38 Lesson 2.2 ~ Multiplying Decimals

Yana had make-your-own banana splits for her birthday party. She had toppings at home, but she purchased three half-gallons of ice cream and 3.6 pounds of bananas. How much did these items cost altogether?

how much did yana spend on three half-gallons of ice cream if each half-gallon cost $3.55?

Write the problem. $3.55 × 3

Use decimal models to visualize.

3.55 3.55 3.55 1 1Multiply like whole numbers. $3.55 × 3 1065 Count the number of places to the $3.55right of the decimal point in the problem. × 3 1065Count the same number of places in the answer starting on the right and moving left. Put the decimal point where you stop. 10.65

Yana spent $10.65 on ice cream.

Ice cream: $3.55 per half gallon Bananas: $0.40 per pound

ExamplE 1

solution

mulTiplying DEcimals

lesson 2.2

Lesson 2.2 ~ Multiplying Decimals 39

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.

2Multiply as if you are finding 36 × 40. 3.6 × 0.40Count the number of digits to the 00right of the decimal points in both + 1440numbers in the problem. 1440

Count the same number of places in the answer starting on the right and moving left. Put the decimal point where you stop. 1.440

Drop any zeros at the end of the decimal. 1.440 = 1.44

Yana spent $1.44 on bananas.

Find the value of 0.3 × 0.016.

Multiply as if you are finding 16 × 3. 0.016 × 0.3 48 Count the number of digits to the 0.016right of the decimal points in both × 0.3numbers in the problem. 48 Count the same number of places in the answer starting on the right and movingleft. Insert zeros to hold the missing .0048 places. Put the decimal point where you stop. 0.3 × 0.016 = 0.0048

ExamplE 2

solution

0.40

0.40 + 0.40 + 0.40 + 0.24 = 1.44

3.6

Color decimal models vertically to match the first decimal.

Color the same decimal models horizontally with the

second decimal.

Where the two colors overlapis the answer.

ExamplE 3

solution

40 Lesson 2.2 ~ Multiplying Decimals

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.

From which store should Jay buy grapes?

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.

ExErcisEs

Find each product.

1. 4.1 × 3 2. 5 × 3.33 3. 7 × $2.17

4. 6.312 × 4 5. $4.89 × 5 6. 6 × 9.765

7. Celia’s cell phone company charges $0.39 per minute if she goes over her allotted minutes for the month. Last month she went over by 15 minutes. How much extra did she owe on her bill?

8. Kenyan bought three pairs of pants that were on sale for $12.99 per pair. a. How much did Kenyan pay altogether for the three pairs of pants? b. Kenyan estimated each pair of pants cost $13.00. If he used $13.00 to find the cost of the pants, how much did he overestimate the actual cost? Use mathematics to justify

your reasoning.

ExplorE! smarT shoppEr

ABC Grocery ZyX GroceryGrapes: $1.39 per pound Grapes: 3 pound container for $4.99Cherry tomatoes: $0.98 per pound Cherry tomatoes: 3.5 pound container for $3.96Fuji apples: $1.29 per pound Fuji apples: 3.25 pound bag for $4.25deli-sliced ham: $3.99 per pound deli-sliced ham: 1.75 pound package for $5.50Chicken breasts: $1.69 per pound Chicken breasts: 4 pound bag for $5.99whole chicken fryer: $0.69 per pound whole chicken fryer: $5.50 for 5 poundsBeef round roast: $1.98 per pound Beef round roast: 4.5 pound roast for $9.23Chocolate Blitz bars: $0.59 each Chocolate Blitz bars: $6.40 for bag of 12Fizzy Pop: $0.70 each Fizzy Pop: $9.99 for 15 pack

Lesson 2.2 ~ Multiplying Decimals 41

Find each product. 9. 3.2 × 7.4 10. 2.5 × 6.6 11. 12.3 × 2.8

12. 10.45 × 4.1 13. 5.72 × 3.4 14. 11.5 × 7.62

15. 0.5 × 0.9 16. 0.3 × 0.46 17. $0.35 × 0.8

18. Hakeem bought 4.2 pounds of almonds. They cost $2.45 per pound. How much did Hakeem pay for the almonds?

19. The price tag under the 11.5-ounce bag of chips at the grocery store says $0.24 per ounce. The price tag under the 8.5-ounce bag of chips says $0.30 per ounce. Which bag of chips costs less overall? Use mathematics to justify your reasoning.

20. Draw a model to show 2.4 × 0.3. What is the product?

rEviEw

list each set of numbers from least to greatest. 21. 0.1, 0.09, 0.05 22. 0.6, 0.62, 0.58 23. 1.31, 1.089, 1.4 estimate the value of each expression using rounding to the nearest whole number. 24. 4.3 + 9.9 25. 22.553 − 10.39 26. 3.6 × 6.54

27. 15.442 − 8.92 28. 7.2 × 2.14 29. 7.57 + 8.62

tic-tAc-toe ~ A pe n n y sAV e d Decide which choice for earning money is the best if you earn money for 20 days, 30 days or 40 days. Support your answer with words and/or symbols.

ChoiCe #1: You start with $0.01. You make double what you had on the previous day. Add that to the amount you had the previous day. example: Day 1 = $0.01

Day 2 = ($0.01 × 2 = $0.02) + Day 1 total ($0.01) = $0.03 Day 3 = ($0.03 × 2 = $0.06) + Day 2 total ($0.03) = $0.09 ChoiCe #2: You start with $0.01. On Day 10, you make 100 times that amount. Add this to the amount you had on Day 1. On Day 20, you make 100 times the amount you had on Day 10. Add this to the amount you had on Day 10. On Day 30, you make 100 times the amount you had on Day 20. Add this to the amount you had on Day 20. example: Day 1 = $0.01 Day 10 = ($0.01 × 100 = $1.00) + Day 1 amount ($0.01) = $1.01

42 Lesson 2.2 ~ Multiplying Decimals

tic-tAc-toe ~ multi ply i ng me thods Write 10 multi-digit multiplication problems. Use the Area Model for five of the problems. Use the Lattice Method for five of the problems. Check your work by using the standard algorithm (taught in lesson 2.1). Write a paragraph explaining the method you like the best and why it is your favorite. Write a paragraph to explain how this method works when multiplying decimals.

Area model: 45 × 13 step 1: Split each factor by place value. (45 = 40 + 5; 13 = 10 + 3) step 2: Write each part of the first factor across the top of the area model (40 and 5). Write each part of the second factor down the area model (10 and 3). step 3: Find the area of each section of the area model by multiplying its length times its width.

40 510 400 50

3 120 15

step 4: Add all of the partial products together (400 + 50 + 120 + 15 = 585). step 5: Check your work using the standard algorithm.

lattice method: 45 × 13 step 1: Create a grid for the numbers (2 boxes by 2 boxes because this problem has two 2-digit factors. step 2: Split each box in half with a diagonal line (see below). step 3: Multiply each number (4 × 1 = 4; 5 × 1 = 5, 4 × 3 = 12, 5 × 3 = 15). The tens of an answer go in the top portion of the box, the ones of an answer go in the bottom portion of a box.

4 5

4 51

1 2

1 5 3

step 4: Add answers in lattice diagonally starting from the right. Ones: 5 + 0 = 5 Tens: 5 + 1 + 2 = 8 Hundreds: 4 + 1 = 5

4 5

1 2

1 5

5 8 5

step 5: Check your work using the standard algorithm.