We included HMH Into Math Grade 5 Answer Key PDF Module 15 Lesson 2 Represent Multiplication with Decimals and Whole Numbers to make students experts in learning maths.
HMH Into Math Grade 5 Module 15 Lesson 2 Answer Key Represent Multiplication with Decimals and Whole Numbers
I Can represent the product of a decimal less than one and a whole number using a visual model.
Spark Your Learning
Mary is shopping at the grocery store. She finds the weight of one banana and buys two more bananas that weigh the same amount. What is the weight of the 3 bananas?
Justify your thinking.
Answer:
Weight of the 3 bananas = 0.84 pounds.
Explanation:
Weight of one banana = 0.28 pounds.
Number of bananas = 3.
Weight of the 3 bananas = Weight of one banana × Number of bananas
= 0.28 × 3
= 0.84 pounds.
Turn and Talk How can you model the situation with an equation? Compare your equation with a classmate.
Answer:
Weight of the 3 bananas = Weight of one banana × 3 = 0.84 pounds.
Explanation:
Weight of one banana = 0.28 pounds.
Number of bananas = 3.
Weight of 3 bananas = 0.28 + 0.28 + 0.28
= 0.84 pounds.
Build Understanding
Question 1.
A starfish moves slowly in the ocean. Its speed is about 0.2 mile each hour. How many miles can a starfish travel in 4 hours?
Use the decimal model to find the distance.
A. How did you use the decimal model to represent the distance traveled in one hour?
Answer:
We can use the decimal model to represent the distance traveled in one hour as 20 miles divided by number of sections given.
=> 2 ÷ 10 = 0.2 miles.
Explanation:
Distance travelled by starfish in an hour = 0.2 mile.
Number of miles can a starfish travel in 4 hours = Distance travelled by starfish in an hour × 4
= 0.2 × 4
= 0.8 miles.
B. How did you use the decimal model to represent the distance traveled in 4 hours?
Answer:
Number of miles can a starfish travel in 4 hours = 0.8 miles.
Explanation:
Distance travelled by starfish in an hour = 0.2 mile.
Number of miles can a starfish travel in 4 hours = Distance travelled by starfish in an hour × 4
= 0.2 × 4
= 0.8 miles.
C. How can you model the solution with an addition expression?
Answer:
Number of miles can a starfish travel in 4 hours = 0.8 miles.
Explanation:
Distance travelled by starfish in an hour = 0.2 mile.
Number of miles can a starfish travel in 4 hours = Distance travelled by starfish in an hour + Distance travelled by starfish in an hour + Distance travelled by starfish in an hour+ Distance travelled by starfish in an hour
= 0.2 + 0.2 + 0.2 + 0.2
= 0.4 + 0.2 + 0.2
= 0.6 + 0.2
= 0.8 miles.
D. How can you model the solution with a multiplication expression?
Answer:
Number of miles can a starfish travel in 4 hours = 0.8 miles.
Explanation:
Distance travelled by starfish in an hour = 0.2 mile.
Number of miles can a starfish travel in 4 hours = Distance travelled by starfish in an hour × 4
= 0.2 × 4
= 0.8 miles.
E. How many miles does a starfish travel in 4 hours?
Answer:
Number of miles can a starfish travel in 4 hours = 0.8 miles.
Explanation:
Distance travelled by starfish in an hour = 0.2 mile.
Number of miles can a starfish travel in 4 hours = Distance travelled by starfish in an hour × 4
= 0.2 × 4
= 0.8 miles.
Question 2.
Adam weighs 6 apples. If each apple weighs 0.34 pound, what is the weight of the 6 apples?
A. Write a multiplication expression to model the situation.
Answer:
Weight of the 6 apples = 2.04 pounds.
Explanation:
Number of apples Adam weighs = 6.
Weight of each apple = 0.34 pound.
Weight of the 6 apples = Number of apples Adam weighs × Weight of each apple
= 6 × 0.34
= 2.04 pounds.
B. Draw a quick picture to represent the problem.
Answer:
Explanation:
A quick picture to represent the problem:
C. How many hundredths are there? How do you regroup them?
Answer:
There are 204 hundredths in 2.04 pounds ÷ 100.
There are 34 hundredths in 34 pounds ÷ 100.
Explanation:
Number of apples Adam weighs = 6.
Weight of each apple = 0.34 pound.
There are 34 hundredths in 34 pounds ÷ 100.
Weight of the 6 apples = Number of apples Adam weighs × Weight of each apple
= 6 × 0.34
= 2.04 pounds.
There are 204 hundredths in 2.04 pounds ÷ 100.
