How do you evaluate #3\frac{2}{5}\times 15\div 3+7#?

Answer 1

24

When there are multiple mathematical operations, then the following rule should be applied to solve the question:

1st solve anything that is in parentheses(P) or brackets (B). 2nd step being to solve and orders(O) or powers or exponents (E) then 3rd step is to solve for any multiplication(M) or division (D) operations and the 4th step being to solve any addition (A) or subtraction (S).

Thus an easy way to remember the operations is: PEMDAS or BODMAS, where each letter represents the mathematical operation.

So, in the question, first convert the mixed fraction #3 2/5# into improper fraction by multiplying #5xx3+2 = 17/5# (See, I have used BODMAS or PEMDAS rule in getting the improper fraction).

Now, the question becomes #17/5 xx 15 -: 3 + 7# or, #17/ cancel (5) xx cancel (15) 3 -:3 + 7# or, #17 xx 3 -: 3 + 7# or, #51/3 + 7# or, #cancel (51)/cancel (3) 17 +7# or, #17 + 7# = 24

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.