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Texas Go Math Grade 4 Lesson 8.2 Answer Key Estimate Products
Essential Question
What strategies can you use to estimate products?
Answer:
There are two methods are there we can use to estimate the product
i) Mental Math Multiplication Method
ii) Place value multiplication method
Unlock the Problem
• Underline any information you will need.
The Smith family opens the door of their refrigerator 32 times in one day. There are 31 days in May. About how many times is it opened in May?
Answer:
992 times
Explanation:
opens the door of their refrigerator 32 times in one day.
There are 31 days in May.
to know how many times is it opened in May
32 x 31
STEP 1 Find half of 32 by dividing by 2
32 /2 = 16
STEP 2 Multiply
16 x 31 = 403
STEP 3 double the 403
2 x 403 = 992
One Way Use rounding and mental math.
Estimate. 32 × 31
STEP 1 Round each factor
STEP 2 Use mental math.
3 × 3 = 9 ← basic fact
30 × 30 = _________
Answer: 900
Explanation:
Round each factor
30 x 30
3 x 3 x 10 x 10
9 x 100 = 900 times
So, the Smith family opens the refrigerator door about 900 times during the month of May.
All 24 light bulbs in the Park family’s home are CFL light bulbs. Each CFL light bulb uses 28 watts to produce light. About how many watts will the light bulbs use when turned on all at the same time?
Answer:
672 watts
Explanation:
All 24 light bulbs in the Park family’s home are CFL light bulbs.
Each CFL light bulb uses 28 watts to produce light
24 x 28 = 672 watts
Another Way Use mental math and compatible numbers.
Compatible numbers are numbers that are easy to compute mentally.
Estimate. 24 × 28
STEP 1 Use compatible numbers.
Answer: 750
Explanation:
25 x 3 x 10
75 x 10 = 750
STEP 2 Use mental math.
25 × 3 = 75
25 × 30 = __________
Answer:
25 x 30 = 750
STEP 2 Use mental math.
25 × 3 = 9 ← basic fact
25 × 30 = 750
So, about 750 watts are used.
Explanation:
To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers.
Try This! Estimate 26 × $79.
(A) Round to the nearest ten
26 × $79 is about ____________ .
Answer:
26 × $79 is about $2,054
Explanation:
In order to estimate products, we round the given factors to the required place value. Estimating products help us to check the reasonableness of an answer.
(B) Compatible numbers
26 × $79 is about ____________ .
Answer:
26 × $79 is about $2,054
Explanation:
Compatible numbers are pairs of numbers that are easy to multiply, mentally.
The numbers 26 and 79 are not compatible for multiplication since the product 2,054 can’t be easily calculated mentally.
To estimate 26 × 79, replace 26 and 79 with the compatible numbers 25 and 80.
Share and Show
Question 1.
To estimate the product of 62 and 28 by rounding, how would you round the factors? What would the estimated product be?
Answer:
62 x 28 = 1736
Explanation:
62 is estimated number is 60 and 28 is 30
the product is 1800
1736 is estimated as 1800
Estimate the product. Choose a method.
Question 2.
96 × 34
Answer: 3,264
Estimate: 3000
Explanation:
In order to estimate products, we round the given factors to the required place value. Estimating products help us to check the reasonableness of an answer.
Question 3.
47 × $39
Answer: 1,833
Estimate: 1800
Explanation:
In order to estimate products, we round the given factors to the required place value. Estimating products help us to check the reasonableness of an answer.
Question 4.
78 × 72
Answer: 5,616
Estimate: 5600
Explanation:
In order to estimate products, we round the given factors to the required place value. Estimating products help us to check the reasonableness of an answer.
Math Talk
Mathematical Processes
Describe how you know if an estimated product will be greater than or less than the exact answer.
Answer:
The difference to be checked between the estimated product and the exact values product.
If then the estimated product will be checked for greater than or less than the exact.
Problem Solving
Practice: Copy and Solve Estimate the product. Choose a method.
Question 5.
61 × 31
Answer: 1,891
Estimated
60 x 30 = 1800
Explanation:
In order to estimate products, we round the given factors to the required place value. Estimating products help us to check the reasonableness of an answer.
