FRACTIONS AND DECIMALS
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1 MATH GRADE 6 UNIT FRACTIONS AND DECIMALS EXERCISES FOR EXERCISES
2 Grade 6 Unit : Fractions and Decimals LESSON : A FRACTION BY A WHOLE NUMBER 6.NS.. C 6.NS.. 0 B D + E 6.NS.. Each person will get cup of lemonade. = = = 6.NS.. She will use ton of mulch for each flower bed. 0 0 = = = NS.. A 6.NS. 6. An expression that shows the amount of flour in half a batch of banana muffins is. 6.NS.. a b. Carlos should use cup of flour. c. = = = = Copyright 0 Pearson Education, Inc.
3 Grade 6 Unit : Fractions and Decimals LESSON : A FRACTION BY A WHOLE NUMBER 6.NS.. 6.NS. 9. a. b. Denzel can use yard of ribbon for each package. c. Rewrite the mixed number as a fraction and multiply by. = 6.NS. 0. An expression that shows the amount of pizza that each person will get is 6. 6.NS.. a. Emma and each of her friends will get of the pizza. b. Each person will get a little less than of the pizza. c. Rewrite the mixed number as a fraction and multiply by 6. 6 = Challenge Problem 6.NS.. Here are example word problems. a. Jason, Martin, Mia, and Emma divide pizza does each friend get? of a pizza into equal shares. How much b. Jason, Martin, Mia, and Emma each eat eat altogether? pizza. How many pizzas did they Copyright 0 Pearson Education, Inc.
4 Grade 6 Unit : Fractions and Decimals LESSON : A WHOLE NUMBER BY A FRACTION 6.NS.. B 6 6.NS.. D 6.NS.. In hour, the plane can travel miles. 6.NS.. The company will need signs. 6.NS.. a. whole whole whole whole whole whole b. The bar model shows 6 divided into thirds. 9 groups of are circled c. To check this division with multiplication, multiply by the reciprocal fraction. 6 = 9 6.NS. 6. a. b. Martin can fill glasses 6 = = = c. 6 = = = 6.NS.. a. b. Martin can fill of the bigger glasses. = = Copyright 0 Pearson Education, Inc. 6
5 Grade 6 Unit : Fractions and Decimals LESSON : A WHOLE NUMBER BY A FRACTION 6.NS.. a. 9 b c. Emma and Mia will make 6 rest stops. 6.NS. 9. Multiply 9 by the reciprocal of, which is. 9 = 9 = 9 = 6 9 = 6 6.NS. 0. a. = = = = 6 b. Emma and Mia will make rest stops. c. This number is times the number of rest stops they would take on a 9 mile hike. Challenge Problem 6.NS.. a is at least, so is at most, and is at least. a a Copyright 0 Pearson Education, Inc.
6 Grade 6 Unit : Fractions and Decimals LESSON : A FRACTION BY A UNIT FRACTION 6.NS.. B 6.NS.. A 6.NS.. C 6.NS.. A 6 6.NS.. Denzel needs to fill the measuring cup times NS. 6. It will take the giant tortoise hour to travel kilometer. 0 0 = = NS.. This model shows. whole 0 = It is hard to find the number of halves in this model. So, I divided it into tenths and then found. 0 0 whole 0 There is one group of tenths and of another group. So = 0 0 = Copyright 0 Pearson Education, Inc.
7 Grade 6 Unit : Fractions and Decimals LESSON : A FRACTION BY A UNIT FRACTION 6.NS.. a. There are eighths in a whole. b. The number of eighths in must be = 6. Therefore 6.NS. 9. Here is one example. Challenge Problem 6.NS. 0. a. = 6. A group of friends has watermelons with lunch. They decide that each serving should include mini-watermelon. How many servings do they have? = = = = They have servings.,,,, 6, b.,,,, 6,, c. Each pattern is the reciprocal of the other. The rule for the first pattern is multiply by. The rule for the second pattern is multiply by. Copyright 0 Pearson Education, Inc. 9
8 Grade 6 Unit : Fractions and Decimals LESSON : A FRACTION BY A FRACTION 6.NS.. D 6.NS.. D 6.NS.. Jason can make bears. 6.NS.. Jan s bag of dog food will last more days. 6.NS.. A 6.NS. 6. C 6.NS.. A 6.NS.. The two fractions have the same denominator so what I need to find out is how many groups of are in. Thus, I can write, or. I can check my work by multiplying the reciprocal fraction. = = = 6.NS. 9. Here is one example. A construction worker is cutting a foot long board into smaller sections. She needs each section to be foot long. Into how many equal sections can she cut the board? Solution: She can cut the board into 6 sections. 9 = = = 6 Copyright 0 Pearson Education, Inc. 0
9 Grade 6 Unit : Fractions and Decimals LESSON : A FRACTION BY A FRACTION 6.NS. 0. The first fraction is the same in each problem. I notice that is smaller than. This means that in the first problem, 6 is being split into smaller pieces. So the solution to the first expression will be greater. Check: 6 = 6 = 0 6.NS.. a. Emma is correct. The total amount of oatmeal available is cups. You need to find how many servings there are if each serving is cup. So, you need to divide by, which is what Emma argued. Carlos made a mistake because he says you multiply the two amounts. If you solved the problem using multiplication, you would multiply by the reciprocal of rather than by itself. b. There are servings. = = = = = Challenge Problem 6.NS.. a b a b = = b a = b b b a Copyright 0 Pearson Education, Inc.
