# 5/6·1/2+2/3÷4/3 How do I solve this problem?

marilynn07 | High School Teacher | (Level 3) Associate Educator

Posted on

You would set this problem up as an order of operations problem.

First you eliminate parentheses

Second you eliminate exponents

Third you multiply and divide in order from left to right

Fourth you add and subtract in order from left to right.

Here is a sentence to help you remember what to do first.

Please         excuse        my dear                Aunt Sally.

(parentheses) exponents multiply and divide add and subtract

5/6*1/2+2/3/4/3

reorder terms (when dividing fractions use the reciprocal of the second fraction and multiply them)

5/6*1/2+2/3*3/4

multiply fractions (you could cross multiply)

5/12+6/12

add fractions (be sure that the denominator for both fractions is the same, and add the numerators)

udonbutterfly | Student, College Freshman | (Level 1) Valedictorian

Posted on

The first thing you want to do is follow the orders of operation some people call it PEMDAS.

First put parenthesis around where the fractions are

(5/6)·(1/2)+(2/3)÷(4/3)

Now first multiply (5/6) by (1/2) and you will get 0.4167 or (5/12)

Now you're going to divide (2/3) by (4/3) and you will get 0.5 or (1/2)

Then you will have an equation like this 0.4167 + 0.5 or (5/12) + (1/2)

Adding them up will now get you 0.9167 or 11/12

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

5/6·1/2+2/3÷4/3

For equation like these remember the order of PEMDAS

Parentheses

Exponents

Multiplication

Division

Subtraction

if you follow the order of PEMDAS the equation should looks like

( 5/6 X 1/2 ) + ( 2/3 ÷ 4/3 )

after multiplying and dividing what's inside the parentheses it should looks like

5/12 + 6/12

= 11/12

nisarg | Student, Grade 11 | (Level 1) Valedictorian

Posted on

5/6·1/2+2/3÷4/3

How do I solve this problem?

`5/6*1/2+2/3*3/4`

`5/12+6/12`

`11/12`

` `

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

5/6·1/2+2/3÷4/3

Use P.E.M.D.A.S

Parentheses

Exponents

Multiplication

Division

Subtraction

in that order

laurto | Student, Grade 10 | (Level 1) Valedictorian

Posted on

PEMDAS

Excuse (Exponents)

My (Multiplication)

Dear (Division)

Sally (Subtraction)

from left to right

princessenotes | Student, Undergraduate | (Level 1) Honors

Posted on

PEMDAS

Parentheses

Exponents

Multiply

( from left to right)

Divide

( from left to right)

Subtraction

neela | High School Teacher | (Level 3) Valedictorian

Posted on

5/6.1/2+2/3 '/. 4/3

Reading: 5 diveded by 6multiplied by1 plus divided by 2 divided by3 divideb4 divided by 3.

The operation   / or '/. are dividing operation.

The operation  . is multiplication.

Procedure: In this case, division and multplication are of equal priority. So do them in first come first serve basis.The addition is last.

Therefrore,

In 5/6*1/2+2/3'/.4/3, we take 5/6*1/2 first

5/6*1/2=5/12  +                                           (1).

Now we take 2/3'/.4/3:

2/3'/.4=(2/3)/4=2/12=1/6.

The result (1/6) divided by 3=(1/6)/3=1/18        (2)

Now do the addtion + between the result flagged at (1) and (2):

5/12+1/18. make them equivalent fractions with a common denominator 36:

5/12=5*3/(12*3) =15/36

1/18=1*2/(18*2)=2/36

So.5/12+1/18=15/36+2/36 =17/36=0.47222....

If you still have doubt check this with a scientific calculator, or a Ms exel  and feed the data in the same fashion you posed here and check the result. They are programmed and order of operations are taken care of in them.

Most people may confuse with second term after plus + here while simplification:

2/3'/.4/3 is equivalent to 2divided by 3divided by4divided by3

Successive divisions are here. No parantesis. / and '/. are the same operations and no priority arises as they look in different shape. There is no freedom to pick any two successive numbers in the middle or last. So you have to effect the divsion from left only , 'On first come first serve basis'.

Therefore 2/3'/.4/3=2/3/4/3 does not give us the freedom to choose the last 4/3 first. So,2/3'/.4/3= 2/3/4/3 = 2/3 first and the result/4. Then divide by3. So,2/3'/.4/3=0.666.../4/3=0.166666/3=0.05555...... or

2/3'/.4/3=2/12/3=2/12/3=2/36=1/18

Hope this helps.
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