We included HMH Into Math Grade 6 Answer Key PDF Module 4 Lesson 2 Multiply Multi-Digit Decimals to make students experts in learning maths.
HMH Into Math Grade 6 Module 4 Lesson 2 Answer Key Multiply Multi-Digit Decimals
I Can multiply multi-digit decimals, up to thousandths.
Step It Out
One way to multiply decimals is by using a decimal grid. The grid represents 1 whole, where each square unit is 0.01.
1. Find the product of 0.5 × 0.4.
A. To represent 0.5, I can shade 
columns, which is squares.
Answer:
To represent 0.5, I can shade 5 columns, which is 0.5 squares.
B. To represent 0.4, I can shade rows, which is squares.
Answer:
To represent 0.4, I can shade 4 rows, which is 0.4 squares
C. Shade the grid to represent 0.5 and 0.4. How many squares have been shaded twice?
Answer:
Each square represents one decimal number.
1 square = 0.1 units
0.5 = 5 squares
0.4 = 4 squares
5 × 4 = 20 squares
D. The double-shaded squares represent the decimal .
So, 0.5 × 0.4 = .
0.5 × 0.4 = 0.20
Another way to multiply decimals is to use an area model.
2. Cara buys 11.2 pounds of pork chops for $3.50 per pound.
A. How can you find the total cost of the pork chops?
________________
Answer:
You can find the total cost of the pork chops by multiplying the total pounds with the cost of the pork per pound.
B. An area model shows partial products using place values. Complete the area model by multiplying to find the partial products. List the partial products.
Answer:
1 pound = $3.50
11.2 pounds = x
x = 11.2 × 3.50
x = 39.2
Thus the cost of 11..2 pounds of pork chops is $39.2
C. What is the sum of the partial products?
________________
________________
Answer:
D. How much does Cara pay for the pork chops?
Answer:
x = 11.2 × 3.50
x = 39.2
Thus the cost of 11..2 pounds of pork chops is $39.2
Turn and Talk What do the labels given on the area model represent?
3. Jared mows the grass every weekend in the summer. The amount of gas he uses per hour is shown. How much gas does he use in 5.8 hours?
A. Write an expression to represent this situation.
Answer:
The expression to represent this situation is 5.8 × 1.2
B. Find an estimate of this product by rounding each factor to the nearest whole number and then
multiplying. ________
Answer:
5.8 to the nearest whole number is 6.
1.2 to the nearest whole number is 1.
6 × 1 = 6
C. Another way to multiply decimals is to multiply as you would with whole numbers. Then count the number of decimal places after the decimal point in the factors. What is the product 58 × 12? How many decimal places are in the factors 5.8 and 1.2?
__________________
__________________
Answer:
Ignore the decimal points and perform the multiplication for 58 and 12.
5.8 × 1.2 = 6.96
D. The product must have the same number of decimal places as the total number of decimal places in the factors. How many decimals places should there be in the product 5.8 × 1.2? _______
Answer:
Rewrite the product with 2 total decimal places.
5.8 × 1.2 = 6.96
E. What is the product of 5.8 × 1.2? Explain how you knew where to place the decimal point.
_______________________
_______________________
Answer:
There are 2 decimal points.
Count the decimal points from the right.
5.8 × 1.2 = 6.96
F. Check your answer for reasonableness.
My estimate of ____ is close to the product ____, so my answer is reasonable.
Answer:
My estimate of 6 is close to the product of 6.96, so my answer is reasonable.
Turn and Talk How close should an estimate be to the product of two decimals for the answer to be reasonable? Explain your reasoning.
Check Understanding
Question 1.
Last summer Rachel worked 38.5 hours per week at a grocery store. She earned $9.70 per hour. How much did she earn in a week? Complete the area model to help find the answer.
Answer:
Given,
Last summer Rachel worked 38.5 hours per week at a grocery store.
She earned $9.70 per hour.
38.5 × 9.70 = $373.45
Thus she earned $373.45 in a week.
Question 2.
Find the product of 2.3 × 0.6.
