Chapter 4A Study Guide & Practice Problems

Division with 1-Digit Divisors

Contents1) Fact Families....................................................................................................................................2

2) Division Vocabulary.........................................................................................................................2

3) Division Notation.............................................................................................................................3

4) Setting up Division Word Problems.................................................................................................4

5) Multi-Step Division (“Long Division”) with a 1-Digit Divisor.............................................................6

6) Zeroes in the Quotient.....................................................................................................................8

7) Divisibility......................................................................................................................................11

8) Divisibility Rules.............................................................................................................................12

The test corresponds to the following material from the enVisionMATH textbook:

Lessons 4-3 (p. 88-89), 4-4 (p. 90-92), 4-5 (p. 94-95), 4-6 (p. 98-100) and part of 4-7 (p. 102-103)

Concepts we have already learned but will be on the next test include: finding ALL the factors of a number (“rainbow partners”), and prime and composite numbers.

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1) Fact FamiliesDivision is the inverse of multiplication. The same numbers from a multiplication problem can be rearranged to express a division fact.

So for this test you should be prepared to know your times tables 0-9 forwards and backwards!

Example:4, 7 and 28 make a “fact family”

Multiplication:4×7=287×4=28

Division:28÷4=728÷7=4

Sample test question:Write 4 math facts using the numbers 8, 9 and 72:

______________________________________________

____________________________________________

2) Division Vocabulary

There are four parts of a division problem: Dividend: what you are dividing Divisor: the number you are dividing by Quotient: the answer; i.e. the result after dividing Remainder: If the dividend cannot be divided evenly, there will be something left over.

Sample test questions:

1) True or False: The remainder in a division problem can never be bigger than the divisor.a) True b) False

2) Fill in the blanks in the sentence below using the words from the word bank:You can check your division by multiplying the divisor by the _________________ then adding the ____________________. If you get the ___________________, then it’s correct!

a) Remainder b) Dividend c) Quotient

3) Division Notation

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We learned THREE different ways to write out a division problem:

dividend ÷divisor=quotient quotient

divisor dividend

dividenddivisor

=quotient

Example:

16÷2=88

2 16162

=8

In each of the different notations above, 16 is the dividend, 2 is the divisor, and 8 is the quotient.

Sample test questions:

Label the dividend, divisor and quotient on the division problems below:

35÷5=7

Change from one division notation to another:

11÷2=5 R1

7 . 9 ) 63

❑❑=¿

4) Setting up Division Word Problems

Read the problem carefully to figure out what you’re dividing (i.e. the dividend), what you’re dividing it by (i.e. the divisor), so that you can solve for the answer (i.e. the quotient).

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Example A:

Gitty collected 29 eggs and is putting them into cartons. She can fit 6 eggs into each carton. How many cartons will Gitty need?

Draw a picture: What are the parts of the problem?

Dividend: 29 eggsDivisor: 6 eggs per cartonQuotient: 4 R5

Answer: 5 cartons (though the last carton won’t be completely full – it will only have 5 eggs inside, not 6)

Write the problem in division notation:

Check answer with multiplication:(6×4 )+5=29

Example 2:

Miriam got a box of 24 fancy chocolates for her birthday. If she eats 3 chocolates per day, how many days will the box last before the chocolates are all gone?

What are the parts of the problem? Write in division notation:

Dividend: 24 chocolatesDivisor: 3 chocolates per dayQuotient: 8 days

Check for reasonableness (this time using repeated subtraction):Start with 24 chocolates. Day 1: eat 3; 21 left. Day 2: eat 3; 18 left. Day 3: eat 3, 15 left. Day 4: eat 3, 12 left. Day 5: eat 3, 9 left. Day 6: eat 3, 6 left. Day 7: eat 3, 3 left. Day 8: eat 3, 0 left.Yes! 8 days to finish the box!

Sample test questions:

Show your work:

The fifth grade is going on a field trip. There are 47

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students altogether, and each van has room for 7

students.

How many vans will they need to take?

___________________________

Check answer with multiplication:

Show your work:

There are 8 slices of pizza in one pie. How many

pies will I need to buy to feed 70 people?

___________________________

Check answer with multiplication:

5) Multi-Step Division (“Long Division”) with a 1-Digit Divisor

Remember the steps of long division:

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Example:

1 4 1 R3

4 ) 5 6 7 - 4

1 6

- 1 6

0 7

- 4

3

11 4 1x 45 6 4

CHECK YOUR ANSWER:

Quotient x divisor141 x 4 = 564

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+ 35 6 7 Now add remainder:

564 + 3 = 567

YES!

