SOLUTION: Please help me solve the following expression with steps.thank you
5/8-5/12(3-1/4)+2/3
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Question 1019652: Please help me solve the following expression with steps.thank you
5/8-5/12(3-1/4)+2/3
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Please help me solve the following expression with steps.thank you
5/8-5/12(3-1/4)+2/3
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(5/8) - (5/12)(11/4) + (2/3)
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(5/8) - (55/48) + (2/3)
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lcd = 48
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(30/48) - (55/48) + (32/48)
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= (30+55+32)/48
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= (117/48)
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= 2.4375
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Cheers,
Stan H.
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Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you use pemdas.
pemdas says.
working from left to right:
1. resolve parentheses first, working from the most embedded set of parentheses to the next most embedded set of parentheses, to the next most embedded, etc., until all sets of parentheses have been resolved.
do the following 3 steps in the order indicated within each set of parentheses, and then overall after all parentheses have been resolved.
2. resolve all exponents and roots, working from left to right.
3. resolve all multiplication and division, working from left to right.
4. resolve all addition and subtraction, working from left to right.
application of pemdas to your problem is shown below:
start with 5 / 8 - 5 / 12 * (3 - 1/4) + 2 / 3
i will only show the first three decimal places of the results of each operation, with 3 dots after it, if required, for brevity.
when you do the actual calculations though, you will need to not round anything until the final result is displayed.
my calculations will be using the complete numbers as stored in the calculator even though i'm displaying the truncated numbers.
i'll explain after the first calculations that does this.
start with 5 / 8 - 5 / 12 * (3 - 1/4) + 2 / 3
i put spaces in between all the operations so you can see them more clearly.
additionally i put a * symbol between 12 and (3... because that's an implied multiplication.
all i did was make it explicit.
so you start with 5 / 8 - 5 / 12 * (3 - 1/4) + 2 / 3
you resolve parentheses first by performing the operation within the set of parentheses.
3 - 1/4 is equal to 2.75
your expression becomes 5 / 8 - 5 / 12 * 2.75 + 2 / 3
all parentheses have been resolved, so you go from left to right resolving all exponents and roots next.
there are none, so you go from left to right resolving all multiplications and divisions next.
start with 5 / 8 - 5 / 12 * 2.75 + 2 / 3
5 / 8 = .625 ,so your expression becomes .625 - 5 / 12 * 2.75 + 2 / 3
5 / 12 = .416..., so your expression becomes .625 - .416... * 2.75 + 2 / 3
.416... * 2.75 = 1.145..., so your expression becomes .625 - 1.145... + 2 / 3
2 / 3 = .666..., so your expression becomes .625 - 1.145... + .666...
you have now resolved all multiplication and division, working from left to right.
what's left is to do addition and subtraction, working from left to right.
start with .625 - 1.145... + .666...
.625 - 1.145... = .520..., so your expression becomes .520... + .666...
.520... + .666... = .145...
that's your final expression.
the full number stored in my calculator is .1458333333333.
the fractional equivalent of this is 7 / 48.
you can confirm this is true by simply placing the expression, as is, in your scientific calculator that has the capability to do parentheses and that follows the pemdas rules.
you will enter 5/8-5/12*(3-1/4)+2/3
the calculator will tell you that the result is .1458333333.
the actual number of 3's displayed is dependent on the number of decimal digits the calculator is capable of displaying on the screen.
if your calculator has a decimal to fraction converter, you will execute that to get 7/48.
here's a tutorial on pemdas that might help you.
https://www.mathsisfun.com/operation-order-pemdas.html
they have questions designed to test your knowledge.
they're worthwhile to go through.
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