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Texas Go Math Grade 5 Lesson 4.3 Answer Key Estimate Quotients
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Carmen likes to ski. The ski resort where she goes to the sky got 3.2 feet of snow during a 5-day period. The average daily snowfall for a given number of days is the quotient of the total amount of snow and the number of days. Estimate the average daily snowfall.
You can estimate decimal quotients by using compatible numbers. When choosing compatible numbers, you can look at the whole-number part of a decimal dividend or rename the decimal dividend as tenths or hundredths.
Estimate. 3.2 ÷ 5
Carly and her friend Marco each find an estimate. Since the divisor is greater than the dividend, they both first rename 3.2 as tenths.
3.2 is _________ tenths.
CARLY’S ESTIMATE
30 tenths is close to 32 tenths and divides easily by 5. Use a basic fact to find 30 tenths ÷ 5.
30 tenths ÷ 5 is ______ tenths or _________.
So, the average daily snowfall is about ________ foot.
MARCO’S ESTIMATE
35 tenths is close to 32 tenths and divides easily by 5. Use a basic fact to find 35 tenths ÷ 5.
35 tenths ÷ 5 is ______ tenths or _________.
So, the average daily snowfall is about ________ foot.
Answer:
Carly and her friend Marco each find an estimate. Since the divisor is greater than the dividend, they both first rename 3.2 as tenths.
3.2 is 32 tenths.
CARLY’S ESTIMATE
30 tenths is close to 32 tenths and divides easily by 5. Use a basic fact to find 30 tenths ÷ 5.
30 tenths ÷ 5 is 6 tenths or 0.6 tenths
So, the average daily snowfall is about 6 foot.
MARCO’S ESTIMATE
35 tenths is close to 32 tenths and divides easily by 5. Use a basic fact to find 35 tenths ÷ 5.
35 tenths ÷ 5 is 7 tenths or 0.7.
So, the average daily snowfall is about 0.7 foot.
Question 1.
Whose estimate do you think is closer to the exact quotient? Explain your reasoning.
Answer: Exact quotient is0.64
Explanation:
CARLY’S ESTIMATE
30 tenths is close to 32 tenths and divides easily by 5. Use a basic fact to find 30 tenths ÷ 5.
30 tenths ÷ 5 is 6 tenths or 0.6 tenths
So, the average daily snowfall is about 6 foot.
MARCO’S ESTIMATE
35 tenths is close to 32 tenths and divides easily by 5. Use a basic fact to find 35 tenths ÷ 5.
35 tenths ÷ 5 is 7 tenths or 0.7.
So, the average daily snowfall is about 0.7 foot.
By seeing this Carly’s estimation is nearest.
0.6is near to the 0.64
Question 2.
Explain how you would rename the dividend in 29.7 ÷ 40 to choose compatible numbers and estimate the quotient.
Answer: 0.7 or 7
Explanation:
280 tenths is close to 297 tenths and divides easily by 40. Use a basic fact to find 297 tenths ÷ 40.
280 tenths ÷ 40 is 7 tenths or 0.7.
So,
You can estimate decimal quotients by using compatible numbers. When choosing compatible numbers, you can look at the whole-number part of a decimal dividend or rename the decimal dividend as tenths or hundredths.
Example
A group of 31 students is going to visit the museum. The total cost for the tickets is $76.15. About how much money will each student need to pay for a ticket?
Estimate. $76.15 ÷ 31
A. Use a whole number greater than the dividend.
Use 30 for the divisor. Then find a number close to and greater than $76.15 that divides easily by 30.
So, each student will pay about $ ________ for a ticket.
Answer:
A. Used a whole number greater than the dividend.
Used 30 for the divisor. Then found the number close to and greater than $76.15 that divides easily by 30.
So, each student will pay about $ 3 for a ticket.
B. Used a whole number less than the dividend.
Used 30 for the divisor. Then found the number close to and less than $76.15 that divides easily by 30.
So, each student will pay about $ 2 for a ticket.
Math Talk
Mathematical Processes
Explain which estimate you think will be a better estimate of the cost of a ticket.
Answer: Estimated answer is 2.45
Explanation:
The number close to and greater than $76.15 that divides easily by 30.
So, each student will pay about $ 3 for a ticket.
2.45is very near to 3
a better estimate of the cost of a ticket is 90 ÷30 = 3
Share and Show
Use compatible numbers to estimate the quotient.
Question 1.
28.8 ÷ 9
________ ÷ _________ = __________
Answer: 30 ÷ 10= 3
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 2.
393.5 ÷ 41
________ ÷ __________ = ___________
Answer: 400 ÷40 = 10
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Estimate the quotient.
Question 3.
161.7 ÷ 7
Answer: 160 ÷ 10 = 16
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 4.
