Questions and Answers on Different Meanings of Fractions - Paper Example

Paper Type:  Course work
Pages:  4
Wordcount:  1047 Words
Date:  2021-06-17
Categories: 

1) What are fractions?

Trust banner

Is your time best spent reading someone else’s essay? Get a 100% original essay FROM A CERTIFIED WRITER!

- Fraction is a part of a whole. A unit or a set is divided into equal pieces and numbers of the pieces used to represent fractional amounts.

- The quotient meaning is the division of two numbers or division problem. It is often written as a mixed number.

- A fraction can be an expression of two quantities. When a ratio compares a part to a whole, the fraction interpretation may be used

- Fractions are used as operators to act on another number to either stretch or shrink the magnitude of a number.

- Fractions can be utilized as measures; this is dependent on the idea of a fraction as a length on the number line.

2) When do students learn different meanings of fractions?

Researchers suggest that the best time to start learning fractions is in the early grades by defining fractions as part of a whole. The other interpretations are taught later in elementary and middle school.

3) Fractions as parts of wholes or sets.

The first relation is considering the entire unit and the symbolic fraction and determining what the part looks like.

The next involves being given the whole unit and the part then determining what fraction the part represents.

The last relationship requires considering the whole after being given the fraction and the part.

4) Fractions as a result of diving two numbers.

A fraction can be viewed as a result of dividing two numbers. For example, can be interpreted as a 1 unit divided into 4 parts.

5) Interpreting fractions as a result of the division of numbers.

Understanding fractions can do this through a linear model in which a point on the line represents a fraction. For example, if one wants to represent 5/4 in a number line ranging from 1 to 10. One can write its mixed fraction 1 then find the point after 1. The other approach is dividing the segment into ten then further into quarters then locate the point representing the 5/4 unit.

6) Using fractions as ratios of two quantities.

Similarities.

Equivalence ratios and rates are formed the same as either dividing forms fractions or multiplying them. The difference comes in the interpretation of the final value. Equivalence fractions are part to the whole comparison of the same number and portion on the number line; equivalence part to part ratios represent same comparison relationship but not the same number.

Differences

Fractions and ratios are different when it gets to operations such as addition and subtraction.

7) Fractions as operators

This is an algebraic interpretation of fractions. For instance, 1/3 can be thought of as a function that one set of elements with another with 1/3 times its elements.

8) What about fractions as operators

Situations, where fractions are used as an operator, are strictly multiplicative. The operator meaning cannot be used in cases of addition or subtraction.

9) Using fractions as measures.

A fraction, in this case, is used as a measure of some distance or region. One can measure a linear distance and record it as a distance from zero or measure the area of a region and use fractions to improve the precision of the measurement.

10) Using fractions as measures.

Fractions can be used to partition the number line to name and identify distances. Given a number line, one can determine the distance by dividing the line into fractions to find the exact position representing the distance from the point zero.

11) Summarizing the bottom paragraph.

Fractions can be interpreted in different ways by students to solve various problems.

12) Fair shares.

This is where a different interpretation of fractions are used to solve a problem. An example of a fishing expedition where an individual is required to identify which fisherman carried the most fish. A fraction can address the problem as a quotient interpretation, part to part ratio, equivalent ratios, part whole and operator interpretation to give the same answer.

13) Equivalence and ordering.

Equivalence relations is one of the most important ideas for students to understand. They are used in computing fractions, ordering, subtracting and adding fractions. Equivalent fractions represent equal value and equal distance in the number line. They are obtained when both numerator and denominator are either divided or multiplied by the same value.

The one underlying assumption in regarding equivalent fractions is that two equivalent fractions imply their wholes are of the same size.

14) Benchmarks.

A benchmark is a standard value used to compare fractions. When using fractions, one considers and 1. In comparing fractions, one first identifies if the fraction is equal to, less than or greater than .

15) Operations with fractions.

Students have difficulty with fractional operations because they perform algorithms with fractions without understanding the meaning of the fractions or the operations.

The part of a full or set interpretation of fractions is the one that is often used in the addition and subtraction. Problem-solving at an early stage should be linked with the actions of the students' on the models they make.

16) Adding and subtracting fractions with models.

Students are taught to link the operations of addition and subtraction to fraction models. When adding 1/3 to 1/6, the model of the two portions can be put together in a hexagon to occupy half. Different algorithms such as the use of improper fraction can be used when adding or subtracting. Using models helps one understand.

17) Modeling fractions.

Modeling can be used in the operation of taking a part of the part. One can use a piece of paper to model the solution of finding a quarter by folding the paper twice through the middle of the leaf then coloring the face to represent a quarter.

18) Dividing fractions.

When dividing fractions, different interpretations of the term are used to understand the meaning of the question. Division situations can be represented by partitive division or repeated subtractions. However, when it comes to multidimensional problems, the invert and multiply algorithm is used.

19) Teaching fractions.

Fractions are an important part of mathematics which should be introduced at an early age since some may find it difficult to understand. All interpretations should be presented informally, and the use of models to help understand fractions also plays an important role.

20) I would like to know more about equivalent fractions and application of operations on fractions. I will pay close attention to division and multiplication as well as addition and subtraction.

Cite this page

Questions and Answers on Different Meanings of Fractions - Paper Example. (2021, Jun 17). Retrieved from https://midtermguru.com/essays/questions-and-answers-on-different-meanings-of-fractions-paper-example

logo_disclaimer
Free essays can be submitted by anyone,

so we do not vouch for their quality

Want a quality guarantee?
Order from one of our vetted writers instead

If you are the original author of this essay and no longer wish to have it published on the midtermguru.com website, please click below to request its removal:

didn't find image

Liked this essay sample but need an original one?

Hire a professional with VAST experience!

24/7 online support

NO plagiarism