Multiplying a Fraction and a Whole Number

Transcription

1 Multiplying a Fraction and a Whole Number Reteaching - Reteaching - Find _. Find _ of, or _. _ is the same as dividing, so _ by. Since _ is times _, _ Find each product.. _. _ 0. _ of. _ 0 of. 00 _. of 0. Reasoning Can you use division and mental math to find _ of? Why or why not? Yes, because is the greatest common factor of and. _ of The chart shows the average high temperatures for different months in Phoenix, Arizona. Phoenix Weather Month Average High February 0 F May 9 F July F. What is _ the average temperature in July? 9. What is _ the average temperature in February?. What is _ the average temperature in May? F F F Topic

2 Multiplying a Fraction and a Whole Number Practice - Find each product.. _. _. _ 0. _ of. 900 _. of 0. Reasoning Without multiplying, tell which is greater, _ of because 9 0 is greater than _. of or 9 of. Explain. Driving Distances Departure City Destination City Distance Pittsfield, Massachusetts Providence, Rhode Island mi Reno, Nevada Wendover, Utah 00 mi Practice -. Mike drove _ of the distance between Pittsfield, Massachusetts, and Providence, Rhode Island. How far did he drive? 9. Bimal drove _ of the distance between Reno, Nevada, and Wendover, Utah. How far did he drive?. Estimation How many more miles does Bimal have to drive to get to Wendover, Utah? mi 0 mi 0 mi. There are students in Mr. Fitch s sixth-grade class. If _ of the students are girls, how many girls are in Mr. Fitch s class? A girls B girls C girls D 0 girls. Writing to Explain Explain how you would find the product of and _. Write the problem as _., so _. _ ( _ ). Topic 9

3 Estimating Products Reteaching - When you are working with fractions and mixed numbers, you can estimate using rounding, compatible numbers, or compatible benchmark fractions. Reteaching - Estimate using a whole number Estimate using a compatible that is compatible with the denominator. benchmark fraction. Change to the nearest Round to a compatible whole number that is benchmark fraction. Since compatible with. close to _ and is a factor of 0 _ twelve, use _. Think: 0.. Think:.. Estimate each product by using compatible numbers or benchmark fractions.. _ 9. _. _. _ _ _ Estimate each product by rounding each factor to the nearest whole number.. _ _. _ _ 9 Round _ : Round _ : Multiply: 0. _ _ =. _. Reasonableness Carlotta estimated that _ reasonable? Why or why not? is 0 is about _. Is her estimate. Critical Thinking Why are the estimates of shown below different? Is one estimate better than the other? Sample answers are shown. 9 No, a better choice for a number compatible to 0 is : 9. 0 _ 9. Sample answer: The first estimate uses a compatible whole number to estimate and the second uses a compatible benchmark fraction. Both are reasonable ways to estimate, and in this case, one method is not better than the other. Topic

4 Estimating Products Estimate each product.. _ _. _. _. _ _ 9. _. _ _ 9. _ _. _ _. _ 9. _ Practice _. _ 9. _.. Show three ways to estimate _. Explain It Mr. Simpson lives Sample answers are shown. _. Identify each method you use. Sample answer: Compatible numbers: _ Rounding: ; Compatible benchmark: _ ;. miles from his office. He estimates that he commutes, or miles each week. Is his estimate an overestimate or an underestimate? Explain. Sample answer: is an underestimate because Mr. Simpson rounded the number of miles for each trip to the lower whole number before he multiplied. _. Which benchmark fraction could you use to estimate the product of?_ 9. Geometry Which is the best estimate for the area of a square with sides equal to _ inches? Practice - A sq in. B sq in. C 9 sq in. D sq in. 0. Joyce and Marianne have money jars. Joyce has dimes in her jar. Marianne has 9 as many dimes as Joyce. Estimate the number of dimes that Marianne has in her jar. A 0 dimes B dimes C dimes D dimes Topic

5 Multiplying Fractions Reteaching - Find _ _. Use the Draw a picture. Shade the squares. There are 0 squares in all. squares have overlapping shading. _ _ 0. Simplify: 0 denominators to determine the number of squares: tall and wide. Reteaching - Multiply the numerators and the denominators. Simplify if possible. _ ( ) ( ) 0 Draw a picture to solve.. _ _ Simplify first. Divide a numerator and a denominator by their GCF. Then multiply. _ _ _ ( ) _ ( ) _ _ _ =. _ _ =. _ _ 9 = Write an equation for each picture... _ _ _ _ Find each product. Simplify if possible.. _ =. _ =. _ _ = 9. _ _ =. _ =. _ =. Number Sense Can you simplify before multiplying _? Explain. 0 Topic Yes. Rewrite as a fraction with in the denominator. Then simplify the and the using their GCF of :. _ _ _ _

