# Questions tagged [fractions]

For questions about the teaching of fractions and their interpretations. Fractions are numbers of the form $p/q$, where $p$ and $q \neq 0$ are integers.

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### How can I teach $\frac{300}{200}$ to 10 years old students while s\he knows canceling the zeroes rule?

I am teaching math to a 10 year old student. He learned that $$\frac{300}{100}=\require{cancel}\frac{3\cancel{00}}{1\cancel{00}}=3$$ and \frac{6000}{300}=\require{cancel}\frac{60\cancel{00}}{3\...
962 views

### Why do some students struggle so much with fractions?

I read on multiple web pages something that implies that that some students really struggle with fractions but I could never find a detailed explanation of why. This question is different from Are ...
207 views

### Concrete way to teach addition and subtraction of fractions

I am teaching 4th-grade kids. The topic is Fraction. Basic understanding of a fraction as a part of the whole and as part of the collection is clear to the kids. Several concrete ways exist to teach ...
79 views

### Applications of unreducible fractions in Basic School

An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (...
1k views

### How to explain fractions to 7 year old kid

I am finding it difficult to convince my kid that 2/4 and 1/2 are same. As per the kid, 2/4 is more than 1/2 since in first case the boy gets 2 candies out of 4 and in second case he gets 1 candy out ...
740 views

### Don't these word problems seem designed to be confusing?

I'm a fairly new private math tutor, and I'm good at math (I have a BS from Caltech with lots of graduate level math), but becoming good at teaching math is something else, which I strive to improve ...
222 views

### Algebra/trig/precalculus review questions that elicit common student errors

This semester I have decided to give students a simple question or two at the beginning of every calculus class that will trap them into making the most common errors that we all know...e.g. the ...
9k views

### How to explain the flipping of division by a fraction?

This question is inspired by @DavidButlerUofA's discussion of "$\div \frac{2}{3}$ as $\times \frac{3}{2}$" in "Are fractions hard because they are like algebra?" Q. How can one best convey to ...
315 views

### How is $\frac{a}{b}$ interpreted?

I was having a discussion with a colleague who is in the process of writing some curriculum, and we ended up having a discussion about what $\frac{a}{b}$ (with all the standard restrictions) meant. We ...
3k views

### Models and strategies for teaching fractions in 7th grade mathematics

I'm a first year student at a university college, and I'm currently teaching 7th grade for a few weeks as a part of my education. I'm struggling a bit with finding models and strategies to develop an ...
1k views

### How to teach quick multiplication and division in head?

I recently started giving maths lessons and it seems like I am at my wits end. My own background is: I'm a masters student in physics, already did several tutorials for younger students, especially ...
2k views

### How to teach sum of fractions to students?

I think almost every middle school student in my country has learned sum of two fractions in this non reflexive way (I'm included when I was kid), doing the following steps: They calculate the lcm. ...
324 views

### On fractions and the least common multiple

At least in my country, the explanation of the basic operations over rational numbers is done very near to the concept of prime numbers, prime factorization, and the calculation of the least common ...
210 views

### Where to find good exercises for term operations?

I'm searching for exercises for practising operations with terms. They should involve working with decimal numbers and fractions (ideally one should convert decimal numbers to simple fractions like ...
14k views

### How to explain the difference between the fraction a / b and the ratio a : b?

I found it difficult to explain the difference between the fraction a / b and the ratio a : b. This subject is for pupils of grade 5. So is there a real difference between them and how to explain the ...
198 views

### How to explain to pupils that “$\frac n{100}$ OF $a$” is equivalent to “$a$ TIMES $\frac{n}{100}$”?

How to explain to pupils that "$\frac n{100}$ OF $a$" is equivalent to "$\frac{n}{100}\times a$"? There is some difficulty in explaining that the first sentence, containing "OF" (which could suggest ...
214 views

Most problems require the student to simplify the final answer and in many context the meaning is obvious: For example, $3/9$ should be simplified to $1/3$ and $\sqrt{16}$ should be simplified to $4$. ...
353 views

### Could schools jump straight into teaching real numbers first then teaching fractions later?

Some students really struggle to learn fractions. Not only that but also, once they've mastered an understanding of real numbers, they can learn about fractions so much faster and more efficiently ...
220 views

### Is there a meeting place for fraction education stakeholders?

Is there a meeting place where all fraction education stakeholders (students, teachers, parents, researchers, fraction software developers) meet and collaborate? If not, do you have an advice on ...
672 views

### Constructive refutation of student misconception

Although @Gareth Shepherd recently posted Addressing fundamental math errors close to the issue, I experienced my problem of misunderstanding in class, where two good K10 students were asked to ...
556 views

### How to explain multiplying and dividing by fractions with real-world examples

I'm looking for a good way to explain how multiplication and division by fractions applies in the real-world the mechanics are receiving reasonably straight forward. How can $2$ divided by $1/2$ ...
5k views

### Should we say that fractions “are” or “represent” numbers?

I never gave this a second thought until a friend who works in education brought it up the other day. Should we say that a fraction like $\frac{1}{2}$ "is" a number, or "represents" a number? In ...
149 views

### How do you explain the whole integer and fractions subject to a kid in 6th grade?

Problems like There is 30 students in the class. $\frac13$ of the students study biology, $\frac15$ of the students study physics and the rest study chemistry. What part of the class studies ...
1k views

### What is the rationale for the absent (+) in mixed fractions?

Why are students taught to represent one and a half as $1 \frac{1}{2}$ rather than $1 + \frac{1}{2}$? This mode of expression seems standard at least throughout North America. I believe that it is bad ...
697 views

### How to teach students when they can and can't cancel factors in a fraction?

I mainly tutor adults in college algebra classes or lower. Sometimes an expression like $\dfrac {x+5}{5}$ will come up, and the students will say: "We can cancel out the $5$'s and get $x+1$, right?" ...
78 views

### Resources for teaching algebraic fractions to a dyscalculic pupil

I have a new student in math class (high school) since last month, and she's being diagnosed with dyslexia and dyscalculia. We are about to go into conic sections and she should be able to do some ...
602 views

### Negative Denominator in Fractions; Importance and Applications

Why do we need fractions such as $\dfrac{3}{-5}$? I need a convincing answer suitable for 8th grade students. Here's what I've already thought of (which don't fully satisfy me!): Solving the equation ...
484 views

### A good antonym for reducing/simplifying equivalent fractions

I am looking for a good antonym for reducing/simplifying equivalent fractions: 'reduce' and 'simplify' both make sense to me when dividing, but I'm struggling to name what it is we do when we multiply ...
282 views

Recently, I read a paper about student's understanding of fraction. Most students mentioned in the paper had given $5/8$ as their answer to the following question: ...
1k views

### Are fractions hard because they are like algebra?

It occurs to me that to really understand the ways that people work with fractions on paper requires a good grasp of the ideas that numbers have multiple representations and that expressions can be ...
2k views

### Is algebra really the gatekeeper to higher math, or is it multiplicative reasoning?

The National Mathematics Advisory Panel final report states that algebra is the gateway to higher math, to a college degree, and higher earnings from employment. It also states that success in algebra ...
223 views

### Teaching “and a half” early, possibly before general proper fractions

Fractions are a well-recognised issue in maths learning, with all sorts of complex issues involved. One particular aspect of this is difficulty recognising fractions as numbers which describe the size ...