Sample test questions:

2 ) 9 3 4 7 ) 8 5 9

6) Zeroes in the Quotient

Sometimes you may end up with zeroes in the quotient, but don’t let it throw you off! Just keep following the same steps as before.

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Example:

0 6 0 3 R0

5 ) 3 0 1 5- 0 3 0- 3 0

0 1- 0 1 5- 1 5

0

On Mrs. Forgy’s math tests, you do not have to start the quotient with a zero if the divisor doesn’t go into the first digit of the dividend. (i.e. you could just write 603)

And you don’t have to specify R0 if there is no remainder.

HOWEVER I find that both are helpful habits to make sure you follow the procedure step-by-step.

Sample test questions:

6 ) 4 2 3 8 ) 4 0 0

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2 ) 2, 1 3 5 9 ) 3 6 8 1

Sample test questions:

Show your work:

Aliza has 373 Chanuka Dollars, and all of them are

purple $1 bills.

She wants to exchange as many as possible for

pink $5 bills.

After the exchange, how many $5 bills will she

have?

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___________________________

How many $1 bills will she have left?

___________________________

Check answer with multiplication:

Show your work:

Nechama and Esther are helping sort shoes at a

gemach. They count 618 individual shoes all

together.

How many pairs of shoes did they sort?

(hint: 1 pair = 2 shoes)

___________________________

Check answer with multiplication:

7) Divisibility

A number is divisible by another number if you can divide and get no remainder.

Examples:

Is 23 divisible by 7?

3 R27 ) 2 3

- 2 12

Another way to visualize it:

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2

3

4

5

6

7

8

9

10

11

12

13

14

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There is a remainder,

so 23 is not divisible by 7.

15 16 17 18 19 20 21

22

23

I put 23 stars into rows, with 7 in each row.2 stars were left over.

So 23 is not divisible by 7.

Is 16 divisible by 8?

28 ) 1 6

- 1 60

There is no remainder,

so 16 is divisible by 8

Another way to visualize it:

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2

3

4

5

6

7

8

9

10

11

12

13

14

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16

I put 16 diamonds into rows, with 8 in each row.

So 16 IS divisible by 8.

Sample test question:

Draw an array of dots below to show if 13 is divisible by 4 (that is, if 4 goes into 13 evenly):

Is 13 divisible by 4? Circle: YES / NO

8) Divisibility Rules

You could always check if a number is divisible by another number by actually doing the division and checking if you get a remainder.

But here are some shortcuts so you can check the divisibility of larger numbers much faster, and without having to actually do the division:

Divisibility Rule

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1Every number is divisible by one!

2The last digit of the number is even (0, 2, 4, 6, 8)

3The sum of the digits of the number is divisible by 3

4The last two digits make a number that is divisible by 4

5The last digit of the number is 0 or 5

6The number is divisible by BOTH 2 and 3

9The sum of the digits is divisible by 9

10The last digit is 0

Example:

Which of the above numbers go evenly into 450?

YES 1: because every number is divisible by 1 YES 2: because the last digit is 0 (i.e. 450 is an even number) YES 3: because the sum of the digits (4 + 5 + 0 = 9) is divisible by 3 NO 4: because 4 doesn’t go evenly into the last two digits of the number (50÷4=12 R2) YES 5: because the last digit of the number is 0 YES 6: because we already saw the number is divisible by BOTH 2 and 3 YES 9: because the sum of the digits (4 + 5 + 0 = 9) is divisible by 9 YES 10: because the last digit is 0

Sample test questions:

1) True or False: 522 is divisible by 6.a) True b) False

2) Which of the numbers below is divisible by BOTH 5 and 9?a) 505 b) 963 c) 720

3) A number is divisible by another number if you can divide and get no ________________________.a) remainder b) sum c) quotient

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4) The divisibility rules say that we only use the digital ____________ when checking if a number is divisible by 3 or 9.

a) difference b) sum c) product

5) This number is a factor of all other numbers.a) 1 b) 0 c) 2

Match each factor to its divisibility rule:

Divisibility Rule

1____ The sum of the digits is divisible by 9

2____ The last digit of the number is 0 or 5

3____ The last digit is 0

4____ The sum of the digits of the number is divisible by 3

5____ Every number is divisible by this number

6____ The last two digits make a number that is divisible by 4

9____ The number is divisible by BOTH 2 and 3

10 ____ The last digit of the number is even (0, 2, 4, 6, 8)

Extra Credit: Write two different 3-digit numbers that are divisible by both 2 and 9.

______________________ ______________________

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