Arithmetic and fractions Flashcards
What does “number” could mean?
Real numbers: positive, negative, zero, fraction, decimal. Zero is the only number netiher positive or negative
Integer
Include all positive & negative numbers that are not fraction.
Which are the first positive integers?
1, 2, 3, 4, 5…
Result of addition
sum
Result of subtraction
difference
Result of multiplication
product
Result of division
quotient
Mental math: addition of two digits
Treat digits separately
∆ 37 + 56 = (30 + 7) + (50 + 6 ) = 80 + 13 = 93
Mental math: subtraction of two digits
We can simplify subtraction by adding the same numer to both terms
∆ 82 - 47 = ( 82 + 3 ) - ( 47 + 3 ) 85 - 50 = 35
Absolute value on number line
Distance of number from origin
| x - 5 | = distance of x from +5
| x + 3 | = distance of x from -3
| x -1 | > 4 equals x < -3 or x >5
x | = distance of x from origin
Order of operations
- G rouping symbols
- E xponents Multiplication &
- D ivision
- A ddition &
- S ubtraction
Be careful when translating to plain text (calculator text ie)
Multiplication and division are at the same level
Nested group symbols () and []: work from inside out
Decimals equivalent notation
Represent negative powers of 10
Operations with decimals
- Addition and subtraction: vertically
- Multiplication: count decimal digits and add them, multiply, place numer of decimal digits
- Power: same as multiplication
- Divide: slide decimal point to right to create whole number, and divide
Image: good hack!
Round to any decimal place
When you are asked to round to a place, look only at the digit in the next place to the right.
∆ 65,_5_35 rounded to the nearest thousand is 66,000, you only looked at the 5 and that0s why you round up.
DO NOT DOUBLE ROUND
Is 0 an integer?
It is. Neither positive or negative.
Is 0 even or odd?
Even
Is 0 positive or negative?
Neither
Dies “non negative” include 0?
Yes: 0, 1, 2, 3, 4…
Prime numbers principal characteristic
Have only 2 factors: itself and 1
Prime numbers from 1-100
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Is 1 a prime number?
No. It has only one factor.
What are the prime even numbers?
Only 2
factors facts
If A * B = C
A and B are factors of C
- 1 is a factor of every positive integer
- Every integer is a factor of itself
____________
If you divide an integer C by another integer B, and the result is another integer (remainder 0), then B is a factor of C.
divisor facts
If C/A = B (B integer)
A is a divisor of C, because it divides evenly into C.
Everu factor is a divisor, every divisor is a factor
multiple
Take any positive integer and multiply it by any whole number, the result is a multiple of the original number.
How to know if a numer is divisible by 2?
Last digit should be even
How to know if a numer is divisible by 5?
Last digit should be 5 or 0
How to know if a numer is divisible by 4?
Last 2 digits should be divisible by 4.
How to know if a numer is divisible by 3?
The sum of all digits should be divisible by 3
How to know if a numer is divisible by 9?
The sum of all digits should be divisible by 9
How to know if a numer is divisible by 6?
Must be divisible by 2 and by 3.
Any even number that is divisible by 3-
