Download Unit 1 Study Guide

Unit 1 Study Guide
6.NS.2 Fluently divide multi-digit whole numbers using a standard algorithmic approach.
Long Division
*Dividend- the number or decimal that is being divided into equal groups.
*Divisor- the number or decimal that divides the dividend.
*Quotient- the result of the division sentence. Quotients can be whole numbers, decimals or fractions.
Divisible- one number is divisible by the second number when the second number divides “evenly” into the
first number with no remainder. (P. 14)
Divisibility Rules:
Numbers
Rule
2
Digit in the ones column must be a 0, 2, 4, 6, 8
3
Add the digits together. If the sum is a multiple of 3, the number can be divided by 3.
4
Digits in the ones and tens column must be a multiple of 4
5
Digit in the ones column must be a 0 or 5
6
MUST be divisible by both 2 and 3
9
Add the digits together. If the sum is a multiple of 9, the number can be divided by 9.
10
Digit in the ones column must be a 0
*In fourth grade, students learned about divisibility rules of 2, 5, and 10. These rules apply to the digit in the
ONES column.
*In fifth grade, students learned about divisibility rules of 3, 6, and 9. The rules of 3 and 9 are very similar.
Students need to add the sum of the digits together to determine divisibility. To determine the rule of 6, both 2
and 3 must be divisible by the number
6NS.3 Fluently add, subtract, multiply and divide multi-digit decimal numbers using a standard
algorithmic approach.
*Decimal- a number that is written in a system based on multiples of 10.
*Terminating decimal- a decimal quotient with a remainder of zero.
*Repeating decimal- a decimal in which a digit or a group of digits repeats without end.
*A decimal point is used to separate the whole number and the decimal.
Add and subtract decimals
-Line up decimals
-Add zeros so that every number has the same amount of places after the decimal point
-Subtract or add from right to left as you would any other problem but bring the decimal down first.
.23 + 33 + 88.4215 =
88.4215
33.0000
+ .2300
121.6515
5 – 4.27 =
5.00
-4.27
0.73
The whole number has a hidden decimal to the right
Multiply decimals
Steps for multiplying decimals
1. Multiply the problem like they are whole numbers
2. Count how many decimal places (Right) are in BOTH numbers from the problem
3. Move the decimal that many places(Right) in the answer
.18
*Remember decimals do not have to line up before you multiply.
Dividing decimals
Steps to divide decimals
1. Divide the problem like a normal whole number problem
2. Count the decimal places in the DIVISOR and move the decimal that many places in the DIVIDEND.
3. Bring the decimal from the DIVIDEND straight up.
Rounding
-Look at the place value being rounded and circle it
-Look at the number to the right of the place value being rounded.
-If the number is 0-4 the rounded place value stays the same
-If the number is 5-9 the rounded place value goes up
Estimation
-First round the decimals to easier numbers to work with then complete like normal.
.32 + 1.2278 + .15009 + 51.23
-In this case rounding to the tenths place is probably going to give a good estimation of the answer. Below is
how you would round the numbers:
.3 + 1.2 + .2 + 51.2 = 52.9 or about 53 you could also round to the whole numbers:
6.NS.4 Find common factors and multiples using two whole numbers.
a. Compute the greatest common factor (GCF) of two numbers both less than or �equal to 100. b. Compute the least common multiple (LCM) of two numbers both less than or equal to 12.
c. Express sums of two whole numbers, each less than or equal to 100, using the distributive property to
factor out a common factor of the original addends. Factor pairs- two natural numbers other than zero that are multiplied together to produce another number.
(P. 5) List all the factor pairs of 21
__21_
1 x 21
3x7
Factors- two numbers that when multiplied together equal another number. (P. 5)
The #21 has 4 factors 1, 3, 7, 21
CF (Common Factors)
15 and 30:
Write out all the factors of 15 and 30.
15______
1 x 15
3x5
__30__
1 x 30
2 x 15
3 x 10
5x6
The CF of 15 and 30 are 1,3,5,15
Multiples- the product of a given whole number and another whole number. (P. 13)
The multiples of the #8 is 8, 16, 24, 32, 40, 48 and so on
8x1 8x2 8x3 8x4 8x5 8x6
Prime and Composite
*0 and 1 are neither prime nor composite.
* Prime numbers have only two factors. The only way to get to the product is by multiplying 1 times itself.
(Example: 19: only way to get to it is 1 X 19).
*Composite numbers have more than 2 factors. 4 has 3 factors (1, 2, and 4). You can multiply 1x4 and 2x2.
Prime Factorization- the expression of a composite number as a product of prime numbers. This string of
numbers is the so-called answer to a “factor tree” problem.
Example: 2 𝑥 52 = 50
Factor Tree- is a way to organize and help you determine the prime factorization of a number.
Example factor tree for 18
18
2 x 9
2x3x3
18= 2 x 32
2 is a prime number, 9 is a composite number
2 is prime, 3 is prime
The product 18 needs to be written as a prime factorization
Common Multiple- a number that is a multiple of two or more numbers.
GCF (Greatest Common Factor)
Example : 16 and 30:
GCF of 15 and 30 is 15
1.
Write out all the factors of 15.
15______
1 x 15
3x5
2.
Write out all the factors of 30.
______30_______
1 x 30
2 x 15
3 x 10
5x6
The Least Common Multiple (LCM)- is the smallest multiple that two or more numbers have in common.
*The LCM is the product of the greatest power of each prime factor as they appear in any of the prime
factorizations.
Example: Find the LCM of 10 and 6
Write out several multiples of the first number: 10
10, 20, 30, 40, 50, 60, 70, 80, 90
Write out several multiples of the second number: 6 =6, 12, 18, 24, 30, 36, 42, 48, 54, 60
What is the Lowest Multiple that 10 and 6 have in common?
LCM of 10 and 6 is 30
GCF and LCM using Prime Factorization
GCF- use ONLY the base (big) numbers that are for both
numbers and use the smallest shared exponent (floating).
LCM- use ALL the base (big) numbers and the biggest
exponents (floating) even on numbers that are NOT shared.
Using the Distributive Property for Common Factors
Distributive Property is used when you can divide the same number out of two separate numbers
For Example:
42 + 8 = 2 (21+ 4) Explanation: the number in front of the parentheses was 2 in the answer. When I divided
the first number (42) by 2, I got 21 as the answer and when I divided the second number (8) by 2, I got 4 as the
second number left inside the parentheses.
Other Examples
a. 24 + 18 = 2 (12 + 9)
b. 39 + 72 = 3 (13 + 24)
c. 20 + 4 = 4 (5 + 1)
Note: Not every distributive property needs to completely factor out all numbers that can be
divisible into both numbers. Example a. from above could have factored 3 out of (12+9) to
make the whole answer 6(4 +3) as another possible answer.