Regrouping numbers = 2 ones + 0.0 tenths + 0.04 hundredths = 2.04 pounds.
0 ones + 0.3 tenths + 0.04 hundredths = 0.34 pounds.
D. How many tenths are there? How do you regroup them?
Answer:
Number of tenths in 2.04 pounds = 0 tenths.
Number of tenths in 0.34 pounds = 3 tenths.
Explanation:
Number of tenths in 2.04 pounds = 0 tenths.
Number of tenths in 0.34 pounds = 3 tenths.
Regrouping numbers = 2 ones + 0.0 tenths + 0.04 hundredths = 2.04 pounds.
0 ones + 0.3 tenths + 0.04 hundredths = 0.34 pounds.
E. What is the weight of the 6 apples?
Answer:
Weight of the 6 apples = 2.04 pounds.
Explanation:
Number of apples Adam weighs = 6.
Weight of each apple = 0.34 pound.
Weight of the 6 apples = Number of apples Adam weighs × Weight of each apple
= 6 × 0.34
= 2.04 pounds.
Turn and Talk How is regrouping decimals similar to and different from regrouping whole numbers?
Answer:
Regrouping in math is a term used to describe the process of changing groups of ones into tens to make adding and subtracting easier. In addition, you regroup when the numbers you are adding come out to two digit numbers if they are not in the furthermost left column.
Explanation:
In math, regrouping can be defined as the process of making groups of tens when carrying out operations like addition and subtraction with two-digit numbers or larger. To regroup means to rearrange groups in place value to carry out an operation.
Check Understanding
Question 1.
Kinshasa buys 2 peppers. Each pepper weighs 0.37 pound. What is the weight of the peppers?
Answer:
Total weight of peppers = 0.74 pounds.
Explanation:
Number of peppers Kinshasa buys = 2.
Weight of each pepper = 0.37 pounds.
Total weight of peppers = Number of peppers Kinshasa buys × Weight of each pepper
= 2 × 0.37
= 0.74 pounds.
Multiply. Use a visual model.
Question 2.
4 × 0.24 = _________
Answer:
4 × 0.24 = 0.96.
Explanation:
4 × 0.24 = 0.96.
Question 3.
3 × 0.4 = ___________
Answer:
3 × 0.4 = 1.2.
Explanation:
3 × 0.4 = 1.2.
On Your Own
Question 4.
Model with Mathematics A square photo has a side length of 0.17 foot. The photo is enlarged by doubling the dimensions. Then it is enlarged again by tripling the new dimensions. Write equations to model each enlargement. What are the side lengths of the enlarged photo?
Answer:
Length of side of square photo = 0.17 foot.
Length of the double enlarged photo = 0.34 foot.
Length of the tripled enlarged photo = 0.51 foot.
Explanation:
Length of side of square photo = 0.17 foot.
The photo is enlarged by doubling the dimensions.
=> Length of the double enlarged photo = 2 × Length of side of square photo
= 2 × 0.17
= 0.34 foot.
Then it is enlarged again by tripling the new dimensions.
=> Length of the tripled enlarged photo = 3 × Length of side of square photo
= 3 × 0.17
= 0.51 foot.
Question 5.
Baby opossums are so tiny that a teaspoon can hold an entire litter. The mass of one baby opossum is 0.13 gram. What is the mass of a litter of 9 baby opossums?
Answer:
Total mass of a litter of 9 baby opossums = 1.17 gram.
Explanation:
Mass of one baby opossum = 0.13 gram.
Mass of a litter of baby opossums = 9.
Total mass of a litter of 9 baby opossums = Mass of one baby opossum × Mass of a litter of baby opossums
= 0.13 × 9
= 1.17 gram.
Multiply. Use a decimal model.
Question 6.
2 × 0.47 = __________
Answer:
2 × 0.47 = 0.94.
Explanation:
2 × 0.47 = 0.94.
Question 7.
__________ = 3 × 0.6
Answer:
1.8 = 3 × 0.6
Explanation:
1.8 = 3 × 0.6.
Question 8.
Use a visual model to find 7 × 0.43.
7 × 0.43 = __________
Answer:
7 × 0.43 = 3.01.
Explanation:
7 × 0.43 = 3.01.
I’m in a Learning Mindset!
Was using a visual mode! effective in helping me understand multiplication with decimals? Explain why or why not.
Answer:
Yes, using a visual model was effective in helping me understand multiplication with decimals because it is easy to understand in images than numeral multiplication process.
Explanation:
Using a visual model was effective in helping me understand multiplication with decimals because it is easy to understand in images than numeral multiplication process.