$17.90 ÷ 9
Answer: 180 ÷ 10 = 18
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 5.
145.4 ÷ 21
Answer: 140÷ 20 = 7
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Problem Solving
Question 6.
Write Math Explain why you might want to find an estimate for a quotient.
Answer:
In a division sum, when the divisor is made up of 2 digits or more than 2 digits, it helps if we first estimate the quotient and then try to find the actual number. Calculate mentally. In the process of division, the estimation of quotient plays a great role in its solution.
Question 7.
H.O.T. What’s the Error? During a 3-hour storm, it snowed 2.5 inches. Jacob said that it snowed an average of about 8 inches per hour.
Answer: 2.5 ÷ 3 = 0.83
Explanation:
He did not estimated with the help of compatible numbers
so, he said average of 8 inches per hour
but the average is 0.8 per hour
Problem Solving
Use the table to solve 8-10.
Question 8.
Estimate the average daily snowfall for Alaska’s greatest 7-day snowfall.
Answer: 26.7
Explanation:
The average daily snowfall for Alaska’s greatest 7-day snowfall is 26.7.
Question 9.
Multi-Step How does the estimate of the average daily snowfall for Wyoming’s greatest 7-day snowfall compare to the estimate of the average daily snowfall for South Dakota’s greatest 7-day snowfall?
Answer: South Dakota’s rain fall is greater
Explanation:
The average daily snowfall for Wyoming’s greatest 7-day snowfall is 12.07
The estimate of the average daily snowfall for South Dakota’s greatest 7-day snowfall is 16.1
South Dakota’s rain fall is greater than the Wyoming’s snowfall
Question 10.
H.O.T. The greatest monthly snowfall total in Alaska is 297.9 inches. This happened in February, 1953. Compare the daily average snowfall for February, 1953, with the average daily snowfall for Alaska’s greatest 7-day snowfall. Use estimation.
Answer: February
Explanation:
The greatest monthly snowfall total in Alaska is 297.9 inches. This happened in February, 1953.
The daily average snowfall for February, 1953 is 10.63
The average daily snowfall for Alaska’s greatest 7-day snowfall is 26.7.
The average daily snowfall for Alaska’s greatest 7-day snowfall is greater than the daily average snowfall for February, 1953
Daily Assessment Task
Fill in the bubble completely to show your answer.
Question 11.
You are participating in a remote control car race. It takes 215.78 seconds for your car to complete five laps. Which is the best estimate of the average time it takes to complete each lap?
(A) 22 seconds
(B) 44 seconds
(C) 30 seconds
(D) 55 seconds
Answer: B
Explanation:
You are participating in a remote control car race.
It takes 215.78 seconds for your car to complete five laps. 215 ÷ 5 = 43
43 is near to 44
43 is the best estimate of the average time it takes to complete each lap.
Question 12.
Communicate Jake buys 12 books at the bookstore for $92.08. Each book costs the same amount. Jake uses 84 to estimate the cost of each book, and then also uses 96 to estimate. Why does he choose these numbers?
(A) 92.08 falls between 84 and 96, and both whole numbers are divisible by 92.08.
(B) 84 and 96 are even numbers.
(C) 92.08 falls between 84 and 96, and both whole numbers are divisible by 12.
(D) 92.08 does not fall between 84 and 96.
Answer: C
Explanation;
92.08 falls between 84 and 96, and both whole numbers are divisible by 12.
Jake buys 12 books at the bookstore for $92.08.
Each book costs the same amount.
Jake uses 84 to estimate the cost of each book,
and then also uses 96 to estimate.
Question 13.
Multi-Step Last week, Alaina ran 12 miles in 131.25 minutes. The next week, Alaina ran 12 miles in 119.5 minutes. About how much faster did she run each mile in the second week?
(A) 0 minutes
(B) 1 minute
(C) 3 minutes
(D) 5 minutes
Answer: B
Explanation:
Last week, Alaina ran 12 miles in 131.25 minutes.
The next week, Alaina ran 12 miles in 119.5 minutes.
She run each mile in the second week is
131.25-119.5 = 11.75
11.75 ÷ 12 = 0.91
which is near to 1
Texas Test Prep
Question 14.
A plant grew 23.8 inches over 8 weeks. Which is the best estimate of the average number of inches the plant grew each week?
(A) 0.2 inch
(B) 2 inches
(C) 0.3 inch
(D) 3 inches
Answer: D
Explanation:
A plant grew 23.8 inches over 8 weeks.
23.8 ÷ 8 =2.9 is 3 the best estimate of the average number of inches the plant grew each week.
Texas Go Math Grade 5 Lesson 4.3 Homework and Practice Answer Key
Use compatible numbers to estimate the quotient.
Question 1.
