# Texas Go Math Grade 4 Lesson 7.6 Answer Key Multiply Using Mental Math

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## Texas Go Math Grade 4 Lesson 7.6 Answer Key Multiply Using Mental Math

Essential Question

How can you use mental math and properties to help you multiply numbers?

Unlock the Problem

Properties of Multiplication can make multiplication easier.

There are 4 sections of seats in the Playhouse Theater. Each section has 7 groups of seats. Each group has 25 seats. How many seats are there in the theater?

Find 4 × 7 × 25. So, there are 700 seats in the theater.
There are 700 seats in the theater.

Explanation:
Here, we have used commutative property which means that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. So
4×7×25 = 4×25×7
= 100×7
= 700.
So, there are 700 seats in the theater.

Math Talk

Mathematical Processes
How could you find 4 × 25 help you find 6 × 25? Remember

The Associative Property states that you can group factors in different ways and get the same product. Use parentheses to group the factors you multiply first.

Try This! Use mental math and properties.

(A) Find (6 × 10) × 10.
(6 × 10) × 10 = 6 × (10 × 10) Associative Property
= 6 × ______________
= ______________
By Associative property
(6 × 10) × 10 = 600.

Explanation:
Here, Associative Property states that the product of three or more numbers remains the same regardless of how the numbers are grouped. So (6 × 10) × 10 = 6 × (10 × 10)
= 6 × (100)
= 600.

(B) Find (4 × 9) × 250.
(4 × 9) × 250 = 250 × (4 × 9) Commutative Property
= (250 × 4) × 9 Associative Property
= ______________ × 9
= ______________
(4 × 9) × 250 = 9,000.

Explanation:
Here, Associative Property states that the product of three or more numbers remains the same regardless of how the numbers are grouped. So (4 × 9) × 250 = 4× (9×250)
= 4× 2,250
= 9,000.

More Strategies Choose the strategy that works best with the numbers in the problems.

Examples

Multiply. 4 × 625
Think: 625 is 600 plus 25.
4 × 625 = 4 × (600 + 25)
= (4 × 600) + (4 × 25)
= ________ + _________
= _________
4 × 625 = 2,500

Explanation:
Here, we have used distributive property to solve 4 × 625 which is
4 × 625 = 4 × (600 + 25)
= (4 × 600) + (4 × 25)
= 2400+100
= 2,500.

(B) Use subtraction.
Multiply. 5 × 398
Think: 398 is 2 less than 400.
5 × 398 = 5 × (400 – 2)
= (5 × _________) – (5 × 2)
= 2,000 – _________
= _________
5 × 398 = 1,990.

Explanation:
By using distributive law of subtraction 5 × 398 = 5 × (400 – 2)
= (5 × 400) – (5 × 2)
= 2000 – 10
= 1,990.

Share and Show

Question 1.
Break apart the factor 112 to find 7 × 112 by using mental math and addition.
7 × 112 = 7 × ( _______ + 12)
= ______________
= ______________
= ______________
7 × 112 = 784.

Explanation:
By using distributive property 7 × 112 = 7 × ( 100 + 12)
= (7 × 100) +(7 ×12)
= (700)+(84)
= 784.

Math Talk

Mathematical Processes
Explain how using an addition strategy is related to using a subtraction strategy.
Here, we are breaking apart a number based on its place value and then adding or subtracting each individual place to find answer.

Find the product. Tell which strategy you used.

Question 2.
4 × 6 × 50
4 × 6 × 50 = 1,200.

Explanation:
Here, Associative Property states that the product of three or more numbers remains the same regardless of how the numbers are grouped. So
4 × 6 × 50 = (4 × 6) × 50
= (24) × 50
= 1,200.

Question 3.
5 × 420
5 × 420 =2,100.

Explanation:
Here, Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. So
5 × 420 = 5 × (400+20)
= (5 × 400)+(5 × 20)
= 2,000+100
= 2,100.

Question 4.
6 × 298
6 × 298 = 1,788.

Explanation:
Here, Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. So
6 × 298 = 6 ×(200+90+8)
= (6 × 200)+(6 × 90)+(6 × 8)
= 1,200+540+48
= 1,788.

Problem Solving

Practice: Copy and Solve Use a strategy to find the product.

Question 5.
16 × 400
16 × 400 = 25,600.

Explanation:
Here, Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. So
16 × 400 = (8×8)×400
= (64)×400
= 25,600.

Question 6.
3 × 31 × 10
3 × 31 × 10 = 930.

