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## Texas Go Math Grade 5 Lesson 2.3 Answer Key Division with 2-Digit Divisors

**Investigate**

**Materials:** base-ten blocks

There are 156 students in the Carville Middle School chorus. The music director wants the students to stand with 12 students in each row for the next concert. How many rows will there be?

A. Use base-ten blocks to model the dividend, 156.

B. Place 2 tens below the hundred to form a rectangle. How many groups of 12 does the rectangle show? How much of the dividend is not shown in this rectangle?

Answer:

When we divide 120 into blocks of ten, there will be 10 blocks of 12.

The dividend that is not shown in the rectangle will be: 36

C. Combine the remaining tens and ones into as many groups of 12 as possible. How many groups of 12 are there?

Answer:

From part (B),

We can observe that

There are remaining 36 blocks after we placed 120 blocks

Now,

We can arrange 36 blocks into 3 groups of 12

Hence, from the above,

We can conclude that

There are 3 groups of 12

D. Place these groups of 12 on the right side of the rectangle to make a larger rectangle.

Answer:

From part A,

There are 10 groups of 12

From part B,

There are 3 groups of 12

So,

The total number of groups of 12 = 10 + 3

= 13 groups of 12

E. The final rectangle shows groups of 12.

So,

There will be 13 rows of 12 students.

**Draw Conclusions**

Question 1.

Explain why you still need to make groups of 12 after Step B.

Answer:

In Step B,

We made 10 groups of 12.

But,

There are 36 remaining blocks

So,

We have to find whether we can make groups of 12 with 36 or not

Hence,

We will still need to make groups of 12 after Step B

Question 2.

Describe how you can use base-ten blocks to find the quotient 176 ÷ 16.

Answer:

The given division expression is: 176 ÷ 16

Now,

Step A:

Divide 176 into 16 base-ten blocks

So,

The 16 ten-base blocks will be equal to 160 and the remainder will be 16

Step B:

Find out whether 16 will be divided into groups of 16

Step C:

We can make 1 group of 16 blocks

Hence, from the above,

We can conclude that

The quotient of 176 ÷ 16 by using the base-ten blocks is: 11

The two sets of groups of 12 that you found in the Investigate are partial quotients. First, you found 10 groups of 12, and then you found 3 more groups of 12. Sometimes you may need to regroup before you can show a partial quotient.

You can use a quick picture to record the partial products.

Divide. 180 ÷ 15

**MODEL** Use base-ten blocks.

STEP 1: Model the dividend, 180, as 1 hundred 8 tens.

Model the first partial quotient by making a rectangle with the hundred and 5 tens. In the Record, cross out the hundred and tens you use.

So,

The rectangle shows 10 groups of 15.

STEP 2: Additional groups of 15 cannot be made without regrouping.

Regroup 1 ten as 10 ones. In the Record, cross out the regrouped ten.

There are now 25 tens and 5 ones.

STEP 3: Decide how many additional groups of 15 can be made with the remaining tens and ones. The number of groups is the second partial quotient.

Make your rectangle larger by including these groups of 15. In the Record, cross out the tens and ones you use.

So,

There are now 12 groups of 15.

**RECORD** Use quick pictures.

Draw the first partial quotient.

Draw the first and second partial quotients.

So,

180 ÷ 15 is 12

**Math Talk**

**Mathematical Processes**

Explain how your model shows the quotient.

Answer:

When we draw a model for the given division expression,

We will draw in the form of partial products

So,

When we add the Partial numbers that are divided, the result will be given the value of the quotient for the given division expression

**Share and Show**

Use the quick picture to divide.

Question 1.

143 ÷ 13

Answer:

The given division expression is: 143 ÷ 13

Now,

By using the model,

Now,

From the above model,

We can observe that

The quotient for the given division expression = 10 + 1

= 11

Hence, from the above,

We can conclude that

The quotient for the given division expression is: 11

**Use base-ten blocks or a quick picture to divide.**

Question 2.