______________
Answer: 1.38
The product of two decimal numbers 2.3 and 0.6 is 1.3
Explanation:
There are 2 total decimal places in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers.
Rewrite the product with 2 total decimal places.
2.3 × 0.6 = 1.38
On Your Own
Question 3.
Denise runs a 10-kilometer race (6.2 miles). Her time per mile is shown. What is her total time for the race? Explain.
Answer:
Given,
Denise runs a 10-kilometer race (6.2 miles)
1 mile = 8.5 minutes
6.2 miles = x
x = 8.5 × 6.2
x = 52.7 minutes
The total time for the race is 52.7 minutes.
Question 4.
Critique Reasoning Antwon says that he can multiply 14 and 12 to find the product of 0.14 × 0.12. Is Antwon correct? Explain your reasoning.
Answer:
14 × 12 = 168
There are 4 total decimal places in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers.
Rewrite the product with 4 total decimal places
0.14 × 0.12 = 0.0168
Question 5.
Attend to Precision A city park is 0.85 mile long and 0.7 mile wide. The city wants to put in new plants and grass that need less watering.
A. Write an expression that can be used to find the area of the park. Then find the area of the park in square miles.
__________________
B. The city calculates that only \(\frac{6}{10}\) of the park will need plants and grass. What decimal can be used to calculate the area of the park that will have plants and grass?
_________________________
C. What is the total area of the park in square miles that will have plants and grass? Explain how you found your answer.
Answer:
Given,
A city park is 0.85 mile long and 0.7 mile wide
The Area of the city park is in the shape of a rectangle.
Area of the rectangle = length × width
A = 0.85 × 0.7
A = 0.595 square mile
For Problems 6—7, use the grid to find the product.
Question 6.
0.2 × 0.7 = ____
Answer:
0.2 × 0.7 = 0.14
To represent 0.2, I can shade 2 columns, which is 0.2 squares.
To represent 0.7, I can shade 7 rows, which is 0.7 squares.
Question 7.
0.4 × 0.8 = ____
Answer:
0.4 × 0.8 = 0.32
To represent 0.4, I can shade 4 columns, which is 0.4 squares.
To represent 0.8, I can shade 8 rows, which is 0.7 squares.
For Problems 8-9, find the product.
Question 8.
10.05 × 5.6 = ____
Answer: 56.28
The product of two decimal numbers 10.5 and 5.6 is 56.28
Question 9.
7.9 × 5.1 = ____
Answer: 40.29
The product of two decimal numbers 7.9 and 5.1 is 40.29
Question 10.
Nita will bake 3.2 batches of muffins for the school bake sale. Each batch uses 1.75 cups of whole-wheat flour. How much whole-wheat flour does Nita need to make the muffins?
A. Estimate the product by rounding each factor to the nearest whole number and multiplying.
____________________
Answer:
Given,
Nita will bake 3.2 batches of muffins for the school bake sale.
Each batch uses 1.75 cups of whole-wheat flour.
3.2 to the nearest whole number is 3.
1.75 to the nearest whole number is 2.
3 × 2 = 6
B. What is the actual product of 3.2 × 1.75?
____________________
Answer:
3.2 × 1.75 = 5.6
C. Using your estimate, is your answer reasonable? Explain.
____________________
Answer:
5.6 to the nearest whole number is 6.
So, the estimation is close to the product 5.6. My answer is reasonable.
Question 11.
Reason How does estimating help you know whether you have placed the decimal point correctly in a product?
Answer:
Estimating the product of the decimal point helps you to calculate easily.
First, we have to round the decimal number to the whole number and then find the product of the numbers.
And then check the estimated product with the actual product of the decimal point.
Question 12.
Colin needs 14.5 yards of fabric to cover a sofa. The fabric he likes costs $7.95 per yard. Write an expression that represents the cost of the fabric. Then simplify the expression to find the cost. Round to the nearest hundredth.
Answer:
Given,
Colin needs 14.5 yards of fabric to cover a sofa.
The fabric he likes costs $7.95 per yard.
Fabric cost = 14.5 × 7.95 = 115.275 ≈ 115.28 sq. yards
115.275 to the nearest hundredth is 115.28
Question 13.
