Final answer:
A mother divides 3 whole objects into 6 equal pieces each and gives you 5 of these pieces. As an improper fraction, this is expressed as 5/18, and since it is less than one whole, the mixed number form is 0 5/18.
Step-by-step explanation:
The question concerns dividing a certain amount of a whole into equal pieces, which falls into the category of fractions. Specifically, we're tasked with converting a quantity of these pieces into both an improper fraction and a mixed number.
Let's break down the scenario given. A mother cuts 3 whole objects into 6 equal pieces each, and then gives you 5 of these pieces. To express this situation with fractions, first, we consider the total number of pieces she has created. Since each whole object is divided into 6 pieces, 3 whole objects result in 3 x 6 = 18 pieces. If you received 5 of these pieces, we denote this as 5/18. This is an improper fraction because the numerator is less than the denominator.
Now, to express this as a mixed number. Since you have less than one whole (which would require at least 6 pieces from the context), there's no whole number part and only the fractional part. Thus, in this case, the mixed number is simply the equivalent of the improper fraction, 0 5/18.
Understanding how to handle fractions helps in visualizing scenarios involving parts of a whole. Determining whether one has more or less than half, for instance, is intuitive with a good grasp of fractional concepts.