# Decomposition of Successive Remainders

Examples, solutions to help Grade 5 students learn how to divide three- and four-digit dividends by two-digit divisors resulting in two- and three-digit quotients, reasoning about the decomposition of successive remainders in each place value.

Common Core Standards: 5.NBT.6

New York State Common Core Math Module 2, Grade 5, Lesson 23

Lesson 23 Application Problem
The rectangular room measures 224 square feet. One side of the room is 14 feet long. What is the perimeter of the room?

Note: This Application Problem builds on the previous day’s lesson involving three-digit totals divided by two-digit divisors.It also provides a review of area and is a two-step problem.

Lesson 23 Concept Development
Problem 1: 6,247 ÷ 29
Problem 2: 4,289 ÷ 52
Problem 3: 6,649 ÷ 63
Problem 4: 3,164 ÷ 45

Mr. Riley baked 1,692 chocolate cookies. He sold them in boxes of 36 cookies each. How much money did he collect if he sold them all at \$8 per box?

Lesson 23 Problem Set

1. Divide, then check using multiplication.
a. 4,859 ÷ 23
b. 4,368 ÷ 52

2. 1,092 flowers are arranged into 26 vases, with the same number of flowers in each vase. How many flowers would be needed to fill 130 such vases?
3. The elephant’s water tank holds 2,560 gallons of water. After two weeks, the zookeeper measures and finds that the tank only has 1,934 gallons of water left. If the elephant drinks the same amount of water each day, how many days will a full tank of water last?

Lesson 23 Homework

1. Divide, then check using multiplication.
a. 9,962 ÷ 41

This video shows how to divide larger values using estimation with number decomposition. This video shows how to divide larger values using estimation with number decomposition. 3-digit Quotients

1. Divide, then check using multiplication.
c. 6,691 ÷ 28

Lesson 23 Homework

1. Divide, then check using multiplication.
a. 9,962 ÷ 41
2. A political gathering in South America held 788 people. Each of South America’s 14 countries were equally represented. The remaining people were guests from the United States. How many guests were from the United States?
1. A chocolate company is packaging 32 ounces of caramels into reusable, plastic cups. When a shipping box is filled with these caramel packages, it weighs 49 pounds 8 ounces.
a. How many caramel filled cups are in the box?
b. Use your remainder to find the weight of each plastic cup.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.