Open Ended Describe a general method to multiply two numbers written in tenths. Show an example.
Answer:
The general method to multiply two numbers written in tenths is to calculate the numbers by ignoring the decimal points and adding the points at the end.
Example:
There are 2 total decimal places in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers.
Rewrite the product with 2 total decimal places.
2.3 × 0.6 = 1.38
Question 14.
Use the area model to find the product 7.34 × 2.6.
The product is _____.
Answer:
The product of 7.34 and 2.6 is 19.084
For problems 15-17, find the product.
Question 15.
23.2 × 4.1 = ___
Answer: 95.12
The product of two decimal numbers 23.2 and 4.1 is 95.12
Question 16.
0.05 × 0.07 = _____
Answer: 0.0035
The product of two decimal numbers 0.05 and 0.07 is 0.0035.
Question 17.
7.89 × 8.7 = ____
Answer: 68.643
The product of two decimal numbers 7.89 and 8.7 is 68.643
Lesson 4.2 More Practice/Homework practice
Multiply Multi-Digit Decimals
Question 1.
At 3 years old, Javier was 36.5 inches tall. By age 13, he was 1.8 times as tall as he was at age 3. How tall was Javier at age 13?
Answer:
Given,
At 3 years old, Javier was 36.5 inches tall.
36.5 × 1.8 = 65.7 inches
Therefore, Javier’s height is 65.7 inches at the age of 13.
Question 2.
STEM The mass of an atom of helium is about 4.002 atomic units. The mass of an atom of beryllium is about 2.25 times the mass of an atom of helium. What is the approximate mass of a beryllium atom?
Answer:
Given that,
The mass of an atom of helium is about 4.002 atomic units.
The mass of an atom of beryllium is about 2.25 times the mass of an atom of helium.
we will multiply the mass of helium by 2.25 times,
4.002 u × 2.25 = 9.0045 u
so the mass of the beryllium atom would be 9.0045 u.
Question 3.
Reason A bedroom is 11.4 feet long and 12.5 feet wide. Shui wants to paint the floor. A gallon of paint will cover approximately 150 square feet. Will one gallon of paint be enough to paint the bedroom floor with 2 coats of paint? Explain your reasoning.
Answer:
Given,
A bedroom is 11.4 feet long and 12.5 feet wide.
The dimensions are in the shape of a rectangle.
Area of the rectangle = l × w
A = 11.4 × 12.5 = 142.5 sq. ft
Shui wants to paint the floor. A gallon of paint will cover approximately 150 square feet.
Multiply the obtained area with 2.
A = 2 × 142.5 = 285 sq. ft
285 sq.ft > 150 sq. ft
Therefore one gallon of paint is not enough to paint the bedroom floor.
Test Prep
Question 4.
The distance from Jupiter to the sun is 5.203 astronomical units. If the distance from Neptune to the sun is about 5.77 times Jupiter’s distance from the sun, how far is Neptune from the sun in astronomical units? Round your answer to the nearest thousandth.
Answer:
Given,
Distance from Jupiter to the sun = 5.203 astronomical units
If the distance from Neptune to the sun is about 5.77 times Jupiter’s distance from the sun.
Therefore, the distance from Neptune from the sun will be 5.203 multiplied by 5.77. This will be:
= 5.203 × 5.77
= 30.02 astronomical units
Question 5.
Math on the Spot Reed bought 1.8 pounds of green beans. The green beans cost $1.27 per pound. What was the total cost of Reed’s green beans? Round your answer to the nearest hundredth.
Answer:
Given,
Reed bought 1.8 pounds of green beans.
The green beans cost $1.27 per pound.
1.8 × 1.27 = 2.286
2.286 to the nearest hundredth is 2.30
For Problems 6-11, find the product.
Question 6.
0.65 × 0.11
________
Answer: 0.0715
The product of two decimal numbers 0.65 and 0.11 is 0.0715.
Question 7.
0.281 × 0.6
________
Answer: 0.1686
The product of two decimal numbers 0.281 and 0.6 is 0.1686.
Question 8.