168 ÷ 12

Answer:

The given division expression is: 168 ÷ 12

Now,

By using the model,

Now,

From the above model,

We can observe that

The quotient for the given division expression = 10 + 4

= 14

Hence, from the above,

We can conclude that

The quotient for the given division expression is: 14

Question 3.

187 ÷ 11

Answer:

The given division expression is: 187 ÷ 11

Now,

By using the model,

Now,

From the above model,

We can observe that

The quotient for the given division expression = 10 + 7

= 17

Hence, from the above,

We can conclude that

The quotient for the given division expression is: 17

Question 4.

182 ÷ 13

Answer:

The given division expression is: 182 ÷ 13

Now,

By using the model,

Now,

From the above model,

We can observe that

The quotient for the given division expression = 10 + 4

= 14

Hence, from the above,

We can conclude that

The quotient for the given division expression is: 14

Question 5.

228 ÷ 12

Answer:

The given division expression is: 228 ÷ 12

Now,

By using the model,

Now,

From the above model,

We can observe that

The quotient for the given division expression = 10 + 9

= 19

Hence, from the above,

We can conclude that

The quotient for the given division expression is: 19

**Problem Solving**

The Pony Express used men riding horses to deliver mail between St. Joseph, Missouri, and Sacramento, California, from April 1860 to October 1861. The trail between the cities was approximately 2,000 miles long.

Question 6.

**H.O.T. Multi-Step** Two Pony Express riders each rode part of a 176-mile trip. Each rider rode the same number of miles. They changed horses every 11 miles. How many horses did each rider use?

Answer:

It is given that

The Pony Express used men riding horses to deliver mail between St. Joseph, Missouri, and Sacramento, California, from April 1860 to October 1861. The trail between the cities was approximately 2,000 miles long.

It is also given that

Two Pony Express riders each rode part of a 176-mile trip. Each rider rode the same number of miles. They changed horses every 11 miles.

So,

According to the given information,

The number of horses did each rider used = (The distance traveled by the two Pony Expresses) ÷ (The number of miles the Pony Expresses changed the horses)

= 176 ÷ 11

Now,

By using the Long Division,

Hence, from the above,

We can conclude that

The number of horses did each rider used throughout the total distance is: 16 horses

Question 7.

Suppose a Pony Express rider was paid $192 for 12 weeks of work. If he was paid the same amount each week, how much was he paid for each week of work?

Answer:

It is given that

A Pony Express rider was paid $192 for 12 weeks of work and he was paid the same amount each week

So,

According to the given information,

The amount he paid for each week = (The total amount a rider paid for some weeks) ÷ (The number of weeks)

= $192 ÷ 12

Now,

By using the Long Division,

Hence, from the above,

We can conclude that

The amount a Pony Express Rider paid for each week of work is: $16

Question 8.

**H.O.T. Multi-Step** It took 19 Pony Express riders a total of 11 days 21 hours to ride from St. Joseph to Sacramento. If they all rode the same number of hours, how many hours did each rider ride?

Answer:

It is given that

It took 19 Pony Express riders a total of 11 days 21 hours to ride from St. Joseph to Sacramento and they all rode the same number of hours

Now,

We know that,

1 day = 24 hours

So,

The total number of hours in 11 days = 24 × 11

= 264 hours

So,

The total number of hours did 19 riders took to travel from St. Joseph to Sacramento = 264 + 21

= 285 hours

Now,

The number of hours did each rider took to travel from St. Joseph to sacramento = 285 ÷ 19

Now,

By using the Long Division,

Hence, from the above,

We can conclude that

The number of hours did each rider took to travel from St. Joseph to sacramento is: 15 hours

**Daily Assessment Task**

**Fill in the bubble completely to show your answer.**

Question 9.

**Use Diagrams** A rover brings 144 rock samples back from Mars. The samples will be divided among 12 teams of scientists for analysis. Which quick picture shows the correct division of the samples between the 12 teams?

Answer:

It is given that

A rover brings 144 rock samples back from Mars. The samples will be divided among 12 teams of scientists for analysis

So,

The correct division of the samples between 12 teams = 144 ÷ 12

Hence, from the above,

We can conclude that

The picture that shws the correct division of the samples between 12 teams is:

Question 10.

