a. What multiplication equation can you use to solve 345 4 15?
b. Multiply 15 by multiples of 10. Fill in the blanks.
15 3 10 5 15 3 20 5 15 3 30 5
c. Now estimate the quotient. The quotient will be between which two tens?
d. If 15 3 20 5 300, what number is left after you subtract this product from 345?
e. Divide what is left by 15. 4 15 5
f. Use the information above to find 345 4 15. Explain your thinking.
There are 345 fifth graders enrolled at Wilson Middle School and 15 fifth-grade classrooms. How many students are in each class if each class has the same number of students?
In the last lesson, you learned how to find products of two- and three-digit factors. Now you will learn how to divide with two-digit divisors.
On the previous page, you used the relationship between multiplication and division along with properties of operations to divide.
You can also use an area model to show division. It is similar to an area model for multiplication. You can think of division as finding a missing factor. The dividend is the product, the divisor is the known factor, and the quotient is the unknown factor.
The area model shows 345 4 15.
20 31
(15 3 3 5 45)(15 3 20 5 300)
452 45
045
15 345
?
15 3452 300
5 23
Start with the greatest place and find the quotient place by place. On the previous page, you estimated the quotient to be between 20 and 30. So, 20 is the greatest ten that can be in the quotient.
• Start by multiplying 15 by 20.
• Subtract the product from the dividend, 345.
• Write the difference, 45, in the next section of the model.
• Think: 15 3 ? 5 45. Multiply 15 by 3 and subtract this product from 45.
• The difference is 0, so there is nothing left to divide.
Reflect1 How is dividing with an area model similar to multiplying with an area model?
Connect It Now you will record the calculations from the model as partial quotients.
2 How many hundreds are in the dividend?
How many groups of 12 are in 600?
This partial quotient is written above the bar.
What equation in the area model shows this?
3 Why is 600 subtracted from 624?
4 How does the area model relate to finding the second partial quotient?
5 Explain how to use the partial quotients to find 624 4 12.
6 Describe how to divide using partial quotients.
Try It Use what you just learned about dividing by a two-digit divisor to solve these problems. Show your work on a separate sheet of paper.
7 An elementary school has 1,134 seeds. The seeds will be planted in 27 rows. Each row will have the same number of seeds. How many seeds will be planted
in each row?
8 Nathan writes an essay with a total of 583 words. Every line of his essay has 11 words.
Pair/ShareExplain how to check the answer to a division problem.
What numbers can I use to estimate the quotient?
What will be the greatest place in the quotient?
10 Each student needs 35 craft sticks for an art project. The art teacher has 7,140 craft sticks. How many students can get crafts sticks from the teacher?
Show your work.
Solution
11 Harrison creates balloon animals for different events. He has 6,440 balloons. He wants to use the same number of balloons for each of 28 events. How many balloons can Harrison use at each event? Circle the letter of the correct answer.
A 23
B 203
C 230
D 2,030
Tina chose A as the correct answer. How did she get that answer?
1 Which equation can NOT be represented by the model below?
5,96442
?
A 5,964 2 ? 5 42
B 5,964 4 ? 5 42
C 42 3 ? 5 5,964
D 5,964 4 42 5 ?
2 Vera makes a table to help solve the problem 672 4 16. Which is the best estimate of the quotient?
10 20 30 40 50 60
160 320 480 640 800 960
A a number between 30 and 40
B a number close to 40
C about 52
D a number between 50 and 60
3 Use the grid to draw a rectangle with an area of 1,125 square units and a side of 25 units.
0 10 20 30 40 50 60
10
20
30
40
50
4 Lisa’s camera has 2,048 megabytes of memory for storing pictures. She has already used half this amount. A high-quality picture uses 16 megabytes of memory. How many high-quality pictures can Lisa store with the remaining memory?
Go back and see what you can check off on the Self Check on page 1.
5 Mr. Kovich writes the problem 32 3 n 5 1,696 on the board. Write a division equation that can be used to find the value of the triangle, and then find the value of the triangle.
Show your work.
Solution
6 Mr. Sullivan is organizing teams for the middle school’s annual field day. There are eight classes at the school and 21 students in each class.
Part A What is the total number of students at the school?
Answer students
Part B Mr. Sullivan wants to have 12 students on each team. How many teams will there be?
Answer teams
Part C How many fewer students will be on each team if he decides to have 24 teams? Explain your answer using diagrams, pictures, mathematical expressions, and/or words.
