Expert: Sherry Wallin - 8/30/2009

Question
QUESTION: hi sherry,
how would you do this problem:
(1/4) - (1/2) ÷ (1/3)
can you show me step by step please?

ANSWER: Raymond, there are two things going on here. One is an order of operations that must be followed and the other is fractional arithmetic. So first decide which operation has to occur first, subtraction or division? Right, division is first. So take 1/2 and divide it by 1/3. There are many ways to do this but the way you were probably taught in 3rd or 4th grade is to invert the 2nd fraction and multiply: 1/2 * 3/1 = 3/2. (Recall when multiplying fractions you multiply the numerators and multiply the denominators). Now take 1/4 and subtract 3/2. Remember when adding or subtracting fractions their denominators must be the same. So how many 4ths is 3 halves? Make the 2 in 3/2 a 4 and that happens when you multiply 2 by 2 so you must also multiply the top by 2 to get 6/4 = 3/2. Back to the problem, we now have: 1/4 - 6/4. Since the denominators are now the same we only have to do the arithmetic with the numerators. So what is 1 take away 6 (1-6)? Yes -5, so you have -5/4 for an answer.

Math Prof

---------- FOLLOW-UP ----------

QUESTION: ok i get that but the answer was -3/4?when i check in the back i curious how did they get that?

Answer
Raymond, I can see how you are confused. Do not always second guess yourself! The back of the book is wrong (and many times it is). People are hired by publishers to make those answer keys and many times they make a mistake or don't even know how to do the problems. (sad but true). If you do not pay attention to the order of operations and just do the math left to right you would get -3/4. Which of course is wrong since you MUST follow the order of operations. Point this out to your teacher.

Math Prof

done wrong: 1/4 - 1/2 = 1/4 - 2/4 = -1/4 and then -1/4 ÷ (1/3) = -1/4 * 3/1 = -3/4 WARNING this is WRONG!