Order of Operation- "Operations" means things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation. But, when you see something like ...
7 + (6 × 52 + 3)
... what part should you calculate first?
Start at the left and go to the right?
Or go from right to left?
Warning: Calculate them in the wrong order, and you will get a wrong answer !
So, long ago people agreed to follow rules when doing calculations, and they are:
Order of Operations
Do things in Parentheses First. Example:
6 × (5 + 3)
6 × 8
48
Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:
5 × 22
5 × 4
20
Multiply or Divide before you Add or Subtract. Example:
2 + 5 × 3
2 + 15
17
Otherwise just go left to right. How Do I Remember It All ... ? PEMDAS !
P= Parentheses first
E= Exponents (ie Powers and Square Roots, etc.)
MD= Multiplication and Division (left-to-right)
AS= Addition and Subtraction (left-to-right)
http://www.mathsisfun.com/operation-order-pemdas.html (see this web page for more explanation - information used from site)
7 + (6 × 52 + 3)
... what part should you calculate first?
Start at the left and go to the right?
Or go from right to left?
Warning: Calculate them in the wrong order, and you will get a wrong answer !
So, long ago people agreed to follow rules when doing calculations, and they are:
Order of Operations
Do things in Parentheses First. Example:
6 × (5 + 3)
6 × 8
48
Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:
5 × 22
5 × 4
20
Multiply or Divide before you Add or Subtract. Example:
2 + 5 × 3
2 + 15
17
Otherwise just go left to right. How Do I Remember It All ... ? PEMDAS !
P= Parentheses first
E= Exponents (ie Powers and Square Roots, etc.)
MD= Multiplication and Division (left-to-right)
AS= Addition and Subtraction (left-to-right)
http://www.mathsisfun.com/operation-order-pemdas.html (see this web page for more explanation - information used from site)
Factor more ...
Factors are the numbers you multiply together to get another number:
Example: 3 and 4 are factors of 12, because 3x4=12.
Also 2x6=12 so 2 and 6 are also factors of 12, and 1x12=12 so 1 and 12 are factors of 12 as well.
So ALL the factors of 12 are 1,2,3,4,6 and 12
(and also -1,-2,-3,-4,-6 and -12).
http://www.mathsisfun.com/definitions/factor.html (see this web page for more explanation - information used from site)
Factors are the numbers you multiply together to get another number:
Example: 3 and 4 are factors of 12, because 3x4=12.
Also 2x6=12 so 2 and 6 are also factors of 12, and 1x12=12 so 1 and 12 are factors of 12 as well.
So ALL the factors of 12 are 1,2,3,4,6 and 12
(and also -1,-2,-3,-4,-6 and -12).
http://www.mathsisfun.com/definitions/factor.html (see this web page for more explanation - information used from site)
Prime Numbers- A number that only has one and itself as a factor
Examples: 1, 2, 3, 5, 7, 11
Composite Numbers- A number that has more than one and itself as a factor
Examples: 4, 6, 8, 9
http://www.mathsisfun.com/prime-composite-number.html (see this web page for more explanation)
Examples: 1, 2, 3, 5, 7, 11
Composite Numbers- A number that has more than one and itself as a factor
Examples: 4, 6, 8, 9
http://www.mathsisfun.com/prime-composite-number.html (see this web page for more explanation)
Multiples- numbers that you count by...
Examples: The first five multiples of 2 are = 2, 4, 6, 8, 10 The first five multiples of 8 are= 8, 16, 24, 32, 40
http://www.mathsisfun.com/definitions/multiple.html (see this web page for more explanation)
Examples: The first five multiples of 2 are = 2, 4, 6, 8, 10 The first five multiples of 8 are= 8, 16, 24, 32, 40
http://www.mathsisfun.com/definitions/multiple.html (see this web page for more explanation)
Prime Factorization- finding which prime numbers multiply together to make the original number.
Here are some examples:Example 1: What are the prime factors of 12 ?It is best to start working from the smallest prime number, which is 2, so let's check: 12 ÷ 2 = 6
Yes, it divided evenly by 2. We have taken the first step!
But 6 is not a prime number, so we need to go further. Let's try 2 again:
6 ÷ 2 = 3
Yes, that worked also. And 3 is a prime number, so we have the answer:
12 = 2 × 2 × 3
As you can see, every factor is a prime number, so the answer must be right.
Note: 12 = 2 × 2 × 3 can also be written using exponents as 12 = 22 × 3
http://www.mathsisfun.com/prime-factorization.html (see this web page for more explanation- information used from this site)
Here are some examples:Example 1: What are the prime factors of 12 ?It is best to start working from the smallest prime number, which is 2, so let's check: 12 ÷ 2 = 6
Yes, it divided evenly by 2. We have taken the first step!
But 6 is not a prime number, so we need to go further. Let's try 2 again:
6 ÷ 2 = 3
Yes, that worked also. And 3 is a prime number, so we have the answer:
12 = 2 × 2 × 3
As you can see, every factor is a prime number, so the answer must be right.
Note: 12 = 2 × 2 × 3 can also be written using exponents as 12 = 22 × 3
http://www.mathsisfun.com/prime-factorization.html (see this web page for more explanation- information used from this site)
Exponent- The exponent of a number says how many times to use the number in a multiplication.
In 8 2nd power the "2" says to use 8 twice in a multiplication,
so 8 2nd power = 8 × 8 = 64
Exponents are also called Powers or Indices.
In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"
http://www.mathsisfun.com/exponent.html (see this web page for more explanation- information used from this site)
In 8 2nd power the "2" says to use 8 twice in a multiplication,
so 8 2nd power = 8 × 8 = 64
Exponents are also called Powers or Indices.
In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"
http://www.mathsisfun.com/exponent.html (see this web page for more explanation- information used from this site)
Mixed Numbers- a number that has a whole number and a fraction.
Improper Fraction- a fraction that has a larger number for the numerator than denominator.
Equivalent Fractions- fractions that are equal to each other.
Improper Fraction- a fraction that has a larger number for the numerator than denominator.
Equivalent Fractions- fractions that are equal to each other.
Dividing Fractions- Turn the second fraction upside down, then just multiply.
There are 3 Simple Steps to Divide Fractions:Step 1. Turn the second fraction (the one you want to divide by) upside-down
(this is now a reciprocal).Step 2. Multiply the first fraction by that reciprocal
Step 3. Simplify the fraction (if needed)
There are 3 Simple Steps to Divide Fractions:Step 1. Turn the second fraction (the one you want to divide by) upside-down
(this is now a reciprocal).Step 2. Multiply the first fraction by that reciprocal
Step 3. Simplify the fraction (if needed)