Math Study Guide: Topic 1: Number Properties (pages 7-12)

Question 1

What is the “order of operations?”

Answer 1

PEMDAS (aka “Please Excuse My Dear Aunt Sally”)

Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)

Example: 7 - 3 ÷ (5 - 2) x 4 + 2 =

7 - 3 ÷ 3 x 4 + 2 =

7 - 4 + 2

3 + 2 =

5

Question 2

What is the “distributive property?”

Answer 2

The distributive property is used when you multiply a number times a parentheses, and inside that parentheses is either a plus or a minus.

a(b + c) = ab +ac
a(b - c) = ab - ac

Example: 8(4 - 1) =

8 x 4 - 8 x 1 =
32 - 8 =

24

Question 3

What is “factoring?”

Answer 3

“Factoring” is when the distributive property is being used backwards.

ab + ac = a(b + c)

Example: 24 x 71 +24 x 29 =

24(71 + 29) =

24 x 100 =

2,400

Question 4

positive x negative = ?

Answer 4

negative

Example: 3 x -2 = -6

Question 5

positive ÷ negative = ?

Answer 5

negative

Example: 12 ÷ -3 = -4

Question 6

negative x negative = ?

Answer 6

positive

Example: -5 x -4 = 20

Question 7

negative ÷ negative = ?

Answer 7

positive

Example: -18 ÷ -2 = 9

Question 8

Adding a negative is the same as doing what?

Answer 8

subtracting

Example: 2 + -5 =

2 - 5 =

-3

Question 9

Subtracting a negative is the same as doing what?

Answer 9

adding

• Example: 2 - (-5) =*
• 2 + 5 =*
• 7*

Question 10

Which number is larger, -2 or -5?

Answer 10

-2

(whichever number is further to the right on the number line)

Question 11

What is “absolute value?”

Answer 11

It measures the distance from zero on the number line

Absolute value must be positive

Example: -5 and +5 both have an absolute value of 5

Question 12

Even + or - Even = ?

Answer 12

Even

Question 13

Even + or - Odd = ?

Answer 13

Odd

Question 14

Odd + or - Odd = ?

Answer 14

Even

Question 15

Even x Even = ?

Answer 15

Even

Question 16

Odd x Odd = ?

Answer 16

Odd

Question 17

What are “prime numbers?”

Answer 17

Prime numbers are numbers greater than 1 that nothing divides into except themselves and 1

• Example:* 5 is a prime number because it’s divisible only by 5 and 1
• Example:* Six is not a prime number because it’s divisible by 2 and 3 as well as by 6 and 1

Question 18

How do you know if a number is divisible by 5?

Answer 18

If it ends in 5 or 0

Question 19

How do you know if a number is divisible by 3?

Answer 19

A number is divisible by 3 if the sum of the number’s digits is divisible by 3

• Example:* 225 is divisible by 3 because 2 + 2 = 9 (and 9 is divisible by 3)
• Example:* 431 is not divisible by 3 because 4 + 3 + 1 = 8 (and 8 is not divisible by 3)

Question 20

How do you know if a number is divisible by 9?

Answer 20

A number is divisible by 9 if the sum of the digits is a multiple of 9

Question 21

How do you know if a number is divisible by 4?

Answer 21

A number is divisible by 4 if its last two digits are a multiple of 4

Example: 3,316 is divisible by 4 because 16 is divisible by 4

Question 22

In the number 4,213.056789, which digit is in the hundreds place?

Answer 22

2

Question 23

In the number 4,213.056789, which digit is in the hundredths place?

Answer 23

5

Question 24

In the number 4,213.056789, which digit is in the units (ones) place?

Answer 24

3

Question 25

In the number 4,213.056789, which digit is in the *ten thousandths* place?

Answer 25

7

Question 26

In the number 4,213.056789, which digit is in the *tenths* place?

Answer 26

0

Question 27

In the number 4,213.056789, which digit is in the *tens* place?

Answer 27

1

Question 28

In the number 4,213.056789, which digit is in the *thousands* place?

Answer 28

4

Question 29

In the number 4,213.056789, which digit is in the *thousandths* place?

Answer 29

6

Question 30

In the number 4,213.056789, which digit is in the *millionths* place?

Answer 30

9

Question 31

In the number 4,213.056789, which digit is in the *hundred thousandths* place?

Answer 31

8

Question 32

In the number 4,213.056789, which digit is in the *ten thousandths* place?

Answer 32

7

Question 33

What is “expanded notation?”

Answer 33

“Expanded notation” is another way of writing a whole number, by multiplying each digit by the proper power of 10 *Example* Write 4,378 in expanded notation 4 x 1,000 + 3 x 100 + 7 x 10 + 8 (or 8 x 1)

Question 34

How do you write 4,378 “expanded notation” in *exponent* form?

Answer 34

4 x 10³ + 3 x 10² + 7 x 10¹ + 8 (or 8 x 10⁰)

Question 35

What is any number raised to the 0^th power?

Answer 35

1

Question 36

What do you do first when you want to “round” to a certain place? What do you do next? And what's the last thing you do?

Answer 36

Look at the number immediately to the **right** of that place If that number is 5, 6, 7, 8, or 9, then round the place **up** to the next number If that number is 0, 1, 2, 3, or 4, then round keep the place **as is** All the places right of the place become zero

Question 37

When is 4,362.18225 rounded to the nearest hundred?

Answer 37

4,000 3 is in the *hundreds* (not *hundredths!!*) place. The number to the right is 6, so round up, and make the 3 a 4.

Question 38

When is 4,362.18225 rounded to the nearest hundredth?

Answer 38

4,362.18 (or 4,362.18000) 8 is in the *hundredths* (not *hundreds!)* place. The number to the right is 2, so do not round up

Question 39

What is the best way to multiply with decimals?

Answer 39

The best way to multiply with decimals is to pretend the decimal points are not there, and then add them back later *Example:* 0.233 x .41 = 233 x 41 = 9,553 Then add the *five* decimals back to get .09553

Question 40

Divide 43.2 by .06 = ?

Answer 40

Move the decimal point in .06 to the right two spaces, which means you also have to move the decimal point in 43.2 to the right two spaces So, you get 4,320 ÷ 6 = 720

Question 41

What does multiplying a number by 10 do to the decimal point?

Answer 41

Multiplying by 10 moves the decimal point one place to the left

Question 42

What does multiplying a number by 10³do to the decimal point?

Answer 42

Move the decimal point three places to the right Because multiplying a number by 10³ is the same as multiplying it by 1000 or 10 x 10 x 10

Question 43

What is multiplying by a negative power of 10 the same as?

Answer 43

Multiplying by a negative power of 10 is the same as dividing by the same positive power of 10 *Example:* Multiplying a number by 10^-2 is the same as dividing by 10² (or dividing by 100)