Transcript Lesson 2.2
Lesson 2.2 Core Focus on Decimals & Fractions Multiplying Decimals Warm-Up Find the value of: 1. 3.2 + 3.2 + 3.2 6.6 2. 3 groups of 6 18 3. 8 groups of 4 32 4. 5.4 + 5.4 + 5.4 + 5.4 21.6 Lesson 2.2 Multiplying Decimals Find products of expressions involving decimals. Multiplying with Decimals 1. Multiply as if the numbers were whole numbers. 2. Count number of places after the decimal points in each factor. 3. Count the same number of places in the product starting from the right and moving left. 4. Insert zeros, if needed, to hold place value. Delete zeros that are not necessary. 5. Put the decimal point where you stop counting in the answer. Example 1 How much did Yana spend on three half-gallons of ice cream if each half-gallon cost $3.55? Write the problem. 3 × 3.55 Use decimal models to visualize. Multiply like whole numbers. 1 1 $3.55 3 1065 Example 1 Continued… How much did Yana spend on three half-gallons of ice cream if each half-gallon cost $3.55? There are two places Count the number of places to the right of the decimal point in the problem. Count the same number of places in the answer starting on the right and moving left. Put the decimal point where you stop. Yana spent $10.65 on ice cream. in this factor after the decimal point in 3.55. 3 × 3.55 11 $3.55 3 10.65 Count two places starting from the right and moving left. Example 2 How much did Yana spend on 3.6 pounds of bananas if they cost $0.40 per pound? Write the problem. 3.6 × 0.40 Use decimal models to visualize. Example 2 Continued… How much did Yana spend on 3.6 pounds of bananas if they There is one cost $0.40 per pound? Multiply like whole numbers. Count the number of digits to the right of the decimal points in both numbers in the problem. Count the same number of places in the answer starting on the right and moving left. Put the decimal point where you stop. 2 3.6 0.40 00 + 1440 1440 1 .440 place after the decimal point in the factor 3.6. There are two places after the decimal point in the factor 0.40. Count three places starting from the right and moving left. Example 2 Continued… How much did Yana spend on 3.6 pounds of bananas if they cost $0.40 per pound? Drop any zeros at the end of the decimal. Yana spent $1.44 on bananas. 1.440 = 1.44 Example 3 Find the value of 0.3 × 0.016. Multiply like whole numbers. Count the number of digits to the right of the decimal points in both numbers in the problem. 0.016 0.3 48 There are three places after the decimal point in the factor 0.016. There is one place after the decimal point in the factor 0.3. Count four places starting from the right and moving left. Count the same number of places in the answer starting on the right and moving left. Insert zeros to hold the missing places. .0048 Put the decimal point where you stop. 0.3 0.016 = 0.0048 Explore! Smart Shopper Jay gets advertisements for the local grocery stores in his newspaper. He wants to save the most money possible. He figures out which stores he should buy which items from. Here is part of his list and the stores with sales on those items. Use the steps on the following slide to decide from which store Jay should buy grapes. ABC Grocery Grapes: $1.39 per pound Cherry tomatoes: $0.98 per pound Fuji apples: $1.29 per pound Deli-sliced ham: $3.99 per pound Chicken breasts: $1.69 per pound Whole chicken fryer: $0.69 per pound Beef round roast: $1.98 per pound Chocolate Blitz bars: $0.59 each Fizzy Pop: $0.70 each ZYX Grocery Grapes: 3 pound container for $4.99 Cherry tomatoes: 3.5 pound container for $3.96 Fuji apples: 3.25 pound bag for $4.25 Deli-sliced ham: 1.75 pound package for $5.50 Chicken breasts: 4 pound package for $5.99 Whole chicken fryer: $5.50 for 5 pounds Beef round roast:4.5 pound roast for $9.23 Chocolate Blitz bars: $6.40 for back of 12 Fizzy Pop: $9.99 for 15 pack Explore! ABC Grocery Grapes: $1.39 per pound Cherry tomatoes: $0.98 per pound Fuji apples: $1.29 per pound Deli-sliced ham: $3.99 per pound Chicken breasts: $1.69 per pound Whole chicken fryer: $0.69 per pound Beef round roast: $1.98 per pound Chocolate Blitz bars: $0.59 each Fizzy Pop: $0.70 each Smart Shopper ZYX Grocery Grapes: 3 pound container for $4.99 Cherry tomatoes: 3.5 pound container for $3.96 Fuji apples: 3.25 pound bag for $4.25 Deli-sliced ham: 1.75 pound package for $5.50 Chicken breasts: 4 pound package for $5.99 Whole chicken fryer: $5.50 for 5 pounds Beef round roast:4.5 pound roast for $9.23 Chocolate Blitz bars: $6.40 for back of 12 Fizzy Pop: $9.99 for 15 pack Step 1 Multiply the price at ABC Grocery ($1.39) by the number of pounds he would buy if he bought grapes at ZYX Grocery (3 pounds). Step 2 Round to the nearest penny or hundredth if the total price when multiplied ends with more than two places after the decimal point. This is the price for the same amount of grapes at ABC Grocery. Step 3 Compare prices. Which store has the lower price? Step 4 Use the procedure from Steps 1–3 for each item. Decide which store has the best price for each item on Jay’s list. Communication Prompt What would be some reasons you might round your answer to the nearest tenth, hundredth or thousandth when completing a multiplication problem including decimals? Exit Problems 1. Find the value of 3 × 29.6. 88.8 2. Find the value of 8.7 × 9.2. 80.04 3. Find the value of 0.14 × 0.32. 0.0448 4. Jeremiah jumped forward four times. Each time his jump measured 24.4 cm. What is the total length of his four jumps? 97.6 cm 5. Marta made 3.5 batches of cookies. Each batch called for 2.25 cups of chocolate chips. How many cups of chocolate chips did she use in all? 7.875 cups