Question 6.
52 × 68
Answer: 3,536
50 x 70 = 3500
Explanation:
In order to estimate products, we round the given factors to the nearest place value.
Estimating products help us to check the reasonableness of an answer.
Question 7.
26 × 44
Answer: 1,144
25 x 45 = 1,125
Estimate: 1100
Explanation:
In order to estimate products, we round the given factors to the nearest place value.
Estimating products help us to check the reasonableness of an answer.
Question 8.
57 × $69
Answer: 3,933
Estimate:55 x 70=3850
Explanation:
In order to estimate products, we round the given factors to the nearest place value.
Estimating products help us to check the reasonableness of an answer.
Question 9.
55 × 39
Answer: 2,145
Estimate: 55 x 40 = 2200
Explanation:
In order to estimate products, we round the given factors to the nearest place value.
Estimating products help us to check the reasonableness of an answer.
Question 10.
51 × 81
Answer: 4,131
Estimate: 50 x 80 = 4000
Explanation:
In order to estimate products, we round the given factors to the nearest place value.
Estimating products help us to check the reasonableness of an answer.
Question 11.
47 × $32
Answer: 1,504
Estimate: 45 x 30 = 1350
Explanation:
In order to estimate products, we round the given factors to the nearest place value.
Estimating products help us to check the reasonableness of an answer.
Question 12.
49 × 64
Answer: 3,136
Estimate:50 x 60 =3000
Explanation:
In order to estimate products, we round the given factors to the nearest place value.
Estimating products help us to check the reasonableness of an answer.
H.O.T. Find two possible
Explanation:
In order to estimate products, we round the given factors to the nearest place value.
Estimating products help us to check the reasonableness of an answer.
Find the two possible factors for the estimated products.
Question 13.
2,800
Answer:
140 x 20
Explanation:
To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers.
A factor is a number that divides into another number exactly without leaving a remainder.
(14 x 2)(10 x 10)
140 x 20 = 2800
140 x 20
Question 14.
8,100
Answer:
90 x 90
Explanation:
To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers.
A factor is a number that divides into another number exactly without leaving a remainder.
(9x 9)(10 x 10)
81 x 100 = 8,100
90 x 90
Question 15.
5,600
Answer:
70 x 80
Explanation:
To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers.
A factor is a number that divides into another number exactly without leaving a remainder.
(7 x 8)(10 x 10)
56 x 100 = 5600
70 x 80
Question 16.
2,400
Answer:
120 x 20
Explanation:
To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers.
A factor is a number that divides into another number exactly without leaving a remainder.
(12 x 2)(10 x 10)
24 x 100 = 2400
120 x 20
Question 17.
Apply On average, a refrigerator door is opened 38 times – each day. Len has two refrigerators in his house. Based on this average, about how many times in a 3-week period are the refrigerator doors opened?
Answer:
228 times
Apply On average, a refrigerator door is opened 38 times – each day.
Len has two refrigerators in his house.
Based on this average, number of times in a 3-week period are the refrigerator doors opened
38 x 2 x 3
38 x 6 = 228 times
Question 18.
The cost to run a refrigerator is about $57 each year. About how much will it have cost to run by the time it is 15 years old?
Answer: $ 855
Explanation:
The cost to run a refrigerator is about $57 each year.
Total cost to run by the time in 15 years old
57 x 15 = $855
Question 19.
H.O.T. Multi-Step If Mel opens his refrigerator door 36 times every day, about how many times will it be opened in April? Will the exact answer be more than or less than the estimate? Explain.
Answer:
1080 times
Estimate: 1000 times
Explanation:
If Mel opens his refrigerator door 36 times every day,
In April month there are 30 days
So, 30 x 36= 1080 times
1080 is more than the exact answer.
Question 20.
H.O.T. Explain why $2,400 and $2,000 are both reasonable estimates for problems A and B below Try This! on page 274.
Answer:
Both are correct as they are the estimates.
Explanation:
In order to estimate products, we round the given factors to the required place value.
Estimating products help us to check the reasonableness of an answer.
Question 21.
