Welcome to Math 6

Today’s lesson is “Division”

(Part 1)

KEY VOCABULARY FOR THIS LESSON

Dividend- the number that is divided.

Divisor- the number that you are dividing by.

Quotient- the answer in a division sentence.

KEY VOCABULARY FOR THIS LESSON

Remainder- the portion of the dividend that is not evenly divisible by the divisor.

Algorithm- a set of rules for solving a problem in a finite number of steps.

OBJECTIVE:

Each student will:Use the standard algorithm to

divide whole numbers by 1, 2 and 3 digit divisors.

Express the quotient either as a whole number with remainder or as a decimal.

In this lesson we will divide whole numbers by whole numbers. And we will also divide decimals by whole numbers.

Before you can be effective at long division:

First be able to do recall the basic multiplication and division facts.

Second, understand and use the patterns of multiplying by multiples of 10, 100, 1000, etc.

Third, understand and use the division patterns with multiples of 10, 100, 1000, etc

Third, be familiar with the standard multiplication algorithm.

In the same way that multiplication is like repeated addition, so is division like repeated subtraction.

Now you can practice the standard algorithm.

When you first learned to divide, if a number couldn’t be divided evenly, you learned to end with a “remainder.”

Since you have learned what rational numbers are, you can now learn how to divide numbers that are less than a whole- like fractions and decimals.

A remainder can also be expressed either as a decimal or as a fraction.

At different times, it is appropriate to express the quotient as a decimal, a fraction or a mixed number. (In this lesson, we will use decimals. In our next lesson we will explore how to divide with fractions.)

In some cases the dividend is already a decimal and the quotient must be expressed as a decimal too.

Money is divided into hundredths of a dollar, so money problems should be expressed as a decimal, as in the following example…

6 friends go to lunch to celebrate a birthday. The cost of all 6 meals was $15. What was the average price per person?

Since 15 is not a multiple of 15, the quotient will not be a whole number.

When there are no more digits in the dividend: • Place a decimal

point and bring it up to the quotient

• Add a 0 onto the remainder, and continue dividing.

Add a 0 onto each remainder until the division is exact. In some cases, if the division doesn’t come out exact, round off the quotient to the required number of decimal digits.

Here is another example:

A member of the school track team ran for a total of 179.3 miles in practice over 61 days. About how many miles did he average per day?

GUIDED PRACTICE

The Children’s Playschool took a school field trip. For the safety of the kids, each teacher was responsible for 24 kids. If 336 kids participated, how many teachers participated?

Guided Practice 1

Guided Practice 2

A tiger eats 17 pounds of meat per day. If the tiger caught prey that weighed 357 pounds, how long will the food last?

Guided Practice 3

Paul will pay for his new car in 36 monthly payments. If his car loan is for $19,061, then how much will Paul pay each month? Round your answer to nearest cent.

Guided Practice 4

A tray can hold 234 eggs. If there are 18 rows in a tray, how many columns are there?

Guided Practice 5

Larry worked 15 days for a total of 116.25 hours. How many hours did he average per day?

GUIDED PRACTICE

Solutions

Solutions

The Children’s Playschool took a school field trip. For the safety of the kids, each teacher was responsible for 24 kids. If 336 kids participated, how many teachers participated?

Guided Practice 1

Guided Practice 2

A tiger eats 17 pounds of meat per day. If the tiger caught prey that weighed 357 pounds, how long will the food last?

Solutions

Guided Practice 3

Paul will pay for his new car in 36 monthly payments. If his car loan is for $19,062, then how much will Paul pay each month? Round your answer to nearest cent.

Solutions

A tray can hold 234 eggs. If there are 18 rows in a tray, how many columns are there?

Guided Practice 4

Solutions

Guided Practice 5

Larry worked 15 days for a total of 116.25 hours. How many hours did he average per day?

Solutions

INDEPENDENT PRACTICE

Independent Practice 1

Sarah collected 900 different leaves. She made a collection of books with 25 leaves in each book. How many books of leaves did Sarah make?

Independent Practice 2

725 noise makers are bought for the school’s New Year’s parties. 32 are sent to each class room. How many class rooms are there?

Independent Practice 3

Dance lessons cost $198.75 for 15 classes. What is the fee for one class?

Independent Practice 4

Six cases of paper cost $159.98. How much does one case cost? Round your answer to the nearest cent.

Independent Practice 5

There are 2.54 centimeters in one inch. How many inches are there in 51.78 centimeters? Round your answer to the nearest thousandth.

Independent Practice 6

614 children are sorted into teams of 18 for a game. How many teams are there?

Independent Practice 7

George and Edna eat lunch at a restaurant. The bill is $27.12. If they share the bill equally, how much does each person pay?

Independent Practice 8

How many mini-buses are needed to carry 530 people if the mini-buses carry 22 people each?

INDEPENDENT PRACTICE

Solutions

Independent Practice 1

Sarah collected 900 different leaves. She made a collection of books with 25 leaves in each book. How many books of leaves did Sarah make?

Answer: 25 books of leaves.

Solutions

Independent Practice 2

725 noise makers are bought for the school’s New Year’s parties. 32 are sent to each class room. How many class rooms are there?

Answer: There are 23 class rooms; there would also be 29 noise makers left over.

Solutions

Independent Practice 3

Dance lessons cost $198.75 for 15 classes. What is the fee for one class?

Answer: $13.25

Solutions

Independent Practice 4

Six cases of paper cost $159.98. How much does one case cost? Round your answer to the nearest cent.

Answer: $26.66

Solutions

Independent Practice 5

There are 2.54 centimeters in one inch. How many inches are there in 51.78 centimeters? Round your answer to the nearest hundredth.

Answer: 20.38 inches.

Solutions

Guided Practice 6

Solutions

614 children are sorted into teams of 18 for a game. How many teams are there?

Answer: 34 teams, but there are two extra children.

Independent Practice 7

George and Edna eat lunch at a restaurant. The bill is $27.12. If they share the bill equally, how much does each person pay?

Answer: $13.56 each

Solutions

Independent Practice 8

How many mini-buses are needed to carry 530 people if the mini-buses carry 22 people each?

Answer: 25 mini-buses.

(The last bus would have only two passengers.)

Solutions

1. Complete the “Green Drink Division” Problem-Solver Page.

Assignments:

Conclusion:

When dividing, be sure you understand what is the best way to express your answer. Make sure you know what it means. This is the essence of communicating in math.

Conclusion:

In our next lesson we will explore how to use a fraction to express the quotient.

Until then, enjoy the assignments. And be sure to finish them all before starting Division Part 2.