Core Focus on Decimals& Fractions

Dividing by 1-Digit Numbers

Lesson 2.3

Warm-Up1. 32 × 5 =

2. 21 × __ = 84

3. Maria split 20 cookies evenly on plates4 for her friends. How many cookies dideach friend get?

4. 8 × 4 = 32. What does 32 ÷ 4 equal?

160

4

5 cookies

8

Dividing by 1-Digit NumbersFind quotients of expressions where whole numbers are divided by 1-digit whole numbers including remainders.

Lesson 2.3

DividendThe number you are dividing.

DivisorThe number you are dividing by.

QuotientThe answer to a division problem.

Vocabulary

Dividend

Divisor

Quotient = 24

24 48 ÷ 2 = 24 or 2 48

Taylor is making necklaces for 4 people. She wants each necklace to have the same number of beads of each color. Listed below are the beads Taylor has.

52 red beads 76 white beads 48 brown beads68 black beads 64 clear beads 80 blue beads

Step 1 Set out 52 Base-Ten Blocks to model the 52 red beads.

5 tens sticks = 50 2 ones cubes = 2 50 + 2 = 52

Explore! Beaded Necklaces

Explore! Beaded Necklaces

Step 2 Separate the 5 tens sticks into 4 piles to show the 4 necklaces Taylor is making.

Extra stick

Step 3 Trade the extra tens stick for 10 ones cubes. Add these to the 2 ones cubes you had to start with.

= + =

1 ten stick = 10 ones 10 ones + 2 ones = 12 ones

Explore! Beaded Necklaces

Step 4 Separate the 12 ones cubes into the 4 piles to show the 4 necklaces Taylor is making.

Each necklace will have 13 red beads.

Explore! Beaded Necklaces

Step 5 Use Steps 1-4 and Base-Ten Blocks to figure out how many...

a. white beads Taylor will have for each necklace.b. brown beads Taylor will have for each necklace.c. black beads Taylor will have for each necklace.d. clear beads Taylor will have for each necklace.e. blue beads Taylor will have for each necklace.

Explore! Beaded Necklaces

Example 1

What is the quotient of 58 ÷ 2?

DIVIDE: Begin division with the digit in the largest place value in the dividend (58). 5 ÷ 2

MULTIPLY: How many times can the divisor go into the number without going over?2 × ____ = ____ (a number close to 5) 2 × 2 = 4.

Write a 2 in the tens place of the quotient.Write the number 4 below the 5.

DIVIDE – MULTIPLY – SUBTRACT – DROP DOWN − REPEAT

2

4

Example 1 Continued…

What is the quotient of 58 2?

SUBTRACT: Subtract 5 – 4 = 1. Write 1 below the number 4 in the tens column. Make sure your partial difference (1) is less than your divisor (2). If it is not, a mistake has been made.

DROP DOWN: Bring the next number in the dividend (8) down with the partial difference and keep the 8 in the ones column.

2

– 41

DIVIDE – MULTIPLY – SUBTRACT – DROP DOWN − REPEAT

8

Example 1 Continued…

What is the quotient of 58 2?

REPEAT:1. Divide: 18 ÷ 2.2. Multiply: 2 × ____ = ____

(18 or a number close to 18) 2 × 9 = 18.3. Subtract: 18 – 18 = 0.4. Drop Down: When the last partial difference is 0,

the divisor divides evenly into the dividend.

58 ÷ 2 = 29

DIVIDE – MULTIPLY – SUBTRACT – DROP DOWN − REPEAT

2

– 41 8

9

– 1 80

CHECK YOUR ANSWER.Use the relationship between multiplication and division.58 2 = 29 so 29 2 = 58

VocabularyRemainderThe number that is left over when the division problem is completed. It is always written after the whole number in the quotient. It can be written with an R for remainder or as a fraction.

Good to Know! Sometimes it makes more sense to write the remainder as a

fraction, especially when working with measurements. Example:325 inches 4 = 81 R1 or . The measurement inches makes more sense in this situation than 81 R1.

When writing a remainder as a fraction, put the remainder over the divisor.

4181 4

181

FractionA number that represents part of a whole number. It is written .

numeratordenominator

Example 2

DIVIDE: Begin division with the digit in the largest place value in the dividend (395). There are 0 groups of 8 in the number 3. Place a 0 in the box above 3 in the hundreds column of the quotient. How many times does 8 divide into 39 without going over?

MULTIPLY: 8 × 4 = 32 (a number close to 39). Write the factor (4) in the quotient above the 9 in the tens column. Write the product (32) on the line below 39.

Terri made 395 chocolate cake pops for her catering business. She can put them into groups of 8 in jars to decorate tables at a party. How many jars will she need?

8 3 9 5 – 3 2

0 4

Example 2 Continued…

SUBTRACT: Subtract 39 – 32 = 7. Write the difference (7) below the number 32. Make sure your partial difference (7) is less than your divisor (8). If it is not, a mistake has been made.

DROP DOWN: Bring the next number (5) in the dividend down to the right of the partial difference in the ones column.

8 3 9 5 – 3 2

7

0 4

Terri made 395 chocolate cake pops for her catering business. She can put them into groups of 8 in jars to decorate tables at a party. How many jars will she need?

5

Example 2 Continued…

REPEAT:1. Divide 75 by 8.2. Multiply 8 9 = 72. The factor (9) goes in the

quotient above the 5 (ones column).3. Subtract the answers from 75. (75 – 72 = 3).4. Drop Down: Nothing to drop down from

dividend.5. The remainder is written after the whole

number part of the quotient as R3.

Terri needs 49 jars for her cake pops.She will have 3 cake pops left over.

8 3 9 5 – 3 2

7

0 4

Terri made 395 chocolate cake pops for her catering business. She can put them into groups of 8 in jars to decorate tables at a party. How many jars will she need?

5

9

– 7 23

R3

It makes sense to write this remainder as R3 because there

are 3 cake pops left after Terri is finished arranging them in jars.Always check your answer

by using multiplication.

If 395 8 = 49 R3, then49 8 + 3 = 395.

Communication PromptWhat are some situations where remainders might be written as fractions?

Exit Problems1. What is 426 ÷ 6?

2. Terry bought 211 inches of fabric. She cut it into 4 equal lengths. How many inches long will each piece be?

3. Jarrod has 92 maple trees to set out at his nursery.He wants to put them in 8 equal rows.

a. How many maple trees will be in each row?

b. How many maple trees will be left over?

71

Each piece of fabric will be52 inches long.

11 trees

4 trees

34