H.O.T. What’s the Question? The estimated product of two numbers, that are not multiples of ten, is 2,800.
Answer:
Daily Assessment Task
Fill in the bubble completely to show your answer.
Question 22.
A scientist watches a thorny dragon eat ants for 32 minutes. It eats at a rate of up to 45 ants every minute. At this rate, about how many ants does the thorny dragon eat in 32 minutes?
(A) 2,000 ants
(B) 1,500 ants
(C) 1,600 ants
(D) 150 ants
Answer:
Option(B)
Explanation:
A scientist watches a thorny dragon eat ants for 32 minutes.
It eats at a rate of up to 45 ants every minute.
Number of ants eaten by the thorny dragon in 32 minutes
Estimates of 32 is 30 and 45 is 50
So, 30 x 50 = 1500
Question 23.
Denise uses 24 beads to make 1 beaded necklace. About how many beads does she need to make 42 beaded necklaces?
(A) 1,500 beads
(B) 100 beads
(C) 800 beads
(D) 150 beads
Answer:
Option(C)
Explanation:
Denise uses 24 beads to make 1 beaded necklace.
Number of beads she need to make 42 beaded necklaces
Estimate of 24 is 20 and 42 is 40
So, compatible pairs 20 x 40 = 800
Question 24.
Multi-Step Mr. Parker jogs for 35 minutes each day. He jogs 5 days in week 1, 6 days in week 2, and 7 days in week 3. About how many minutes does he jog?
(A) 400 minutes
(§) 350 minutes
(C) 200 minutes
(D) 800 minutes
Answer:
Option(D)
Explanation:
Mr. Parker jogs for 35 minutes each day.
He jogs 5 days in week 1, = 5 x 35 =175 minutes
6 days in week 2, 35 x 6 = 210 minutes
and 7 days in week 3, 7 x 35 = 245
Total minutes he jogs = 175 + 210 + 245 = 630
Nearest estimate: 800
TEXAS Test Prep
Question 25.
Which is the best estimate for the product 75 × 23?
(A) 2,600
(B) 2,200
(C) 160
(D) 1,600
Answer:
Option(D)
Explanation:
23 x 75 = 1725
Estimate of 23 is 20 and 75 is 80
So, 20 x 80 = 1600
Texas Go Math Grade 4 Lesson 8.2 Homework and Practice Answer Key
Estimate the product. Choose a method.
Question 1.
42 × 28
Answer:
Estimate:1200
Explanation:
Compatible numbers, these are a pair of numbers used in multiplication to estimate the product.
Estimates of 42 is 40 and 28 is 30.
So, compatible pairs are
40 x 30 =1200
Question 2.
95 × 33
Answer:
Estimate: 3000
Explanation:
Compatible numbers, these are a pair of numbers used in multiplication to estimate the product.
Estimate of 95 is 100 nd 33 is 30
So, compatible pairs are
100 x 30 = 3000
Question 3.
61 × 58
Answer:
Estimate: 1200
Explanation:
Compatible numbers, these are a pair of numbers used in multiplication to estimate the product.
Estimate of 61 is 60 and 58 is 60
So, compatible pairs are
60 x 60 = 1200
Question 4.
77 × 13
Answer:
Estimate: 800
Explanation:
Compatible numbers, these are a pair of numbers used in multiplication to estimate the product.
Estimate of 77 is 80 and 13 is 10
Compatible pairs are 80 x 10 = 800
Find two possible factors for the estimated product.
Question 5.
1,600
Answer:
40 x 40
Explanation:
Factors are the numbers that divide the numbers exactly with a remainder zero.
So, 40 is the factor of estimated product.
Question 6.
4,500
Answer:
90 x 50
Explanation:
Factors are the numbers that divide the numbers exactly with a remainder zero.
So, 90 and 50 are the factor of estimated product.
Question 7.
6,000
Answer:
60 x 100
Explanation:
Factors are the numbers that divide the numbers exactly with a remainder zero.
So, 60 and 100 are the factor of estimated product.
Question 8.
3,200
Answer:
80 x 40
Explanation:
Factors are the numbers that divide the numbers exactly with a remainder zero.