78.8 ÷ 8
_________ ÷ _________ = __________
Answer: 80 ÷ 10= 8
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 2.
646.1 ÷ 34
_________ ÷ __________ = __________
Answer: 600 ÷ 30 = 20
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Estimate the quotient.
Question 3.
434.2 ÷ 62
Answer: 400 ÷ 60 = 6.6
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 4.
$14.60 ÷ 5
Answer: 15÷ 5 =3
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 5.
35.6 ÷ 6
Answer: 36 ÷ 6 = 6
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 6.
$82.15 ÷ 23
Answer: 100 ÷ 25 = 4
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 7.
63.2 ÷ 18
Answer: 60 ÷ 20 = 3
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 8.
227.5 ÷ 21
Answer: 220 ÷ 20 = 11
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 9.
36.9 ÷ 9
Answer: 36÷ 9 = 4
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 10.
143.2 ÷ 7
Answer: 140 ÷ 7 = 20
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Question 11.
$9.65 ÷ 5
Answer: 10 ÷ 5 = 2
Explanation:
You can estimate decimal quotients by using compatible numbers.
When choosing compatible numbers,
you can look at the whole-number part of a decimal dividend
or rename the decimal dividend as tenths or hundredths.
Problem Solving
Question 12.
Gino opens a savings account and deposits about the same amount each month for 5 months. At the end of 5 months he has deposited $33.55. About how much did Gino deposit each month?
Answer:
Question 13.
Thunderstorms brought a total of 5.8 inches of rain to the first week of spring. Estimate the average daily rainfall for the first week of spring.
Answer:
Lesson Check
Fill in the bubble completely to show your answer.
Question 14.
Aaron gives an estimate of 2 for the quotient in a division problem. His teacher says his estimate is reasonable. If the divisor is 4, which number could be the dividend in Aaron’s problem?
(A) 80.4
(B) 8.24
(C) 0.84
(D) 2.84
Answer: B
Explanation:
The nearest whole number for 8.24 is 8
when its divisor is 4
8 divided by 4 is 2
so, His teacher says his estimate is reasonable.
Question 15.
Natalie buys 4 pieces of wood to build a square pen for her rabbit. She decides the perimeter will be 6.96 meters. Which wood length should she buy to build each side of the pen so that she has enough wood, but has the least amount of wood left over?
(A) 1 meter
(B) 2 meters
(C) 2.5 meters
(D) 3 meters
Answer: B
Explanation:
Natalie buys 4 pieces of wood to build a square pen for her rabbit
She decides the perimeter will be 6.96 meters. 6.96 ÷ 4 = 1.74
2 meters she buy to build each side of the pen so that she has enough wood
Question 16.
It takes the printer in Reba’s office 240.42 seconds to print out six reports. About how long does it take to print out each report?
(A) 50-51 seconds
(B) 24-25 seconds
(C) 40-41 seconds
(D) 30-31 seconds
Answer: C
Explanation:
It takes the printer in Reba’s office 240.42 seconds to print out six reports.
240.42 ÷ 6 = 40.07
40.07seconds it take to print out each report
Question 17.
Ross and Lydia estimate the quotient for 387.5 ÷ 73. Ross uses a whole number greater than the dividend. Which equation shows how Lydia uses compatible numbers to get a closer estimate?
(A) 400 ÷ 80 = 5
(B) 450 ÷ 75 = 6
(C) 360 ÷ 60 = 6
(D) 375 ÷ 75 = 5
Answer: A
Explanation:
Ross uses a whole number greater than the dividend.
400 ÷ 80 = 5
Lydia uses compatible numbers to get a closer estimate
Question 18.
Multi-Step Mr. Williams owns an orchard. He has 211.9 pounds of grapefruits and 169.6 pounds of oranges to sell. He divides the fruit evenly into 8 shipments. About how many pounds are in each shipment?
(A) 50 pounds
(B) 30 pounds
(C) 400 pounds
(D) 20 pounds
Answer: A pounds
Explanation:
Mr. Williams owns an orchard. He has 211.9 pounds of grapefruits
and 169.6 pounds of oranges to sell.
211.9 + 169.6 = 381.5
381.5 ÷ 8 = 47.68
He divides the fruit evenly into 8 shipments.
In each shipment 50 pounds of fruit.
Question 19.
Multi-Step Cara has $25. She buys a shirt for $13.68. She buys a hat that is half the cost of the shirt. Which is the best estimate for the amount of money Cara should expect to have left?
(A) $4
(B) $3
(C) $6
(D) $7
Answer: C
Explanation:
Cara has $25.
She buys a shirt for $13.68. That is 25 – 13 = 12
She buys a hat that is half the cost of the shirt. 12÷ 2 = 6
6 is the best estimate for the amount of money Cara should expect to have left.