Into Math Grade 7 Module 6 Lesson 2 Answer Key Estimate to Check Reasonableness

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HMH Into Math Grade 7 Module 6 Lesson 2 Answer Key Estimate to Check Reasonableness

I Can use underestimates and overestimates to check the reasonableness of answers.

Step It Out

1. Sandi says that her family of 4 will go to the park 3 times this year. She says they will save about $200 if they buy the season pass. Use estimation to determine whether her statement is reasonable.
A. Estimate the cost of 4 season passes.

Answer:
$979.96 = $980

Explanation:

B. Overestimate the cost of 4 day passes for 3 days. Use the Distributive Property to make calculations easier. 4 day passes:

Answer:

C. Sandi’s estimation of saving about $200 (is / is not) reasonable. Explain.
Answer:
Sandi’s estimation of saving about $200 is not reasonable.

Explanation:
cost of 4 season passes = $980
Cost of 4 days passes for 3 days = $996
$996 – $980 = $16
So it is not reasonable.

Turn and Talk If the family of 4 visited the park 4 times, would season passes save them money? Explain.
Answer:
$249.99 × 4 = $980
$980
Season passes will not save them money.

2. Estimate -3.8 • 3 – \(\frac{117}{20}\) using integers. Tell whether your estimate is an underestimate or an overestimate. Explain.

Answer:

It is an underestimate.

3. Tasha and Lydia have a yard-service company. Their last three jobs brought in $287.50, $184.25, and $95. Lydia worked about 65% of the hours on those jobs. Use compatible numbers to estimate Lydia’s share of the earnings.

Money earned from jobs:
$287.50 + $184.25 + $95
Estimated money earned:


Lydia’s estimated share:

Turn and Talk What are two different ways to estimate 65%?

Check Understanding

Question 1.
The soccer club held a spaghetti dinner. They sold 39 child tickets for $3.75 each and 27 adult tickets for $5.95 each. The amount for 11 child tickets was refunded.

A. Estimate the amount of income received by the soccer club. Show your work.
_______________________
_______________________
Answer:
265.65

Explanation:
They sold 39 child tickets for $3.75 each and 27 adult tickets for $5.95 each
(3.75 × 39) + (27 × 5.95) – (11 × 3.75)
146.25 + 160.65 – 41.25
306.9 – 41.25
265.65

B. Was the estimate for the amount of income in Problem 1 an overestimate or underestimate? Explain.
_______________________
_______________________
_______________________
Answer:
The estimate for the amount of income in Problem 1 is an underestimate.

Question 2.
Mrs. Gomez earns $19.50 per hour and gets a 5% raise. Use compatible numbers to estimate her new hourly rate. Explain.
Answer:
Her new hourly rate is 20.475.

Explanation:
Given,
Mrs. Gomez earns $19.50
And she got a raise of 5%
$19.50 × \(\left(\frac{105}{100}\right)\)
\(\frac{(19.50 × 105)}{100}\)
\(\frac{2047.5}{100}\)
20.475

On Your Own

Question 3.
A desert tour includes 305 people traveling by van. Each van can transport 18 people.

A. Estimate the number of vans needed.
Answer:
The number of vans needed is 17.

Explanation:
A desert tour includes 305 people
Each van can transport 18 people
305 ÷ 18 = 16.99 = 17

B. Construct Arguments Is it an overestimate or underestimate? In this situation, would it be better to overestimate or underestimate? Explain your choice.
Answer:
Overestimate

Explanation:
The number of vans is estimated to be 17 so the given situation is overestimated.

Question 4.
Critique Reasoning A bag of dry pet food costs the pet store $18.66. A case of canned food costs $11.43. The owner puts in an order for 27 bags of dry food and 34 cases of canned food. The owner thinks he owes $1,835.49.

A. Estimate the total amount of the order.
Answer:
The total amount of the order is 892.

Explanation:
(27 × $18.66) + (34 × $11.43)
503.82 + 388.62
$892.44
The total amount of the order is $892.
The owner thinks he owes $1,835.49.
$1835.49 – $892
$943.49

B. Is the owners total reasonable? Explain your answer.
Answer:
The owner thinks he owes $1,835.49.
$1835.49 – $892
$943.49
So the answer is not reasonable.

Question 5.
STEM Sound travels about 1,125.33 feet in a second. An engineer detects the sound of an explosion from a test site 8 seconds after the blast.

A. Use the equation d = rt to estimate how far away the engineer was in feet and in miles from the blast.
Answer:
The estimation is 141 feet.

