Chapter 3 Study Guide & Practice ProblemsMultiplying Whole NumbersContents1.Multiplication as Repeated Addition22.Properties of Multiplication33.Multiplying One-Digit Numbers by One-Digit Numbers (Times Tables 0-9)44.Multiplying Two-Digit Numbers by One-Digit Numbers65.Multiplying Three-or-More-Digit Numbers by One-Digit Numbers76.Multiplying Two-Digit by Two-Digit Numbers87.Multiplying Three-or-More-Digit Numbers98.Multiplying by Multiples of 10119.Multiplication Word Problems1210.Extra Credit14

1) Multiplication as Repeated Addition

Multiplication and addition are related a multiplication equation is just a shorter way of saying how many times youre adding the same number.Example:PictureAdditionMultiplication

5 + 5 + 5 = 15

How many times did we add 5? 3 times!5 x 3 = 15

Sample test questions:

1) Write 6 x 7 = 56 as two different addition problems: a. ________________________________________________________

b. _______________________________________________________________________

2) Write 8 + 8 + 8 + 8 + 8 + 8 = 48 as a multiplication problem: _________________________________

3) Word Problem:

Meiras bookshelf has 4 shelves. Each shelf can hold 7 books.How many books can her entire bookshelf hold?

Draw a pictureWrite as an addition problem:

Write as a multiplication problem:

2) Properties of Multiplication

The numbers youre multiplying are called factors.The answer to a multiplication problem is the product.

Identity Property: Any number times one is that same number. Example: 29 x 1 = 29 Hint: Identity is who you are the number keeps its identity. Zero Property: Any number times zero equals zero. Example: 6 x 0 = 0 Commutative Property: If you change the order of the factors, the product stays the same. Example: 4 x 7 = 7 x 4 Hint: Commute = back and forth Associative Property: If you group the factors differently in parentheses, the product stays the same. Example: 3 x (2 x 8) = (3 x 2) x 8 Hint: Association = a group of peopleSample test questions:Fill in the blanks from the word bank below: 1) If you change the order of the __________________, the product stays the same.

2) 5 x (2 x 6) = (5 x 2) x 6 is an example of the _____________________________.

3) Zero multiplied by any other number will always have a __________________ equal to zero.Word Bank

differenceaddendsfactors

Identity PropertyCommutative PropertyAssociative Property

productexponentsum

3) Multiplying One-Digit Numbers by One-Digit Numbers (Times Tables 0-9)Sample test questions:6 x 7 = _______

9 x 2 = _______3 x 8 = ______

8 x 5 = _______

4 x 7 = _______2 x 6 = ______

Multiply the Numbers in the Middle Wheel by the Center Number4) Multiplying Two-Digit Numbers by One-Digit Numbers

Example:1

42

x8

336

1) Multiply the ones columns: 2 x 8 = 16 Write the 6 in the ones column of the answer and carry the 1 to the tens column2) Multiply the tens column: 4 x 8 = 32 Remember to add the 1 that you carried! So you really have 33 tens3) Write 33 in the tens and hundreds column of the answer. Important tip: remember to line up your place value columns properly!

Sample test questions:

95

x4

76

x2

13

x3

5) Multiplying Three-or-More-Digit Numbers by One-Digit Numbers

Example:2

207

x4

828

1) Multiply the ones columns: 7 x 4 = 28 Write the 8 in the ones column of the answer and carry the 2 to the tens column2) Multiply the tens column: 0 x 3 = 0 Remember to add the 2 that you carried! So you really have 2 tens. Write 2 in the tens column of the answer3) Multiply the hundreds column: 2 x 4 = 8 Write 8 in the hundreds column of the answer

Sample test questions:

5,086

x3

749

x8

6) Multiplying Two-Digit by Two-Digit Numbers

Example:

52

x34

208

+1,56

1,768

1) Multiply 52 by the ones column: 52 x 452

x4

208

2) Multiply 52 by the tens column: 52 x 3 Remember to put a smiley face zero in the ones column to push everything over into the proper place value columns52

x3

1,560

3) Add the two partial products together to get the final and total product:208

+1,560

1,768

Sample test questions:

4537

x92x61

7) Multiplying Three-or-More-Digit NumbersIts just like multiplying by two-digit numbers, but longer!

Example:

109

x432

218

+3,27

+43,6

47,088

1) Multiply 109 by the ones column: 109 x 21

109

x2

218

2) Multiply 109 by the tens column: 109 x 3Remember to put a smiley face zero in the ones column to push everything over into the proper place value columns2

109

x3

3,27

3) Multiply 109 by the hundreds column: 109 x 4This time there are two smiley face zeroes to push everything over into the proper place value columns the ones and tens places are filled with zeroes3

109

x4

43,6

4) Add the three partial products together to get the final and total product:1

218

+3,270

+43,600

47,088

Sample test questions: 812x 241

395x 76

8) Multiplying by Multiples of 10

THREE STEPS:1) Count and circle the zeroes at the end of the factors2) Do the multiplication without the zeroes3) Add the zeroes back to the product

Example:80,100x 201,602,000

1) Count and circle the zeroes There are three zeroes altogether at the end of the factors Remember: DO NOT count the zeroes in the middle of a factor!2) Multiply without the zeroes: 801 x 23) Add the three zeroes back at the end of the product

Sample test questions: 5,000x 4,000 3,900x 300

9) Multiplication Word Problems

Examples:

Use the space in this column to write out & solve each problem. Make sure to copy your final answer to the column on the left.

There are 24 hours in one day.There are 7 days in one week.

How many hours are in one week?

168 hours

2 24x 7168

Check with addition: 2 .(Sunday) 24(Monday) + 24(Tuesday) + 24(Wednesday) + 24(Thursday) + 24(Friday) + 24(Shabbos) + 24168

Tari used 1,134 feet of yarn to knit a winter hat. Esther used 8 times as much yarn to knit a sweater.

How many feet of yarn did Esther use?

9,072 feet of yarn

1,134x 8

Sample test questions:

Use the space in this column to write out & solve each problem. Make sure to copy your final answer to the column on the left.

1) Sara is buying tiny tap shoes for her amazing dancing pet spiders.

Each spider has 8 legs.

Sara has 14 pet spiders.

How many shoes will she need to buy?

____________________________

2) There are 60 seconds in a minute.There are 60 minutes in an hour.

How many seconds are in 2 hours?

_____________________________

3) The distance from the Sun to the Earth is 92,960,000 miles.

Jupiter is about 5 times farther away from the Sun than the Earth.

What is the distance from the Sun to Jupiter?

_______________________________

10) Extra Credit1) Introduction to Exponents

An exponent shows how many times you are multiplying the same number times itself.Example:Addition FormMultiplication FormExponent FormAll have the same STANDARD FORM

(2 + 2)+(2 + 2)2 x 2 x 223

2 + 2 + 2 + 2 = 8

2 x 2 x 2 = 8

23 = 8

Base the number youre multiplying Exponent the number of times youre multiplying it by itself

3 + 3 + 33 x 3323 + 3 + 3 = 93 x 3 = 932 = 9

Can I write 6 x 4 as an exponent? No, because youre not multiplying the number by itself!Sample test questions:1) Write 7 x 7 x 7 x 7 x 7 in exponent form: __________________________________

2) Write 84 in multiplication form: _________________________________________

3) Find the standard form of 53 : __________________________________________

II. The Lattice Method of Multiplication:

Example: 14 x 56 = ?