Explanation:
Here, Associative Property states that the product of three or more numbers remains the same regardless of how the numbers are grouped. So
3 × 31 × 10 = (3 × 31)× 10
= (93)× 10
= 930.

Question 7.
3 × 199
3 × 199 = 597.

Explanation:
Here, Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. So
3 × 199 = 3 ×(100+90+9)
= (3 × 100)+(3 × 90)+(3 × 9)
= 300+270+27
= 597.

Question 8.
3 × 1,021
3 × 1,021 = 3,063.

Explanation:
Here, Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. So
3 × 1,021 = 3 ×(1000+20+1)
= (3×1000)+(3×20)+(3×1)
=3,000+60+3
=3,063.

H.O.T. Algebra Use mental math to find the unknown number.

Question 9.
21 × 40 = 840, so 21 × 42 = _________ .
21 × 42 = 882.

Explanation:
Here, Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. So
21 × 42 = 21×(40+2)
= (21×40)+(21×2)
= 840+42
= 882.

Question 10.
9 × 60 = 540, so 9 × 59 = __________ .
9 × 59 = 531.

Explanation:
Here, Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. So
9 × 59 = 9 × (50+9)
= (9×50)+(9×9)
= 450+81
= 531.

Problem Solving

Use the table for 11-13. Question 11.
Three hundred people buy tickets at the gate for Section N. How much money is collected for Section N at the gate?
The money collected for Section N at the gate is $75. Explanation: Given that there are three hundred people bought tickets at the gate for Section N and the price of each ticket is$25, so the money collected for Section N at the gate is $25×3 =$75.

Question 12. H.O.T. Multi-Step Reasoning When the full season tickets first went on sale, 2,000 Full Season tickets sold for Section N. Two weeks after the tickets first went on sale, another 1,500 full season tickets were sold for Section N. How much money was spent on full season tickets for Section N in total? How much more money was spent when the tickets first went on sale than after the first two weeks?
The total money spent are 70,000.

Explanation:
Given that the first sale tickets sold are 2,000 for Section N which is 2,000×20= 40,000 and in next sale 1500 tickets sold out which is 1500×20= 30,000. So the total money spent are 40,000+30,000= 70,000.

Question 13.
Tina and 3 of her friends buy the full season plan for Section M. If there are 45 games in the full season, how much money do they spend?
The will spend $4,500. Explanation: Given that Tina and 3 of her friends which means a total of 4 members bought full season for Section M which costs$25 for each, So total cost is 25×4= 100. So if there are 45 games in full seasons then 45×100= $4,500. Question 14. H.O.T. Multi-Step What’s the Error? Louisa says that 40 × 3,210 is 12,840. Describe and correct her error. Answer: Louisa answer was incorrect. Explanation: Louisa answer was incorrect, as the multiplication of 40 × 3,210 is 1,28,400 but Louisa mentioned 12,840. Daily Assessment Task Fill in the bubble completely to show your answer. Question 15. A customer wants to buy 4 model sets for$109 each. Matt uses mental math to find the total cost. How much should Matt charge the customer?
(A) $113 (B)$409
(C) $436 (D)$440
C.

Explanation:
Given that a customer wants to buy 4 model sets for $109 each and Matt uses mental math to find the total cost. So Matt uses distributive property to solve 4×109 which is 4×109 = 4×(100+9) = (4×100)+(4×9) = 400+36 =$436.
So, Matt chargers $436. Question 16. There are 5 shelves for tennis balls. Each can holds 3 tennis balls. There are 20 cans on each shelf. The work below shows how Isabelle finds the total number of tennis balls. Which strategy does she use? 5 × 3 × 20 = 5 × 20 × 3 = 100 × 3 = 300 (A) Associative Property (B) Commutative Property (C) Distributive Property (D) Halving and Doubling Answer: A. Explanation: Here, Isabelle uses Associative Property which means that the product of three or more numbers remains the same regardless of how the numbers are grouped. Question 17. Multi-Step Mr. Jackson buys 5 boxes of clay for camp. Each box has 12 different color packs. Each pack costs$6. How much does Mr. Jackson spend on clay?
(A) $72 (B)$36
(C) $30 (D)$360
D.