**Analyze** The Mars rover is going to travel across a crater that is 360 cm (about 12 ft) in diameter. The rover must stop every 15 cm to recharge its batteries. How many times will the rover recharge while it crosses the crater?

(A) 24

(B) 15

(C) 30

(D) 25

Answer:

It is given that

The Mars rover is going to travel across a crater that is 360 cm (about 12 ft) in diameter. The rover must stop every 15 cm to recharge its batteries

Now,

According to the given information,

The number of times will the rover recharge while it crosses the crater = (The distance Mars rover is going to travel) ÷ (The time took by rover torecharge its batteries)

= 360 ÷ 15

Now,

By using the long Division,

Hence, from the above,

We can conclude that

The number of times will the rover recharge while it crosses the crater is:

Question 11.

**Multi-Step** On Monday, the rover traveled 330 cm. On Tuesday, it traveled 180 cm. If the rover stopped every 15 cm to recharge, how many more times did it need to recharge on Monday than on Tuesday?

(A) 24

(B) 22

(C) 12

(D) 10

Answer:

It is given that

On Monday, the rover traveled 330 cm. On Tuesday, it traveled 180 cm. If the rover stopped every 15 cm to recharge

Now,

According to the given information,

The difference between the number of times the rover recharge on Monday and Tuesday = (330 ÷ 15) – (180 ÷ 15)

= 22 – 12

= 10 times

Hence, from the above,

We can conclude that

The difference between the number of times the rover recharge on Monday and Tuesday is:

**Texas Test Prep**

Question 12.

**Analyze** Three Pony Express riders each rode part of a 252-mile trip. If they used a total of 18 horses and rode each horse the same number of miles, how many miles did they ride before replacing each horse?

(A) 54 miles

(B) 14 miles

(C) 84 miles

(D) 42 miles

Answer:

It is given that

Three Pony Express riders each rode part of a 252-mile trip. If they used a total of 18 horses and rode each horse the same number of miles

Now,

According to the given information,

The number of miles the three Pony Express riders rode before replacing each horse = 252 ÷ 18

Now,

By using the Long Division,

Hence, from the above,

We can conclude that

The number of miles the three Pony Express riders rode before replacing each horse is:

### Texas Go Math Grade 5 Lesson 2.3 Homework and Practice Answer Key

**Use base-ten blocks or a quick picture to divide.**

Question 1.

180 ÷ 12

Answer:

The given division expression is: 180 ÷ 12

Now,

By using the model,

Now,

From the above model,

We can observe that

The quotient for the given division expression = 10 + 5

= 15

Hence, from the above,

We can conclude that

The quotient for the given division expression is: 15

Question 2.

216 ÷ 18

Answer:

The given division expression is: 216 ÷ 18

Now,

By using the Model,

Now,

From the above model,

We can observe that

The quotient for the given division expression = 10 + 2

= 12

Hence, from the above,

We can conclude that

The quotient for the given division expression is: 12

Question 3.

224 ÷ 16

Answer:

The given division expression is: 224 ÷ 16

Now,

By using the Model,

Now,

From the above model,

We can observe that

The quotient for the given division expression = 10 + 4

= 14

Hence, from the above,

We can conclude that

The quotient for the given division expression is: 14

Question 4.

176 ÷ 16

Answer:

The given division expression is: 176 ÷ 16

Now,

By using the Model,

Now,

From the above model,

We can observe that

The quotient for the given division expression = 10 + 1

= 11

Hence, from the above,

We can conclude that

The quotient for the given division expression is: 11

**Problem Solving**

Question 5.

Ryan read 145 pages of his book. If he read 29 pages every night, how many nights did it take him to complete the book?

Answer:

It is given that

Ryan read 145 pages of his book and he read 29 pages every night

Now,

According to the given information,

The number of nights did it take Ryan to complete the book = 145 ÷ 29

Now,

By using the Long Division,

Hence, from the above,

We can conclude that

The number of nights did it take Ryan to complete the book is: 5 nights

Question 6.

