# Texas Go Math Grade 5 Lesson 3.3 Answer Key Multiplication with Decimals and Whole Numbers

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## Texas Go Math Grade 5 Lesson 3.3 Answer Key Multiplication with Decimals and Whole Numbers

Essential Question
How can you use properties and place value to multiply a decimal and a whole number?

Unlock the problem

In 2010, the United States Mint released a newly designed Lincoln penny.
A Lincoln penny has a mass of 2.5 grams. If there are 5 Lincoln pennies on a tray,
what is the total mass of the pennies?

• How much mass does one penny have?
2.5 grams,

Explanation:
Given a Lincoln penny has a mass of 2.5 grams.

• Use grouping language to describe what you are asked to find.
Total mass of the pennies,

Explanation:
Given In 2010, the United States Mint released a newly designed Lincoln penny.
A Lincoln penny has a mass of 2.5 grams. If there are 5 Lincoln pennies on a tray,
what is the total mass of the pennies?

Multiply. 5 × 2.5
Estimate the product. Round to the nearest whole number.
5 × _25__ = _12.5__

One Way
Use the Distributive Property.

Another Way

Show partial products.

Step 1
Multiply the tenths by 5.

Step 2
Multiply the ones by 5.

Step 3

12.5

Example
Use place value patterns.
Having a thickness of 1.35 millimeters, the dime is the thinnest coin produced by
the United States Mint. If you stacked 8 dimes,
what would be the total thickness of the stack?
Multiply. 8 × 1.35
Step 1
Write the decimal factor as a whole number.
Think: 1.35 × 100 = 135

Step 2
Multiply as with whole numbers.

Step 3
Place the decimal point.
Think: 0.01 of 135 is 1.35. Find 0.01 of 1,080 and record the product.

A stack of 15 dimes would have a thickness of _10.80_ millimeters.
8 X 1.35 = 10.80,
A stack of 15 dimes would have a thickness of 10.80 millimeters,

Explanation:
Given having a thickness of 1.35 millimeters, the dime is the thinnest coin produced by
the United States Mint. If you stacked 8 dimes,
The total thickness of the stack,
Step 1:
Writing the decimal factor as a whole number.
Think: 1.35 × 100 = 135

Step 2:
Multiply as with whole numbers.

Step 3:
Placing the decimal point.
Think: 0.01 of 135 is 1.35. Finding 0.01 of 1,080 and record the product.

Therefore a stack of 15 dimes would have a thickness of 10.80 millimeters.

Share and Show

Place the decimal point in the product.

Question 1.

6.81 X 7 = 47.67,

Explanation:

Question 2.

3.7 X 2 =

Explanation:

Question 3.

19.34 X 5 = 96.70,

Explanation:

Find the product.

Question 4.

6.32 X 3 =18.96,

Explanation:

Question 5.

4.5 X 8 = 36.0,

Explanation:

Question 6.

40.7 X 5 = 203.5

Explanation:

Math Talk
Mathematical Processes

Explain how you can determine if your answer to Exercise 6 is reasonable.
40.7 X 5 = 203.5,

203.5

Explanation:
Step 1
Multiply the tenths by 5.
407
X 5
5—->5 X 7 =35,

Step 2
Multiply the zero by 5.
407
X 5
3  —->5 X 0 = 0 + 3,

Step 3
Multiply the ten by 5
407
X 5
200 —->5 X 40 =200 ,

Step 4
407
X 5
000.50
003.00
200.00
203.50

Problem Solving

Practices Copy arid Solve Find the product.

Question 7.
8 × 7.2
8 X 7.2 = 57.6,

Explanation:
7.2
X 8
57.6
Step 1
Multiply the tenths by 8.
72
X 8
6   —-> 8 X 2 = 16,

Step 2
Multiply the one by 8.
72
X 8
57 —->8 X 7 = 56 + 1,

Step 3
72
X 8
.60
57.00
57.60

Question 8.
3 × 1.45
3 X 1.45 = 4.35,

Explanation:
1.45
X  3
4.35
Step 1
Multiply the hundredths by 3.
145
X 3
15  —-> 3 X 5 = 15,

Step 2
Multiply the tenths by 3.
145
X 3
13—->3 X 4 = 12 + 1,

Step 3
Multiply the one by 3,
145
X 3
3 —->3 X 1 = 3,
145
X 3
0.05
1.30
3.00
4.35

Question 9.
9 × 8.6
9 x 8.6 = 77.4,

Explanation:
8.6
X 9
77.4

Step 1
Multiply the tenths by 9.
86
X 9
54  —-> 9 X 6 = 5.4,

Step 2
Multiply the one by 9.
86
X 9
72—->9 X 8 = 72,

Step 3:
86
X 9
05.4
72.0
77.4

Question 10.
6 × 0.79
6 X 0.79 = 4.74,

Explanation:
0.79
X  6
4.74
Step 1
Multiply the hundredths by 6.
0.79
X  6
54  —-> 6 X 9 = 54,

Step 2
Multiply the tenths by 6.
0.79
X   6
42—-> 6 X 7 = 42,

Step 3
Multiply the one by 6,
0.79
X 6
0 —-> 6 X 0 = 0,
0.79
X  6
0.54
4.20
0.00
4.74

Question 11.
4 × 9.3
4 X 9.3 = 37.2,

Explanation:
9.3
X  4
37.2
Step 1
Multiply the tenths by 4.
9.3
X 4
1.2—->4 X 3 = 1.2,

Step 2
Multiply the one by 4,
9.3
X 4
36 —->4 X 9 = 36,
145
X
01.20
36.00
37.20

Question 15.
H.O.T. Write Math Julie multiplies 6.27 by 7 and claims the product is 438.9.
Explain without multiplying how you know Julie’s answer is not correct.
Decimal point place value is incorrect,

Explanation:
Given Julie multiplies 6.27 by 7 and claims the product is 438.9,
without multiplying Julie’s answer is not correct because in 6.27
we have decimal point before hundredths,
So in 438.9 we have decimal point before tenths,
therefore Julie is incorrect.

Problem Solving

Use the table for 16-18.

Question 16.
Sari has a bag containing 6 half dollars. What is the mass of the half dollars in Sari’s bag?

Question 17.
Felicia is running a game booth at a carnival. One of the games requires
participants to guess the mass, in grams, of a bag of 9 dimes.
What Is the actual mass of the dimes in the bag?
20.43 is the actual mass of the dimes in the bag,

Explanation:
Stated Felicia is running a game booth at a carnival. One of the games requires
participants to guess the mass, in grams, of a bag of 9 dimes.
So the actual mass of the dimes in the bag is 9 X 2.27 =
2 6
2.27
X   9
20.43

Question 18.
Multi-Step Chance has $2 in quarters. Blake has$5 in dollar coins.
Whose coins have the greatest mass? Explain.

Blake coins have the greatest mass,

Explanation:
Given Chance has $2 in quarters mass , Chance coins mass is$2 X 5.67 grams = 11.34 grams,
Blake has $5 in dollar mass, So Blake have coins mass is$5 X  8.1 grams= 40.5 grams, on comparing between Chance and Blake,
Blake coins have the greatest mass.

Question 19.
Apply A hummingbird weighs 5.8 grams. If the hummingbird eats
8 times its body weight each day, how much does the bird eat in four days?
(A) 23.2 grams
(B) 46.4 grams
(C) 185 .6 grams
(D) 464 grams
(C) 185 .6 grams,

Explanation:
Applying a hummingbird weighs 5.8 grams,
If the hummingbird eats 8 times its body weight each day,
the bird eat in each day is  5.8 grams X 8 = 46.4 grams,
In four days the bird will eat 4 X 46.4 grams = 185.6 grams,
which matches with (C).