Explanation:
Given,
d = 1125 t = 8 seconds
1125 ÷ 8
140.625
141

B. If the engineer wants to find the exact spot of the blast should she use the estimate or an exact answer? Explain your choice.
Answer:
She should use the estimation to find the exact spot of the blast.

Question 6.
Use Structure The school basketball team had the following scores for its games this year: 47, 36, 42, 29, 39, 49, 44, and 32. Estimate how many points they scored this year. Explain your estimate.

Answer:
The points they score every year is 40.

Explanation:
Given,
this year: 47, 36, 42, 29, 39, 49, 44, and 32.
47 + 36 + 42 + 29 + 39 + 49 + 44 + 32
318
No of the terms are 8
318 ÷ 8
39.75
40

Question 7.
Sam buys a drink for $2.05 and a sandwich for $4.20 each day Monday through Friday for lunch. He also leaves a $1.25 tip each day. Estimate what he pays for lunch for the week. Is this an underestimate or overestimate?
Answer:
He pays $8 for lunch for the week. It is overestimate.

Explanation:
Given,
Sam buys a drink for $2.05
sandwich for $4.20
He also leaves $1.25 tip each day.
Total $2.05 + $4.20 + $1.25 = $7.5 = $8

Question 8.
Use compatible numbers to estimate \(\frac{-594}{-27}\) • \(\left(\frac{-924}{21}\right)\). Is -482 a reasonable answer? Explain your answer.
Answer:
The answer is not reasonable. By solving the expression the answer we got is -968 and not -482.

Explanation:
Given,
\(\frac{-594}{-27}\) • \(\left(\frac{-924}{21}\right)\)
\(\frac{-594}{-27}\) × \(\left(\frac{-924}{21}\right)\)
(-594 × -924) = 548856
-27 × 21 = 567
-548856 ÷ 567
-968

Question 9.
Open Ended Two 3-digit numbers are added. Give an example where you would not want to round both 3-digit numbers to the nearest hundred to get the best estimate.
Answer:

Question 10.
Marin evaluated -0.238 • \(\frac{2}{10}\) – (1,003 • 0.0062) and got -6.65 rounded to the nearest hundredth.

A. Estimate the value of the expression.
Answer:
The value of the expression is -6.2662.

Explanation:
Given,
-0.238 • \(\frac{2}{10}\) – (1,003 • 0.0062)
-0.238 × \(\frac{2}{10}\) – (1,003 × 0.0062)
Apply Bodmas rule
-0.238 × \(\frac{2}{10}\) – (6.2186)
-0.238 × \(\frac{1}{5}\) – (6.2186)
\(\frac{-0.238}{5}\) – (6.2186)
-0.0476 – 6.2186
-6.2662

B. Construct Arguments Is the estimate an overestimate or underestimate? Explain.
Answer:
Underestimate.

Explanation:
The given expression is underestimated because the number is not to the nearest hundredth.

Lesson 6.2 More Practice/Homework

Estimate to Check Reasonableness

Question 1.
Students sold 342 tickets to the school carnival at $11.75 each. Nine tickets were refunded. Estimate the amount of money that the school took in. Is your estimate an overestimate or underestimate?
Answer:
$3913, estimate.

Explanation:
Given,
students sold 342 tickets at $11.75 each
Nine tickets were refunded
342 – 9 = 333
333 × $11.75
$3912.75
$3913.

Question 2.
Construct Arguments The dimensions of a room with one window and one door at a community center are shown. Ivan wants to have the four walls painted. The painter says the area is 542.2 square feet. Estimate the total area that needs to be painted. Was the painter’s answer reasonable? Explain.
_______________________
_______________________

Answer:
The painter’s answer is not reasonable because the painted area is 3350 square feet.
But the painter says the area is 542.2 square feet. Hence it is not reasonable.

Explanation:
Area of the painted = 2 (lb + bh + hl)
l = 29.5 b = 38.375 and h = 8
2 ((29.5 × 38.375) + (8 * 38. 375) + (8 × 29.5))
2 ((1132.06) + (306.95) + (236))
2 (1675)
3350 square feet.

Question 3.
Estimate 20 • 37 • \(\frac{21}{5}\) ÷ 98. Is it an overestimate or underestimate? Explain.
Answer:
Overestimate

Explanation:
Given,
20 • 37 • \(\frac{21}{5}\) ÷ 98
Let us solve the given expression
20 × 37 × \(\frac{21}{5}\) ÷ 98
20 × 37 × \(\frac{21}{5}\) × \(\frac{1}{98}\)
15540 ÷ 490
31.71 = 32

Question 4.
Carol says that –\(\frac{520}{105}\) • \(\frac{16}{15}\) • (-\(\frac{1}{2}\)) is less than 2.5. Do you agree? Explain.
Answer:
No, The given question –\(\frac{520}{105}\) • \(\frac{16}{15}\) • (-\(\frac{1}{2}\)) is not less than 2.5.

