slide 60 / 315 27 A bookstore packs 6 books in a box. The 28 There is gallon of distilled water in the total weight of the books is 14 2/5 pounds. If each book has the same class science supplies. If each pair of weight, what is the weight of one book? students doing an experiment uses A 5/12 pound Answer gallon of distilled water, there will be 2 2/5 pounds Answer B 8 2/5 pounds C gallon left in the supplies . How many D 86 2/5 pounds students are doing the experiments?