Question 20.
Use Symbols Which expression shows how to use the
Distributive Property to find 5.17 X 9?
(A) 5.17 + 9
(B) 9 × (5.1) + 7
(C) 9 × (5.1 + 7)
(D) 9 × (5 + 0.17)
(D) 9 × (5 + 0.17),

Explanation:
Using Symbols the expression that shows how to use the
Distributive Property to find 5.17 X 9 is first we write 5.17 as
(5 + 0.17) and applying distributive law we get 9  X (5 + 0.17)
matches with (D).

Question 21.
Multi-Step The cost to park a car in a parking lot is $1.10 per hour. Maleek parked his car for 4 hours on Monday 4 hours on Tuesday and 4 hours on Wednesday. How much did he spend on parking in all? (A)$4.10
(B) $4.40 (C)$13.10
(D) $13.20 Answer: (D)$13.20,

Explanation:
The cost to park a car in a parking lot is $1.10 per hour. Maleek parked his car for 4 hours on Monday, 4 hours on Tuesday and 4 hours on Wednesday, Number of hours from Monday, Tuesday and Wednesday = 4 + 4 + 4 = 12 hours, Maleek spends on parking in all is$1.10 X 12 = $13.20 matches with (D). Texas Test Prep Question 22. Every day on his way to and from school, Milo walks a total of 3.65 miles. If he walks to school 5 days, how many miles will Milo have walked? (A) 1,825 miles (B) 18.25 miles (C) 182.5 miles (D) 1.825 miles Answer: (B) 18.25 miles, Explanation: Given Every day on his way to and from school, Milo walks a total of 3.65 miles. If he walks to school 5 days number of miles Milo will have to walk is 5 X 3.65 miles = 3.65 X 5 0.025 03.00 15.00 18.25 (B) 18.25 miles. ### Texas Go Math Grade 5 Lesson 3.3 Homework and Practice Answer Key Find the product. Question 1. 4 × 7.12 Answer: 4 X 7.12 = 28.48, Explanation: Given to find 4 X 7.12 7.12 X 4 00.08 00.40 28.00 28.48 Question 2. 3 × 0.29 Answer: 3 x 0.29 = 0.87, Explanation: 0.29 X 3 0.27 0.60 0.87 Question 3. 8 × 2.9 Answer: 8 X 2.9 = 23.20, Explanation: 2.9 X 8 07.20 16.00 23.20 Question 4. 7 × 18.3 Answer: 7 X 18.3 = 128.1, Explanation: 18.3 X 7 02.10 56.00 70.00 128.10 Question 5. 5 × 9.26 Answer: 5 X 9.26 = 46.30, Explanation: 9.26 X 5 00.30 01.00 45.00 46.30 Question 6. 2 × 42.1 Answer: 2 X 42.1 = 84.2, Explanation: 42.1 X 2 00.20 04.00 80.00 84.20 Question 7. 7 × 0.34 Answer: 7 X 0.34 = 2.38, Explanation: 0.34 X 7 0.28 2.10 0.00 2.38 Question 8. 9 × 7.21 Answer: 9 X 7.21 = 64.89, Explanation: 7.21 X 9 00.09 01.80 63.00 64.89 Question 9. 4 × 5.2 Answer: 4 X 5.2 = 20.8, Explanation: 5.2 X 4 00.8 20.0 20.8 Question 10. 7 × 17.2 Answer: 7 X 17.2 = 120.40, Explanation: 17.2 X 7 01.40 49.00 70.00 120.40 Question 11. 4 × 3.92 Answer: 4 X 3.92 = 15.68, Explanation: 3.92 X 4 00.08 03.60 12.00 15.68 Question 12. 8 × 0.21 Answer: 8 X 0.21 = 1.68, Explanation: 0.21 X 8 0.08 1.60 0.00 1.68 Question 13. Logan multiplies 5.31 by 3 and says the product is 159.3. Explain why Logan’s answer is not correct. Answer: After decimal point value we have hundredths but product is tenth’s , Logan is incorrect, Explanation: As per Logan multiplies 5.31 by 3, we should get hundredths but the product says it is tenths, therefore Logan is incorrect. Problem Solving Question 14. Minnie rides her bike 2.76 miles each day. How many miles will she bike in 7 days? Answer: 19.32 rides her bike in 7 days, Explanation: Given Minnie rides her bike 2.76 miles each day, Number of miles she biked in 7 days is 2.76 X 7 00.42 04.90 14.00 19.32 Question 15. Dominick buys a package of soup mix that is 1.38 ounces. How many ounces are 6 packages of soup mix? Answer: Ounces in 6 packages of soup mix are 8.28 ounces, Explanation: We have Dominick buys a package of soup mix that is 1.38 ounces. Number of ounces are 6 packages of soup mix is 1.38 X 6 0.48 1.80 6.00 8.28 Texas Test Prep Lesson Check Fill in the bubble completely to show your answer. Question 16. Sandra uses 6.39 ounces of beans in a recipe. If she triples the recipe, how many ounces of beans will Sandra need? (A) 17.29 ounces (B) 18.83 ounces (C) 19.17 ounces (D) 20.19 ounces Answer: (C) 19.17 ounces, Explanation: Given Sandra uses 6.39 ounces of beans in a recipe. If she triples the recipe the number of beans will Sandra need is 6.39 X 3 00.27 00.90 18.00 19.17 matches with (C). Question 17. Kip uses the Distributive Property to rewrite an expression. (4 × 3) + (4 × 0.7) What is the value of the expression? (A) 3.07 (B) 11.7 (C) 14.8 (D) 29.6 Answer: (C) 14.8, Explanation: Given Kip uses the Distributive Property to rewrite an expression (4 X 3) + (4 X 0.7) so the value of the expression is (12) + (2.8) = 14.8 matches with (C). Question 18. Manny charges$1.25 for a cup of lemonade at the lemonade stand.
He sells 9 cups. How much money does Manny collect?
(A) $10.75 (B)$11.00
(C) $11.25 (D)$11.75
(C) $11.25, Explanation: Given Manny charges$1.25 for a cup of lemonade at the lemonade stand,
He sells 9 cups. Manny collected
$1.25 X 9 0.45 1.80 9.00 11.25 which matches with (C). Question 19. Fabric costs$11.99 a yard. Leo buys 4 yards of red fabric and 3 yards of blue fabric.
How much does Leo spend on fabric?
(A) $47.96 (B)$35.97
(C) $77.33 (D)$83.93
(D) $83.93, Explanation: Given Fabric costs$11.99 a yard,
Leo buys 4 yards of red fabric and 3 yards of blue fabric.
Leo spent on fabric costs
$11.99 X 7 000.63 006.30 007.00 070.00$83.93,
matches with (D).

