What are the common misconceptions in adding and subtracting fractions?

Basic Fractions

A common misconception in adding or subtracting fractions is pupils treating the numerators and denominators as whole numbers so end up adding or subtracting the denominators as well (see above illustration 1 - misconception).

What are common misconceptions about fractions?

Most misconceptions in fractions arise from the fact that fractions are not natural numbers. Natural numbers are the positive whole numbers that we count with, e.g. 1, 2, 3, 97, 345, 234,561 etc. These are the kinds of numbers children spend most of their time learning.

What are errors and misconceptions?

In other words a misconception is an erroneous piece of knowledge or theory or formula while errors are incorrect applications or executions of the concepts, theories or formulas (even though they might be correctly understood).

What is a common mistake when using equivalent fractions?

Common mistakes students make:

Using the word reduce to describe finding equivalent fractions leads children to think that the fraction is getting smaller or shrinking.

Why do students struggle with fractions?

The biggest reason fractions are so difficult is because each fraction with a different denominator is in an entirely different number system! In a fraction, the denominator tells you what base you're in.

Math Antics - Adding and Subtracting Fractions

What challenges could learners experience in addition and subtraction of common fractions?

The study found that learners made a number of errors in the addition and subtraction of fractions, including conceptual errors, carelessness errors, procedural errors and application errors. This finding supports findings that primary school children experience difficulties when learning the concept of fractions.

What are your struggles in solving fractions?

One reason students struggle with fraction operations is that fractions are just less intuitive than whole numbers. Students constantly add and subtract whole numbers in their everyday lives, even without realizing it. On occasion, they even multiply and divide.

What is a common mistake when adding and subtracting mixed numbers?

3)Believing that only whole numbers need to be manipulated in computations with fractions greater than one. When adding or subtracting mixed numbers, students may ignore the fractional parts and work only with the whole numbers (e.g., 53/5 – 21/7 = 3).

What is conceptual understanding fractions?

Conceptual understanding of equivalent fractions involves more than remembering a fact or applying a procedure. It is based on an intricate relationship between declarative and procedural knowledge; between fraction interpretation and representation.

What is the main cause of errors and misconceptions in the learning of mathematics?

The main cause of errors and misconceptions is superficial understanding, which was most probably due to teachers rushing to complete the extensive syllabus, and consequently, students resorted to memorizing rules because of surface understanding.

What is a common misconception about the operation of multiplication?

It is a very common misconception that multiplication makes things bigger. The word 'multiple' itself carries a sense of many or a great number. Children first encounter multiplication in the context of whole numbers, a situation where you mostly end up with a larger number.

What are the misconceptions in multiplication?

How do you correct misconceptions in maths?

Facilitate a discussion about the mistake, focusing on having the pupil explain their thinking e.g. by asking questions such as “How did you come up with that answer?” and “Why do you think it's correct?” This clears up whether the error was a simple case of 'slip of the mind', or a misconception.

What is a common error of students in place value?

a failure to recognise the structural basis for recording 2 digit numbers (eg, sees and reads 64 as “sixty-four”, but thinks of this as 60 and 4 without recognising the significance of the 6 as a count of tens, even though they may be able to say how many tens in the tens place)

How do you add and subtract fractions with different denominators?

How do you teach adding and subtracting mixed numbers?

Step 1: Find the Lowest Common Multiple (LCM) between the denominators. Step 2: Multiply the numerator and denominator of each fraction by a number so that they have the LCM as their new denominator. Step 3: Add or subtract the numerators and keep the denominator the same.

What is a common mistake many students make when dividing by fractions?

Students may have difficulty simplifying fractions because of a shaky understanding of division. Students often order fractions incorrectly and cannot place them on a number line. They cannot easily count fractions the way they count whole numbers (1,2,3,4…).

Why do some students have difficulty solving questions that involve operations with fractions and decimals?

The results showed that students' difficulties in solving mathematics word problems on the operation which involve whole numbers, fractions, and decimals are caused by: 1) Students' difficulties in the word problem, 2) Students' difficulties in understanding the concept of fractional operations, 3) Students have less ...

What is found challenging in fractions and decimals?

The challenge I faced while learning fractions was the addition and subtraction of fractions. 3. The challenge I faced while learning decimals was to interpret the greater value of numbers with a decimal.

What are 3 misconceptions that students have about fractions?