10 Grade 6 Unit : Fractions and Decimals LESSON 6: SOLVING WORD PROBLEMS 6.NS.. B The width of a rectangle with an area of square centimeter and a length of centimeter C The number of minute intervals in hour D The number of inch segments that a 0. inch long ribbon can be cut into E The number of quarters in $0.0 6.NS.. Jason s sister has pennants. 6.NS.. The path is miles long. 6 6 = = = = 6 = 6.NS.. teaspoons 6.NS.. Emma will need buckets. 0 = = = = = 6.NS. 6. miles 6.NS.. a., = = = 9 6 = 9 Denzel and his father traveled 9 miles. b. Here is one example. How many hours does it take Denzel and his father to travel 9 speed of 6 miles per hour? miles at a Copyright 0 Pearson Education, Inc.
11 Grade 6 Unit : Fractions and Decimals LESSON 6: SOLVING WORD PROBLEMS 6.NS.. a. 6 = = = = = Mia s backyard is yards wide. b. Here is one example. What is the area of Mia s backyard if it has a length of yards? yards and a width of 6.NS. 9. Here is one example. a. Martin wants to play a new arcade game. According to the rules, players have to earn as many points as possible in each round of the game. The time limit for each round is 6 hour. If Martin has to leave the arcade in hour, how many hour 6 rounds of the game can he play? 6 = = 6 = 6 Martin can play rounds. b. How long did it take Jan to complete problem sets of her homework if each problem set took her 6 hour? 6 = It took Jan hour. Copyright 0 Pearson Education, Inc.
12 Grade 6 Unit : Fractions and Decimals LESSON 6: SOLVING WORD PROBLEMS Challenge Problem 6.NS. 0. a. Both equal 6. b. Both equal. c. Both equal 0. d. The difference and product of consecutive unit fractions are the same. For example, the next two sets of consecutive unit fractions after the examples in parts a c continue to show the pattern. = = = 6 = Copyright 0 Pearson Education, Inc.
13 Grade 6 Unit : Fractions and Decimals LESSON : DIVIDING WHOLE NUMBERS 6.NS.. Each friend earned $ NS.. There will be homeroom classes. 6.NS.. 00 < 0. 6.NS.. He bought soccer balls. 6.NS.. He will need cases. 6.NS NS.. B C. E 6.NS.. a. R b. c. d.. 6.NS. 9. Here are examples of word problems. Solution of : Denzel has $60 dollars to spend on tofu burgers for a party for the whole school. How many boxes of tofu patties can he buy if each box costs $? ) (Denzel will get $ change back from his $60.) Solution of : 60 people will be attending the school party. How many tables will Denzel and the other party organizers need if each table seats? (If they use only tables, people won t have a place to sit. So, they need to round up to tables.) Copyright 0 Pearson Education, Inc.
14 Grade 6 Unit : Fractions and Decimals LESSON : DIVIDING WHOLE NUMBERS 6.NS. 0. a. Carlos will be able to print 6 copies with 6 sheets of paper left over. 6 ) = 6 R6 Challenge Problem b. He will need to borrow sheets of paper. 6.NS. Here are example word problems. a. Emma s family has rented a garden plot in the local community garden. The plot is,0 square feet. If the family would like to divide the plot into equal sections, what will be the size of each section? Each section of the family s garden plot will be ft. Solution: Each section of the family s garden plot will be. ft. b. Denzel won,0 tickets playing skee-ball at the arcade. He plans to share his tickets with his younger siblings and cousins. If Denzel shares his tickets equally so that he and his siblings and cousins all get the same number of tickets, how many tickets will each person get? Each person will get tickets. In this situation, it doesn t make sense to use decimals or fractions, because you can t have part of a ticket. So, the answer needs to be a whole number. When you do the long division, there is a remainder of 6; these are tickets that are left over R6 ) Each person gets tickets with 6 left over. Copyright 0 Pearson Education, Inc. 6
15 Grade 6 Unit : Fractions and Decimals LESSON 9: REVIEW DECIMAL OPERATIONS 6.NS NS.. A NS NS NS.. a b. Jan s garden has an area of.0 m. 6.NS. 6. a b. Jason can make. gallons of chartreuse paint =. 6.NS.. Emma has $.0 more than Denzel =.0 6.NS.. Martin can cover. driveways =. 6.NS < Challenge Problem 6.NS. 0. a. c is multiplied by 0. b. c is divided by 0. c. c is divided by 0. d. c is multiplied by 0. Copyright 0 Pearson Education, Inc.
