If your equation has fractional exponents or roots be sure to enclose the fractions in parentheses. For example:
5^(2/3) is 5 raised to the 2/3
5r(1/4) is the 1/4 root of 5 which is the same as 5 raised to the 4th power
Entering fractions
If you want an entry such as 1/2 to be treated as a fraction then enter it as (1/2). For example, in the equation 4 divided by ½ you must enter it as 4/(1/2). Then the division 1/2 = 0.5 is performed first and 4/0.5 = 8 is performed last. If you incorrectly enter it as 4/1/2 then it is solved 4/1 = 4 first then 4/2 = 2 last. 2 is a wrong answer. 8 was the correct answer.
Math Order of Operations - PEMDAS, BEDMAS, BODMAS, GEMDAS, MDAS
PEMDAS is an acronym that may help you remember order of operations for solving math equations. PEMDAS is typcially expanded into the phrase, "Please Excuse My Dear Aunt Sally." The first letter of each word in the phrase creates the PEMDAS acronym. Solve math problems with the standard mathematical order of operations, working left to right:
Parentheses, Brackets, Grouping - working left to right in the equation, find and solve expressions in parentheses first; if you have nested parentheses then work from the innermost to outermost
Exponents and Roots - working left to right in the equation, calculate all exponential and root expressions second
Multiplication and Division - next, solve both multiplication AND division expressions as they occur, working left to right in the equation. For the MDAS rule, you'll start with this step.
Addition and Subtraction - next, solve both addition AND subtraction expressions as they occur, working left to right in the equation
PEMDAS Caution
Multiplication DOES NOT always get performed before Division. Multiplication and Division are performed as they occur in the equation, from left to right.
Addition DOES NOT always get performed before Subtraction. Addition and Subtraction are performed as they occur in the equation, from left to right.
The order "MD" (DM in BEDMAS) is sometimes confused to mean that Multiplication happens before Division (or vice versa). However, multiplication and division have the same precedence. In other words, multiplication and division are performed during the same step from left to right. For example, 4/2*2 = 4 and 4/2*2 does not equal 1.
The same confusion can also happen with "AS" however, addition and subtraction also have the same precedence and are performed during the same step from left to right. For example, 5 - 3 + 2 = 4 and 5 - 3 + 2 does not equal 0.
A way to remember this could be to write PEMDAS as PE(MD)(AS) or BEDMAS as BE(DM)(AS).
Order of Operations Acronyms
The acronyms for order of operations mean you should solve equations in this order always working left to right in your equation.
PEMDAS stands for "Parentheses, Exponents, Multiplication and Division, Addition and Subtraction"
You may also see BEDMAS, BODMAS, and GEMDAS as order of operations acronyms. In these acronyms, "brackets" are the same as parentheses, and "order" is the same as exponents. For GEMDAS, "grouping" is like parentheses or brackets.
BEDMAS stands for "Brackets, Exponents, Division and Multiplication, Addition and Subtraction"
BEDMAS is similar to BODMAS.
BODMAS stands for "Brackets, Order, Division and Multiplication, Addition and Subtraction"
GEMDAS stands for "Grouping, Exponents, Division and Multiplication, Addition and Subtraction"
MDAS is a subset of the acronyms above. It stands for "Multiplication, and Division, Addition and Subtraction"
Operator Associativity
Multiplication, division, addition and subtraction are left-associative. This means that when you are solving multiplication and division expressions you proceed from the left side of your equation to the right. Similarly, when you are solving addition and subtraction expressions you proceed from left to right.
Examples of left-associativity:
a / b * c = (a / b) * c
a + b - c = (a + b) - c
Exponents and roots or radicals are right-associative and are solved from right to left.
Examples of right-associativity:
2^3^4^5 = 2^(3^(4^5))
2r3^(4/5) = 2r(3^(4/5))
For nested parentheses or brackets, solve the innermost parentheses or bracket expressions first and work toward the outermost parentheses. For each expression within parentheses, follow the rest of the PEMDAS order: First calculate exponents and radicals, then multiplication and division, and finally addition and subtraction.
You can solve multiplication and division during the same step in the math problem: after solving for parentheses, exponents and radicals and before adding and subtracting. Proceed from left to right for multiplication and division. Solve addition and subtraction last after parentheses, exponents, roots and multiplying/dividing. Again, proceed from left to right for adding and subtracting.
Answers & Comments
Answer:
Use the given functions to set up and simplify
PMDAS.45x=(10÷40)+4÷8=34PMDAS=PMDAS
Step-by-step explanation:
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Answer:
11.75
Solution:
UNDERLINED is complete step.
