Numbers and Fractions Flashcards
Integers
-3,-2,-1,0,1,2,3
Like whole numbers but have negatives. Still no fractions
Whole Numbers
0, 1, 2, 3, …
No negatives or partial numbers like fractions
Rational numbers
Any number that can be written as a fraction except those with zero in the denominator. Includes integers, fractions and whole numbers
p/q: p and q are integers, q is not zero
Irrational numbers
A real number that can’t be written as a simple fraction, no clear ratio(nal)
Some Square roots are irrational
3.14159…=?/?
Decimal goes on forever without repeating
Real numbers
Any rational, irrational, integer or whole number
Choose the correct statement:
A. no rational numbers are integers
B. All irrational numbers are real numbers
C. No irrational numbers are real numbers
D. All integers are whole numbers
B
What are som tasks that students use number lines for?
Counting Math operations Measuring Graphing Estimating
When showing inequalities in a number line, what is the difference between an empty dot and a filled in dot?
Empty dot shows that number is not included in the solution (x>5)
Solid dot shows it is included in solution (x>=5)
Communicative property
ORDER
For multiplication and addition order is not important
4+7=7+4. 8x3=3x8
If you live in a community, it doesn’t matter where, you’re still part if community
Associative property
Grouping not important when adding or multiplying
3 + (4+7)=(3+4)+7
2(83)=(28)3
You spend time with your associates in a group
True or False:
Associative and commutative properties work with subtraction and division?
False. Order and grouping make a big difference while subtracting and dividing
Identity property
Any number plus zero equals that number 4+0=4
Any number times one equals that number 8*1=8
The number wants to be the same; it wants to be itself
Multiplicative property of zero
Any number times 0 is 0
8*0=0
Distributive property
Combines addition/subtraction and multiplication for expanding or simplifying expressions with parenthesis
a(b+c)=ab+ac
a(b-c)=ab-ac
Prime numbers
Have exactly two factors, one and the number itself.
Prime numbers up to 25
2,3,5,7,11,13,17,19,23
Composite numbers
Have more than two factors, but not an infinite number or factors (like zero)
All even numbers except two are composite numbers
Divisibility rules:
2
Numbers divisible by 2 are even or end in zero
Divisibility rules:
3
First find sum of digits. If sum is divisible by 3, then whole number is divisible by three
837
8+3+7=18=3*6
Divisibility rules:
4
If the final two digits of a number greater than 100, than number is divisible by four
1,072
Last two digits 72 are divisible by four, so whole number is divisible by 4
Divisibility rules:
5
If number ends in zero or 5 it is divisible by 5
Divisibility rules:
6
Must be divisible by both 2 and 3, therefore it must be an even number whose sum is divisible by three
Ex: 534
It is even do it’s divisible by 2 and the sum of the digits, 12, is divisible by three so it is divisible by 6
Divisibility rules:
8
Only useful for numbers greater than 1,000. A number divisible by 8 ends with a three-digit number divisible by 8
Ex: 7,488
488 is divisible by 8 and 61, so whole number can be divided by 8
Divisibility rules:
9
Similar to
Rule for 3. Sum of digits must be able to be divided by 9.
Ex: 72,954
7+2+9+5+4=27 which is divisible by 9
What must be in place before adding or subtracting fractions and mixed numbers?
A common denominator
When should you convert mixed numbers to improper fractions?
When multiplying or dividing, but not for addition and subtraction
What is the process for multiplying fractions?
1 convert to improper fraction
- Try to cancel out shared factors (any factors shared in both the denominator and numerator can be cancelled even if not in the same fraction)
- Multiply straight across in both numerator and denominator
- Simplify fraction to express it in its lowest terms
What is the process of dividing fractions?
Same as multiplication, but multiply by the reciprocal (flip fraction upside down)
3/4 ➗ 2/3 = 3/4 x 3/2
10 ➗ 2= 10 x 1/2