6 Multiplying Fractions Write an equation for each picture. Practice -.. _ 9 _ Find each product. Simplify if possible... _ _ 9 _... _ 9. _. _ _. 9 Pamela spent _ of an hour doing homework. She solved math problems for _ of that time and read her science book for _ of that time. What fraction of one hour did Pamela spend: _. solving math problems?. reading her science book?. Of the students in Mr. Moore s room, live within a mile of school. Of those students, _ live within half a mile of school. What fraction of all students in Mr. Moore s class live within half a mile of school? _ Practice - A B C D. Writing to Explain Without multiplying, tell which is greater: or 9. Explain. is greater because and 9 is more than 9 is less than. Eighty-one times 9 is greater than. Topic

7 Multiplying Mixed Numbers Reteaching - How to find the product of two mixed numbers: Find _ _. Step Estimate the product by rounding. Step Write each mixed number as an improper fraction. Look for common factors and simplify. Step Multiply the numerators and denominators. Write the product as a mixed number. _ is close to 0, so the answer is reasonable. Round _ to and _ to : 0 _ and _ 9 _ _ _ 9_ / / _ Reteaching - Find each product. Simplify if possible.. _ _ 9 _. _ _. _ _. _. _. _ _ 0 Evaluate each expression for K _. K. _ K 9. _. Reasonableness What is a reasonable estimate for _ Explain.. K _ 9 _?. The cups of mushrooms in a recipe is _ times the cups of onions. The cups of onions is _. Solve c _ _ to find c, the cups of mushrooms., since _ rounds to and rounds to and. c of mushrooms 9_ Topic

8 Multiplying Mixed Numbers Practice - Find each product. Simplify if possible.. _. _ _. _. _ _. _ _. _. _ _. _ Evaluate each expression for S _. 9. _ _ 9_. _ S. _ S. _ Use the table to answer the questions. _ S 9. If Berkeley receives _ times its average January rainfall, how much rain will it receive? _. How much rain will Berkeley receive if it is _ times the October average? _ in. in. Average Rainfall in Berkeley, California January April _ in. October _ in. Practice -. Which month has about twice the rainfall as April? January. Jessie stacked photographs of zoo animals on top of each other to create a display. Each photo is _ in. high. How high is the display? A _ in. B _ in. C _ in. D in.. Writing to Explain Explain how you would find _ using the Distributive Property. Multiply and _ products to get _, and then add the or _. Topic

9 Problem Solving: Multiple-Step Problems Reteaching - Some word problems have hidden questions that must be answered before you can solve the problem. A paved trail is miles long. Rita runs _ of the length of the trail and walks the rest of the way. How many miles of the trail does Rita walk? What do you know? Rita runs _ of an -mile trail. What are you asked to find? How many miles of the trail that Rita walks. How can you find the distance that Rita Subtract the distance Rita ran from the walks? length of the trail. What is the hidden question? The hidden How many miles did Rita run? question will help you find data you need to To answer, find solve the problem. _. Use the data to solve:, so Rita walked of the miles. Reteaching - Write and answer the hidden question(s) in each problem. Then solve the problem.. April surfed for _ of the hours she was at the beach. She spent the rest of the time building a sand castle. How many hours did she spend building the castle? Hidden question: How many hours did April surf? _ ; hours. Bill put gasoline in of his -gallon cans and of his -gallon cans. He filled all the cans to the exact capacity. How many gallons of gasoline did he buy? Hidden question : Hidden question : How many gallons are in two -gallon cans? How many gallons are in four -gallon cans? ; gallons of gas. It costs Le Stor $0 to buy a shirt. The store sells the shirt for _ times its cost. What is the profit for 0 of these shirts? Hint: Profit equals sales minus cost. Hidden question : Hidden question : Topic What is the selling price of the shirt? _ $0 $0 What is the profit for one shirt? $0 $0 $0 0 $0 $,000

10 Problem Solving: Multiple-Step Problems Practice - Write and answer the hidden question(s) in each problem. Then solve the problem.. Tiwa spent _ hours setting up her computer. It took her times as long to install the software. How long did it take Tiwa to set up the computer and install software? Hidden question(s): How many hours did it take to install software? _ _ ; hours. Lon bought 0 ounces of sliced ham. He used _ of the ham to make sandwiches for his friends and _ of the ham in an omelet. How many ounces of ham were left? Hidden question(s):. Lionel cut off _ of a -inch piece of rope. Marsha cut off _ of a -inch piece of rope. They compared their cut pieces. Whose piece is longer? How much longer? Hidden question(s):. Melanie bought CDs. The country music CD cost $. The rock music CD cost _ as much as the country music CD. The platinum edition CD cost twice as much as the rock CD. What was the cost of the three CDs? Hidden question(s): How many ounces of ham were used to make sandwiches? / 0 = 0; How many ounces of ham were used in the omelet? 0 _ 0 0 ; ounces How long is Lionel s cut piece? _ ; How long is Marsha s cut piece? _ 9 Marsha s rope is inch longer: 9. How much did the rock CD cost? _ $ $; How much did the platinum CD cost? $ $0 $ $ $0 $ Practice -. Writing to Explain Choose one of the problems above. Explain how you determined the hidden question and why it was necessary to answer that question in order to solve the problem. Sample answer: In Problem, the question asks for the time spent on two tasks, so I needed to add the two times to answer the question. Only the time for one task was given in the problem, so the hidden question had to be to find the other time. Topic