Explanation:
Given,
–\(\frac{520}{105}\) • \(\frac{16}{15}\) • (-\(\frac{1}{2}\))
–\(\frac{520}{105}\) × \(\frac{16}{15}\) × (-\(\frac{1}{2}\)

Question 5.
Estimate 210 ÷ 5.2 • 9\(\frac{3}{4}\) + (-205). Is 188.75 a reasonable answer? Explain your answer.
Answer:
188.75

Explanation:
Given,
210 ÷ 5.2 • 9\(\frac{3}{4}\) + (-205).
210 ÷ 5.2 × \(\frac{39}{4}\) – 205
Follow the BODMAS rule
40.38 × \(\frac{39}{4}\) – 205
(40.38 × 39) ÷ 4 – 205
1575 ÷ 4  -205
393.75 – 205
188.75
The given answer is reasonable

Test Prep

Question 6.
Which is the best estimate for the area of a piece of property that is 52 yards by 77 yards?
A. 50 × 70 = 3,500 yd²
B. 50 × 80 = 4,000 yd²
C. 60 × 70 = 4,200 yd²
D. 60 × 80 = 4,800 yd²
Answer:
B. 50 × 80 = 4,000 yd²

Explanation:
The best estimate for the area of a piece of property that is 52 yards by 77 yards is 50 × 80 = 4,000 yd²

Question 7.
A car can travel 32 miles using 1 gallon of gas. The car has 12 gallons of gas.

A. Can the car travel 370 miles without needing more gas? Estimate and explain.
________________________
________________________
________________________
Answer:
Yes, the car can travel 370 miles without needing more gas. Because the estimation is 384 for 12 gallons of gas.

Explanation:
Given,
Distance = 32 miles using 1 gallon of gas
12 gallons of gas
32 × 12
384

B. Explain why an underestimate is not a wise choice for estimating the gasoline needed for a roadtrip.
________________________
________________________
Answer:

Question 8.
Zana calculates –\(\frac{15}{49}\)[19 + (-3)] ∙ \(\frac{19}{11}\) = -8\(\frac{248}{539}\). Is the answer reasonable? Explain.
Answer:
The answer is reasonable.

Explanation:
Given,
–\(\frac{15}{49}\)[19 + (-3)] ∙ \(\frac{19}{11}\) = -8\(\frac{248}{539}\).
–\(\frac{15}{49}\)[19 – 3] × \(\frac{19}{11}\) = -8\(\frac{248}{539}\).
–\(\frac{15}{49}\) × 16 × \(\frac{19}{11}\) = -8\(\frac{248}{539}\).
–\(\frac{(15 × 16 × 19)}{(49 × 11)}\) = –\(\frac{4560}{539}\).
–\(\frac{4560}{539}\) = –\(\frac{4560}{539}\)
On both sides the answer is equal
Hence the answer is reasonable.

Spiral Review

Question 9.
A bottle contains 0.78 liter of medicine. Each dose is supposed to be 0.02 liter. How many doses are in the bottle?
Answer:
0.0156 liter.

Explanation:
Each dose is supposed to be 0.02 liter
0.78 × 0.02 = 0.0156

Question 10.
Which costs less per banana, 8 bananas for $1.95 or 12 bananas for $2.29? Explain.
Answer:
12 bananas for $2.29.

Explanation:
Given,
8 bananas for $1.95 = 1.95 ÷ 8 = $0.24 per banana.
12 bananas for $2.29 = 2.29 ÷ 12 = $0.19 per banana
$0.19 > $0.24

Question 11.
Which property is demonstrated by 1,326 • 367 = 367 • 1,326?
Answer:
The property is demonstrated by 1,326 • 367 = 367 • 1,326 is called commutative property.

Explanation:
Given,
1,326 • 367 = 367 • 1,326
A × B = B × A
This is called commutative property.

Question 12.
James is building a rectangular fire pit. He dug a hole 20 inches by 20 inches. He decides to make each side of the fire pit 4 inches longer instead. What is the percent increase in the area of the fire pit?
__________________
Answer:
44%

Explanation:
Area of the rectangle = l × b
Area of the James pit = 20 × 20 = 400 square inch.
New size = 20 + 4 = 24 inches
New area = 24 × 24 =576 square inch.
Increase in area = 576 – 400 = 176
percentage increase in the area = (increase ÷ original size) × 100
= (176 ÷ 400) × 100
= 0.44 × 100
= 44%
The percentage area of the fire pit is 44%