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About Josh
Expertise
When I work through problems, I emphasize principles and key ideas which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponentials & Logarithms. Basic Calculus. Probability, Permutations and Combinations. Mathematical Induction. Complex numbers. Physics problems.
Experience
Experience:
I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.
Supplementary Website:
See a selection of past questions in my maths repository under "Question Archive"
Education Credentials:
Bachelor degree in Engineering Science.
"Everyone struggles with something."
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You are here: Experts > Science > Math for Kids > Basic Math > Fraction Question
Expert: Josh - 11/5/2009
Question
By looking at the denominator and the numerator how can you tell if the fraction is greater or less than 1/2?
Answer
Hi Crystal,
There are several ways to answer this question. The best answer for you would depend on your knowledge and maths experience. A particular answer will not work for everyone.
Answer 1: One can tell from experience. As you gain more exposure to simple fractions, e.g., 1/3, 1/4, 2/5 etc., the answer becomes more intuitive. You can visualize in your mind what proportion is represented by a given fraction. For example, if 1/2 is 50%, 1/4 is 25%, then 1/3 is somewhere in between.
Answer 2: A sure way to checking this is by using a calculator, or through long division. But usually, intuition works best. With something like 7/18 for instance, half of 18 is 9. So, the numerator has got to be larger than 9 (at least 10/18) to exceed a half.
Answer 3: A more formal approach is by considering an inequality.
Suppose we want to check whether 3/8 is greater than 1/2.
If TRUE, then we must have 3/8 > 1/2.
Using "cross-multiplication" (do a search on Google if you want to see examples), we get 3 x 2 = 6 on the left hand side and 1 x 8 = 8 on the right hand side. We yield a contradiction, as 6 is clearly NOT greater than 8. So, our original assumption was wrong. 3/8 is NOT greater than 1/2.
Another example: Is 5/8 greater than 1/2?
If TRUE, then we must have 5/8 > 1/2.
Using "cross-multiplication", we get 5 x 2 = 10 on the left hand side and 1 x 8 = 8 on the right hand side. This time, it checks out. So, our original assumption was right. 5/8 is greater than 1/2.
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