Note that in the first step, the radical is treated as a grouping symbol, like parentheses. Also, in the third step, the fraction bar is considered a grouping symbol so the numerator is considered to be grouped.
For some activities we perform, the order of certain operations does not matter, but the order of other operations does. For example, it does not make a difference if we put on the right shoe before the left or vice-versa. However, it does matter whether we put on shoes or socks first. The same thing is true for operations in mathematics.
Commutative properties
The
commutative property of addition states that numbers may be added in any order without affecting the sum.
$a+b=b+a$
We can better see this relationship when using real numbers.
It is important to note that neither subtraction nor division is commutative. For example,
$\text{\hspace{0.17em}}17-5\text{\hspace{0.17em}}$ is not the same as
$\text{\hspace{0.17em}}5-17.\text{\hspace{0.17em}}$ Similarly,
$\text{\hspace{0.17em}}20\xf75\ne 5\xf720.$
Associative properties
The
associative property of multiplication tells us that it does not matter how we group numbers when multiplying. We can move the grouping symbols to make the calculation easier, and the product remains the same.
hi can you give another equation I'd like to solve it
Daniel
what is the value of x in 4x-2+3
Olaiya
if 4x-2+3 = 0
then
4x = 2-3
4x = -1
x = -(1÷4) is the answer.
Jacob
4x-2+3
4x=-3+2
4×=-1
4×/4=-1/4
LUTHO
then x=-1/4
LUTHO
4x-2+3
4x=-3+2
4x=-1
4x÷4=-1÷4
x=-1÷4
LUTHO
A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was 1350 bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after 3 hours?
A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So, the length of the guy wire can be found by evaluating √(90000+160000). What is the length of the guy wire?