Open Middle®
Directions: Find three fractions whose product is -5/24. You may use fractions between -8/9 to 8/9 no more than one time each.
Find at least 2 possible combinations.
Hint
What properties hold true for multiplying fractions?
Answer
Answers vary
e.g : (5/6)(-1/2)(1/2),(-5/6)(1/3)(3/4)
e.g : (5/6)(-1/2)(1/2),(-5/6)(1/3)(3/4)
Source: Al Oz
The part of the problem that states the fractions must be between -1/9 and 1/9 make the problem impossible, right? I believe that part of the instructions needs to be revised.
Good catch Megan. We’ll look into this.
We’ve updated the problem so that it works. Thanks again for catching it.
The problem says that fractions can’t be repeated, but the first sample uses 1/2 twice.
(5/6)(-1/3)(3/4) = -5/24
In measurements, fractions appear whenever units are not small enough to express quantities in integers. For example, five quarter-dollars will buy you exactly as mush as a dollar and a quarter. One and a half dollar stands for exactly the same quantity as three half-dollars or six quarter-dollars.
Fractions are unavoidable and sooner or later we all have to learn to work with fractions. The mathematical usage of the word fraction has a very clear everyday connotation as a part of a bigger object. It would be unthinkable nowadays to just introduce fractions as a pair of numbers and postulate their basic properties. Still, to express fractions one needs a pair of numbers with a meaning and intuition attached to them.
When multiplying fractions, the numerators (top numbers) are multiplied together and the denominators (bottom numbers) are multiplied together. To divide fractions, rewrite the problem as multiplying by the reciprocal (multiplicative inverse) of the divisor. To add fractions that have the same, or a common, denominator, simply add the numerators, and use the common denominator. However, fractions cannot be added until they are written with a common denominator. The figure below shows why adding fractions with different denominators is incorrect.
(5/6)(-1/3)(3/4) = -5/24