= 45 x (10/40) + 4/8
= 45 x (0.25)+ 4/8
= 45 x 0.25 <-- 45 x 0.25 = 11.25
= 11.25 + 0.5
= 11.75
If your equation has fractional exponents or roots be sure to enclose the fractions in parentheses. For example:
5^(2/3) is 5 raised to the 2/3
5r(1/4) is the 1/4 root of 5 which is the same as 5 raised to the 4th power
Entering fractions
If you want an entry such as 1/2 to be treated as a fraction then enter it as (1/2). For example, in the equation 4 divided by ½ you must enter it as 4/(1/2). Then the division 1/2 = 0.5 is performed first and 4/0.5 = 8 is performed last. If you incorrectly enter it as 4/1/2 then it is solved 4/1 = 4 first then 4/2 = 2 last. 2 is a wrong answer. 8 was the correct answer.
Math Order of Operations - PEMDAS, BEDMAS, BODMAS, GEMDAS, MDAS
PEMDAS is an acronym that may help you remember order of operations for solving math equations. PEMDAS is typcially expanded into the phrase, "Please Excuse My Dear Aunt Sally." The first letter of each word in the phrase creates the PEMDAS acronym. Solve math problems with the standard mathematical order of operations, working left to right:
Parentheses, Brackets, Grouping - working left to right in the equation, find and solve expressions in parentheses first; if you have nested parentheses then work from the innermost to outermost
Exponents and Roots - working left to right in the equation, calculate all exponential and root expressions second
Multiplication and Division - next, solve both multiplication AND division expressions as they occur, working left to right in the equation. For the MDAS rule, you'll start with this step.
Addition and Subtraction - next, solve both addition AND subtraction expressions as they occur, working left to right in the equation
PEMDAS Caution
Multiplication DOES NOT always get performed before Division. Multiplication and Division are performed as they occur in the equation, from left to right.
Addition DOES NOT always get performed before Subtraction. Addition and Subtraction are performed as they occur in the equation, from left to right.
The order "MD" (DM in BEDMAS) is sometimes confused to mean that Multiplication happens before Division (or vice versa). However, multiplication and division have the same precedence. In other words, multiplication and division are performed during the same step from left to right. For example, 4/2*2 = 4 and 4/2*2 does not equal 1.
The same confusion can also happen with "AS" however, addition and subtraction also have the same precedence and are performed during the same step from left to right. For example, 5 - 3 + 2 = 4 and 5 - 3 + 2 does not equal 0.
A way to remember this could be to write PEMDAS as PE(MD)(AS) or BEDMAS as BE(DM)(AS).
Order of Operations Acronyms
The acronyms for order of operations mean you should solve equations in this order always working left to right in your equation.
PEMDAS stands for "Parentheses, Exponents, Multiplication and Division, Addition and Subtraction"
You may also see BEDMAS, BODMAS, and GEMDAS as order of operations acronyms. In these acronyms, "brackets" are the same as parentheses, and "order" is the same as exponents. For GEMDAS, "grouping" is like parentheses or brackets.
BEDMAS stands for "Brackets, Exponents, Division and Multiplication, Addition and Subtraction"
BEDMAS is similar to BODMAS.
BODMAS stands for "Brackets, Order, Division and Multiplication, Addition and Subtraction"
GEMDAS stands for "Grouping, Exponents, Division and Multiplication, Addition and Subtraction"
MDAS is a subset of the acronyms above. It stands for "Multiplication, and Division, Addition and Subtraction"
Operator Associativity
Multiplication, division, addition and subtraction are left-associative. This means that when you are solving multiplication and division expressions you proceed from the left side of your equation to the right. Similarly, when you are solving addition and subtraction expressions you proceed from left to right.
Examples of left-associativity:
a / b * c = (a / b) * c
a + b - c = (a + b) - c
Exponents and roots or radicals are right-associative and are solved from right to left.
Examples of right-associativity:
2^3^4^5 = 2^(3^(4^5))
2r3^(4/5) = 2r(3^(4/5))
For nested parentheses or brackets, solve the innermost parentheses or bracket expressions first and work toward the outermost parentheses. For each expression within parentheses, follow the rest of the PEMDAS order: First calculate exponents and radicals, then multiplication and division, and finally addition and subtraction.
You can solve multiplication and division during the same step in the math problem: after solving for parentheses, exponents and radicals and before adding and subtracting. Proceed from left to right for multiplication and division. Solve addition and subtraction last after parentheses, exponents, roots and multiplying/dividing. Again, proceed from left to right for adding and subtracting.