Mrs. McDonald passed out 189 photos that she had taken during the school year. If each of her 21 students received the same number of photos, how many did each receive?

Answer:

It is given that

Mrs. McDonald passed out 189 photos that she had taken during the school year and each of her 21 students received the same number of photos

Now,

According to the given information,

The number of photos did Mrs.McDonald received = 189 ÷ 21

Now,

By using the Long Division,

Hence, from the above,

We can conclude that

The number of photos did Mrs.McDonald received is: 9 photos

**Lesson Check**

**Fill in the bubble completely to show your answer.**

Question 7.

Susanna made a total of $132 for the school fundraiser. She sold pizza combo meals for $12 each. How many combo meals did Susanna sell?

(A) 10

(B) 11

(C) 13

(D) 12

Answer:

It is given that

Susanna made a total of $132 for the school fundraiser. She sold pizza combo meals for $12 each.

Now,

According to the given information,

The number of combo meals did Susanna sold = $132 ÷ $12

Now,

By using the Long Division,

Hence, from the above,

We can conclude that

The number of combo meals did Susanna sold is:

Question 8.

Carlos’ horse ran around the track a total of 336 times. If the horse ran 21 laps each day, how many days did it take the horse to complete all of the laps?

(A) 20

(B) 16

(C) 18

(D) 12

Answer:

It is given that

Carlos’ horse ran around the track a total of 336 times. If the horse ran 21 laps each day

Now,

According to the given information,

The number of days did it took for the horse to complete all of the laps = 336 ÷ 21

Now,

By using the Long Division,

Hence, from the above,

We can conclude that

The number of days did it took for the horse to complete all of the laps is:

Question 9.

Milos rode his bicycle in a marathon for 154 miles. He took a rest stop every 22 miles. How many rest stops did Milos take during the marathon?

(A) 8

(B) 7

(C) 10

(D) 9

Answer:

It is given that

Milos rode his bicycle in a marathon for 154 miles. He took a rest stop every 22 miles

Now,

According to the given information,

The number of rest stops did Milos took during the marathon = 154 ÷ 22

Now,

By using the Long Division,

Hence, from the above,

We can conclude that

The number of rest stops did Milos took during the marathon is:

Question 10.

There are 325 books on the library wall. There are 13 rows of books, each with an equal number of books. How many books are in each row?

(A) 28

(B) 21

(C) 25

(D) 19

Answer:

It is given that

There are 325 books on the library wall. There are 13 rows of books, each with an equal number of books

Now,

According to the given information,

The number of books in each row = 325 ÷ 13

Now,

By using the Long Division,

Hence, from the above,

We can conclude that

The number of books in each row is:

Question 11.

**Multi-Step** Lilly was paid $308 for 14 weeks of work. If she was paid the same amount each week, how much did she earn after 2 weeks?

(A) $38

(B) $28

(C) $22

(D) $44

Answer:

It is given that

Lilly was paid $308 for 14 weeks of work and she was paid the same amount each week

Now,

According to the given information,

The amount of money earned by Lilly each week = $308 ÷ 14

Now,

By using the Long Division,

So,

The amount of money earned by Lilly in 2 weeks = 2 × $22

= $44

Hence, from the above,

We can conclude that

The amount of money earned by Lilly in 2 weeks is:

Question 12.

**Multi-Step** Manny drove 910 miles during a two-week period. If he drove the same number of miles each day, how many miles had he driven after 5 days?

(A) 182 miles

(B) 250 miles

(C) 650 miles

(D) 325 miles

Answer:

It is given that

Manny drove 910 miles during a two-week period and he drove the same number of miles each day

Now,

We know that,

1 week = 7 days

Now,

According to the given information,

The number of miles did Manny rode each day = 910 ÷ 14

Now,

By using the Long Division,

So,

The number of miles did Manny rode in 5 days = 5 × 65

= 325 miles

Hence, from the above,

We can conclude that

The number of miles did Manny rode in 5 days is: