Math Study Guide: Topic 1: Number Properties (pages 7-12) Flashcards
What is the “order of operations?”
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
What is the “distributive property?”
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
What is “factoring?”
“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
positive x negative = ?
negative
Example: 3 x -2 = -6
positive ÷ negative = ?
negative
Example: 12 ÷ -3 = -4
negative x negative = ?
positive
Example: -5 x -4 = 20
negative ÷ negative = ?
positive
Example: -18 ÷ -2 = 9
Adding a negative is the same as doing what?
subtracting
Example: 2 + -5 =
2 - 5 =
-3
Subtracting a negative is the same as doing what?
adding
- Example: 2 - (-5) =*
- 2 + 5 =*
- 7*
Which number is larger, -2 or -5?
-2
(whichever number is further to the right on the number line)
What is “absolute value?”
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
Even + or - Even = ?
Even
Even + or - Odd = ?
Odd
Odd + or - Odd = ?
Even
Even x Even = ?
Even
Odd x Odd = ?
Odd
What are “prime numbers?”
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
How do you know if a number is divisible by 5?
If it ends in 5 or 0
How do you know if a number is divisible by 3?
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)
How do you know if a number is divisible by 9?
A number is divisible by 9 if the sum of the digits is a multiple of 9
How do you know if a number is divisible by 4?
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
In the number 4,213.056789, which digit is in the hundreds place?
2
In the number 4,213.056789, which digit is in the hundredths place?
5
In the number 4,213.056789, which digit is in the units (ones) place?
3
In the number 4,213.056789, which digit is in the ten thousandths place?
7
In the number 4,213.056789, which digit is in the tenths place?
0
In the number 4,213.056789, which digit is in the tens place?
1
In the number 4,213.056789, which digit is in the thousands place?
4
In the number 4,213.056789, which digit is in the thousandths place?
6
In the number 4,213.056789, which digit is in the millionths place?
9
In the number 4,213.056789, which digit is in the hundred thousandths place?
8
In the number 4,213.056789, which digit is in the ten thousandths place?
7
What is “expanded notation?”
“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)
How do you write 4,378 “expanded notation” in exponent form?
4 x 103 + 3 x 102 + 7 x 101 + 8 (or 8 x 100)
What is any number raised to the 0th power?
1
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?
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
When is 4,362.18225 rounded to the nearest hundred?
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.
When is 4,362.18225 rounded to the nearest hundredth?
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
What is the best way to multiply with decimals?
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
Divide 43.2 by .06 = ?
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
What does multiplying a number by 10 do to the decimal point?
Multiplying by 10 moves the decimal point one place to the left
What does multiplying a number by 103do to the decimal point?
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
What is multiplying by a negative power of 10 the same as?
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)