Question 20.
Multi-Step On the first day of summer, a rainstorm brought 2.29 Inches of rain to the area.
During the rest of the summer, there was 3 times as much rain as on the first day.
What was the total number of Inches of rainfall for the summer?
(A) 6.29 inches
(B) 5.67 inches
(C) 6.87 Inches
(D) 9.16 inches
(C) 6.87 Inches,

Explanation:
Given on the first day of summer a rainstorm brought 2.29 Inches of rain to the area.
During the rest of the summer there was 3 times as much rain as on the first day.
The total number of Inches of rainfall for the summer is
2.29
X  3
0.27
0.60
6.00
6.87 inches matches with (C).

Question 21.
Multi-Step Nicky bought 14.2 pounds of coffee for the coffee shop.
The shop usually uses 5 times that amount of coffee during one week.
How much more coffee will Nicky need to purchase to get the
right amount of coffee for the week?
(A) 71 pounds
(B) 56.8 pounds
(C) 85.2 pounds
(D) 50 pounds
(A) 71 pounds,

Explanation:
Nicky bought 14.2 pounds of coffee for the coffee shop.
The shop usually uses 5 times that amount of coffee during one week.
More coffee will Nicky need to purchase to get the right amount of coffee for the week
is 14.2
X     5
01.0
20.0
50.0
71.0 pounds matches with (A).

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