So, 80 and 40 are the factor of estimated product
Problem Solving
Question 9.
A bus holds 58 people. For the last away game, 27 bus loads of fans traveled to the game. About how many fans went to the game on the buses?
Answer:
58 x 27 = 1566
Explanation:
A bus holds 58 people.
For the last away game, 27 bus loads of fans traveled to the game.
Number of fans went to the game on the buses
58 x 27 = 1566
Question 10.
The fence posts along Tom’s driveway are 96 inches apart. There are 32 fence posts, About how many inches long is the fence?
Answer:
96 x 32 = 3072
Explanation:
The fence posts along Tom’s driveway are 96 inches apart.
There are 32 fence posts,
Number of inches long is the fence 96 x 32 = 3072
Question 11.
Will the exact answer to Problem 9 be more than or less than the estimate? Explain.
Answer:
The exact answer to Problem 9 is less than the estimate.
Explanation:
The answer for question number 9 is 1566
Estimate of 1566 is 1600
Question 12.
Nona used compatible numbers to estimate that 25 × 42 is about 1,000. Gerry rounded and estimated that the product is about 1,200. Which estimate is closest to the exact answer? Explain.
Answer:
Gerry estimate is closest to the exact answer.
Explanation:
Nona used compatible numbers to estimate that 25 × 42 is about 1,000.
Gerry rounded and estimated that the product is about 1,200.
Gerry rounded the compatible pairs as 30 x 40 = 1200
Gerry estimate is closest to the exact answer.
Fill in the bubble completely to show your answer.
Question 13.
Which is the best estimate for the product of 26 × 78?
(A) 2,400
(B) 1,600
(C) 2,000
(D) 1,400
Answer:
Option(A)
Explanation:
26 x 78 = 2028
Estimate of 26 is 30 and 78 is 80
So, 30 x 80 = 2400
Question 14.
For which two factors is the product closest to 4,800?
(A) 24 × 24
(B) 56 × 83
(C) 47 × 66
(D) 92 × 38
Answer:
Option(B)
Explanation:
Estimate of 56 is 60 and 83 is 80
60 x 80 = 4800
Question 15.
A store has 12 rows of eye glasses in a display. There are 27 pairs of glasses in each row. Which estimate is closest to the number of pairs of glasses in the store’s display?
(A) 300
(B) 240
(C) 360
(D) 200
Answer:
Option(A)
Explanation:
A store has 12 rows of eye glasses in a display.
There are 27 pairs of glasses in each row.
12 x 27 = 324
Estimate 300 is closest to the number of pairs of glasses in the store’s display.
Question 16.
A factory uses 28 screws for each bookcase they make. In one day, they produce 44 bookcases. About how many screws are needed each day?
(A) 1,500
(B) 1,000
(C) 800
(D) 1,200
Answer:
Option(D)
Explanation:
A factory uses 28 screws for each bookcase they make.
In one day, they produce 44 bookcases.
28 x 44 = 1232
Number of screws needed each day 1200
Estimate of 28 is 30 and 44 is 40
40 x 30 = 1200
Question 17.
Multi-Step A theater has 17 rows of seats on the floor and 11 rows of seats in the balcony. There are 55 seats in each row. Which is the best estimate of the total number of seats in the theater?
(A) 180
(B) 1,500
(C) 2,400
(D) 1,800
Answer:
Option(B)
Explanation:
A theater has 17 rows of seats on the floor and
11 rows of seats in the balcony.
There are 55 seats in each row.
(17 + 11) x 55 = 1540
The best estimate of the total number of seats in the theater is 1500
Question 18.
Multi-Step There are 48 beads in a package. Mariah bought 4 packages of blue, 9 packages of gold, 6 packages of red, and 2 packages of silver beads. Which is the best estimate of the total number of beads she bought?
(A) 1,000
(B) 800
(C) 1,200
(D) 2,400
Answer:
Option(A)
Explanation:
There are 48 beads in a package.
Mariah bought 4 packages of blue, 9 packages of gold, 6 packages of red, and 2 packages of silver beads. 48 x (4+9+6+2) = 1008
The best estimate of the total number of beads she bought are 1000.