Explanation:
Given that Mr. Jackson buys 5 boxes of clay for camp and each box has 12 different color packs which is 5×12 = 60. Each pack costs $6, so Mr. Jackson spend on clay is 60×$6 = $360. TEXAS Test Prep Question 18. Which of the following shows a strategy to use to find 3 × 198? (A) (3 × 200) – (3 × 2) (B) (3 × 200) + (3 × 2) (C) (3 × 198) – 6 (D) 198 – 6 Answer: A. Explanation: Here we can use (3 × 200) – (3 × 2) to find 3 × 198. ### Texas Go Math Grade 4 Lesson 7.6 Homework and Practice Answer Key Use a strategy to find the product. Question 1. 5 × 75 × 2 = ______________ Answer: 5 × 75 × 2 = 750. Explanation: Here, Associative Property states that the product of three or more numbers remains the same regardless of how the numbers are grouped. So 5 × 75 × 2 = 5 ×(75 × 2) = 5 ×(150) = 750. Question 2. 6 × 302 = ______________ Answer: 6 × 302 = 1,812 Explanation: Here, Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. So 6 × 302 = 6 × (300+2) = (6 × 300)+(6 × 2) = 1800+12 = 1,812. Use mental math to find the unknown number. Question 3. 7 × 80 = 560, so 14 × 40 = ______________ Answer: 14 × 40 = 560. Explanation: Here, Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. So 14 × 40 = (7 + 7) × 40 = (7×40) + (7×40) = 280+280 = 560. Question 4. 32 × 30 = 960, so 32 × 31 = ______________ Answer: 32 × 31 = 992. Explanation: Here, Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. So 32 × 31 = 32 × (30+1) = (32 × 30) + (32 × 1) = 960+32 = 992. Problem Solving Use the table 5-7 Question 5. For the first concert, 300 people bought single tickets for section B. How much money was spent on single tickets? Answer: The money spent on single tickets is$14,400.

Explanation:
Given that 300 people bought single tickets for section B, so the money spent on single tickets is 300×$48 which is$14,400.

Question 6.
Raoul buys 2 season tickets for section A. There are 14 concerts in the series. How much money does Raoul spend?
The money that was spend by the Raoul is $100. Explanation: Gvien that Raoul bought 2 season tickets for section A which is 2×$50 which is $100. So the money that was spend by the Raoul is$100.

Question 7.
There are 248 section A season ticket holders and 304 section B season ticket holders at the second concert. How much money was spent by season ticket holders for the second concert?
The money spent by season ticket holders for the second concert is $240. Explanation: Given that there are 248 section A season ticket holders which is 248×$50 =$12,400 and 304 section B season ticket holders at the second concert which is 304×$40 = $12,160. So the money spent by season ticket holders for the second concert is$12,400-$12,160 which is$240.

Lesson Check

Question 8.
Terrance found the product for 9 × 81 like this:
9 × 81 = (9 × 80) + (9 × 1)
= 720 + 9 = 729
Which strategy did he use?
(A) Commutative Property
(B) Associative Property
(C) Distributive Property
(D) halving and doubling
C.

Explanation:
Here, we have used Distributive Property to find the property of 9 × 81.

Question 9.
Eileen multiplied 40 × 88 = 3,520. Which of the following has a product of 3,520?
(A) 80 × 44
(B) 20 × 44
(C) 176 × 80
(D) 176 × 40
A.

Explanation:
Given that Eileen multiplied 40 × 88 = 3,520 and the equation for the product 3,520 is 80 × 44.

Question 10.
The Smith’s are selling some of their extra chairs. They are selling 4 chairs each for $125. How much will the Smith’s make if they sell all the chairs? (A)$500
(B) $400 (C)$425
(D) $575 Answer: A. Explanation: Given that the Smith’s are selling some of their extra chairsand they are selling 4 chairs each for$125 which is $125×4 =$500.

Question 11.
There are 42 straws in a box. Nathan bought 5 boxes. How many straws did Nathan buy?
(A) 220
(B) 110
(C) 210
(D) 120
C.

Explanation:
Given that there are 42 straws in a box and Nathan bought 5 boxes, so the number of straws did Nathan bought is 42×5 which is 210.

Question 12.
Multi-Step The science museum sells dinosaur models to schools and libraries for $107 each. The town library buys 3 dinosaur models. The town elementary school buys 5 models. What is the total cost of the models the town buys? (A)$567
(B) $780 (C)$136
(D) $856 Answer: D. Explanation: Given that the science museum sells dinosaur models to schools and libraries for$107 each and the town library bought 3 dinosaur models which is 3×$107 =$321 and the town elementary school bought 5 models which is 5×$107 =$535. So the total cost of the models the town bought is $321+$535 which is \$856.

Question 13.
Multi-Step Kyle and Karen each bought 5 books of ride tickets at the fair. Each book has 15 tickets. How many tickets did they buy altogether?
(A) 75
(B) 150
(C) 300
(D) 200