16 Grade 6 Unit : Fractions and Decimals LESSON 0: MULTIDIGIT DECIMALS 6.NS NS NS... 6.NS NS.. C.6 6.NS. 6. B.00 6.NS.. A.9 6.NS.. The cost of the suntan lotion and towel is $.0. $6. + $.9 $.0 So, the cost of the two other items is $.. $. $.0 $. Two items with a sum equal to this amount are sunglasses and a beach ball. $9.9 + $.9 $. 6.NS. 9. a. The cost of the fruit bars Jan bought is $6.6. $6. $9.9 $6.6 Jan bought fruit bars to share ) b. Jan got $.9 in change. $0.00 $6. $.9 Copyright 0 Pearson Education, Inc.
17 Grade 6 Unit : Fractions and Decimals LESSON 0: MULTIDIGIT DECIMALS 6.NS. 0. a. Mia can buy bottles.. R.9. ) Challenge Problem b. Mia would need to borrow $0.. ($.9 ) $ = $0. 6.NS.. a. Multiply the price by 0.0 and add that amount to the price. t = p + 0.0p, where t is the total cost with tax and p is the price OR Multiply the price by.0. t =.0p, where t is the total cost with tax and p is the price b. Item Price Cost Including Tax Suntan Lotion $.9 $. Bottled Water $.9 $.9 Flip-flops $. $9. Towel $6. $.0 Beach Ball $.9 $.00 Fruit Bar $0. $0.9 Sunglasses $9.9 $. Copyright 0 Pearson Education, Inc. 9
18 Grade 6 Unit : Fractions and Decimals LESSON : REASONING ABOUT OPERATIONS 6.NS... > 6.NS.. < 9 6.NS > 6.NS.. < 6.NS.. > 6.NS NS.. Multiplying will give a smaller result in any real-world situation in which a positive number is multiplied by a fraction (between 0 and ). Here is one example. Mia and Emma are conducting science experiments. Each experiment uses cup of saltwater solution. If the girls conduct experiments, the result will be a number less than. 9 = cups of salt water solution 6.NS.. Dividing will give larger results in any real-world situation in which a positive number is divided by a fraction (between 0 and ). Here is one example. Martin and Denzel have oranges. If they cut each of the oranges in half the result will be a number larger than. = 6 slices 6.NS. 9. a. There are fewer than 0 servings per box. b. There are servings per box. Copyright 0 Pearson Education, Inc. 0
19 Grade 6 Unit : Fractions and Decimals LESSON : REASONING ABOUT OPERATIONS 6.NS. 0. a. Emma walks fewer than 0 miles each week. Challenge Problem If Emma walked mile each of the 0 times, her total would be 0 miles in a week. But she doesn t walk a whole mile; she walks less than a mile. So her total is less than 0 miles in a week. b. Emma walks miles each week. 6.NS.. Here are some possible combinations of numbers. a (starting Number) b (multiply by) c (product) c >, =, < a c >, =, < b c greater than both a and b? c less than both a and b? c between a and b? < < 0. No Yes No 0... > 0.. < No No Yes 0. 0 > 0. < 0 No No Yes 0... <. > 0. No No Yes 0 0. < 0 > 0. No No Yes > > Yes No No > 0 > 0 Yes No No > 0 0 > Yes No No a. b. c. Copyright 0 Pearson Education, Inc.
20 Grade 6 Unit : Fractions and Decimals LESSON : PUTTING IT TOGETHER 6.NS.. Here is one example. Word or Phrase Bar model Examples 6 = Multiply by the reciprocal fraction 9 = 0 9 = = = = 9 0 = 9 = 0 = 9 = 9 = Convert fractions to common denominators = = = 0 0 = =. 0 Copyright 0 Pearson Education, Inc.
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