1.3 × 0.8
________
Answer: 1.04
The product of two decimal numbers 1.3 and 0.8 is 1.04
Question 9.
2.54 × 3.7
________
Answer: 9.398
The product of two decimal numbers 2.54 and 3.7 is 9.398
Question 10.
10.01 × 5.15
________
Answer: 51.55
The product of two decimal numbers 10.1 and 5.15 is 51.55
Question 11.
13.49 × 0.806
________
Answer: 10.87
The product of two decimal numbers 13.49 and 0.806 is 10.87
Test Prep
Question 12.
A quart of water weighs about 2.09 pounds. Approximately what would 15.5 quarts of water weigh?
Answer:
Given,
A quart of water weighs about 2.09 pounds.
2.09 × 15.5 = 32.395 pounds.
The approximate weight of 15.5 quarts of water is 32.395 pounds.
Question 13.
A #15 drill bit measures 0.18 inch in diameter. The diameter of a large construction drill bit is about 2.3 times the diameter of a #15 bit. Approximately how large is the construction drill bit in diameter?
Answer:
The diameter of a construction drill bit is said to be 2.3 times larger than that of a normal #15 drill bit.
If the diameter of a #15 drill bit is 0.18 inches, the diameter of a construction drill bit would be:
Diameter of drill bit x Conversion factor to the construction drill bit
= 0.18 x 2.3
= 0.414 inches
Question 14.
Match the products to the expressions.
Answer:
The product of two decimal numbers 2.53 and 0.83 is 2.0999
2.53 × 0.83 = 2.0999
The product of two decimal numbers 0.7 and 0.02 is 0.014
0.70 × 0.02 = 0.014
The product of two decimal numbers 3.57 and 0.26 is 0.9282
3.57 × 0.26 = 0.9282
The product of two decimal numbers 1.3 and 0.26 is 1.157
1.30 × 0.89 = 1.157
Question 15.
In 1930, the average movie length was 1.5 hours. Hamlet, one of the longest movies in America, was released in 1996. Hamlet is about 2.69 times as long as the average movie in the 1930s. Approximately how long is Hamlet’?
A. 1.19 hours
B. 1.793 hours
C. 4.035 hours
D. 4.19 hours
Answer:
Given,
In 1930, the average movie length was 1.5 hours.
Hamlet, one of the longest movies in America, was released in 1996.
Hamlet is about 2.69 times as long as the average movie in the 1930s.
1.5 × 2.69 = 4.035 hours
Option C is the correct answer.
Spiral Review
Question 16.
A Dutch door is a door that is split in half to allow the top and bottom to open separately. The top section of a Dutch door is 3.25 feet tall and the bottom section is 3\(\frac{3}{4}\) feet tall. Write an inequality that compares the heights of the top and bottom sections of the door.
Answer:
Given,
A Dutch door is a door that is split in half to allow the top and bottom to open separately. The top section of a Dutch door is 3.25 feet tall and the bottom section is 3\(\frac{3}{4}\) feet tall.
3\(\frac{3}{4}\) in the decimal form can be written as 3.75
3.75 > 3.25
Question 17.
Drew’s gas tank is \(\frac{3}{4}\)-full. He uses \(\frac{1}{6}\) of a full tank’s gas per day driving to and from work. How many days can Drew drive to and from work with the gas he has in the tank? Explain.
Answer:
Drew’s gas tank is \(\frac{3}{4}\)-full. He uses \(\frac{1}{6}\) of a full tank’s gas per day driving to and from work.
\(\frac{3}{4}\)/\(\frac{1}{6}\)
\(\frac{3}{4}\) . 6
= \(\frac{9}{2}\)
= 4 \(\frac{1}{2}\) days
Thus it takes 4 \(\frac{1}{2}\) days to Drew drive to and from work with the gas he has in the tank.
Question 18.
Write the list of rational numbers in order from least to greatest. -2.15, \(\frac{3}{10}\), -1.6, -1\(\frac{4}{5}\), 0.8
__________________
Answer:
The list of rational numbers in order from least to greatest are -2.15, -1\(\frac{4}{5}\), -1.6, 0.6 and 0.8