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

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.

The operation + is addtion.

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.