**The Fear of Fractions!**

divide is a new concept with an entirely different notation which makes it unmanageable for students to understand. A depart of the reason why students find it strenuous is besides that they have only ever worked with wholly numbers. So naturally, fractions seem unfamiliar to them.

The struggles and challenges with fractions are real.

The National Assessment of Educational Progress, 2005 states that “ The mathematics education literature is resounding in its findings that understanding fractions is a challenging area of mathematics for north american students to grasp ”. It ’ s this initial fear of fractions that propels far and makes comprehending the addition and subtraction of fractions burdensome .

This article will help students understand how to add and subtract fractions with comfortable steps and ocular models. We ’ ll besides look at some tricks to simplify adding and subtracting fractions.

Read on to make sure that fractions are your kids ’ friends and not a enemy !

**Table of Contents**

**What are Fractions?**

Most curriculums focus on fractions as shaded regions or areas, but they are beyond that. Students much see fractions as an act of dividing and shading parts of shapes, so they miss out on the fact that fractions are numbers between the whole numbers.

Take a close look at the ruler double below. The scar between 0 and 1 represent numbers that are different from unharmed numbers. These are called fractions .

Fractions – numbers between whole numbers It ’ randomness important to emphasize that fractions are numbers that help us be accurate and accurate with amounts. We don ’ thymine always have one entire kilogram or one full column inch while measuring. consequently, it becomes critical to find a way to represent these “ parts ” and that is where fractions take charge .

Fractions are written as a/b where “ a ” is the number on the top and is called the numerator. While “ bel ” is the total at the bottom and is called the denominator .

For model : For the fraction 1/2 ; 1 is the numerator and 2 is the denominator .

Students often confuse the numerator with the denominator and frailty versa. An comfortable way for these confuse terms is to remember them like – D for down and D for the denominator. So the Denominator constantly goes down !

**TYPES OF FRACTIONS:**

The most coarse types of fractions are :

Types of fractions The most normally use fractions while adding and subtracting fractions are :

**Like and Unlike Fractions** .

Fractions with the **same denominators** are called **Like fractions.**

**Example: **

Like fractions Fractions with **different denominators** are called **unlike fractions** .

**Example: **

Unlike Fractions Another type of fraction that students must know before learning to add and subtract fractions is : ** Equivalent Fraction**

Fractions that have unlike numerators and denominators but are equal to the like value are called equivalent Fractions .

Example :

All fractions 1/2, 2/4, 3/6, and 4/8 represent the same value which is ‘ HALF ’

As fractions are like any other numbers, they can be represented through different models .

**Models for Representing Fractions:**

The most common models for representing fractions are :

**a) ****Area Model:**

In the area exemplary, fractions are represented as parts of an area or a region .

circular and orthogonal fraction sets are used to develop an understand that fractions are parts of a unharmed .

Examples of Area Model :

Area Model

**b)**** ****Linear Model:**

In the linear model, fractions are considered as length rather of areas. The number line is an significant linear exemplar for students to grasp fractions as numbers .

The linear model for the divide ¾ will be :

Linear Model

**c) ****Discrete Model:**

In the discrete model, the whole is sympathize to be a set of discrete objects. Subsets of this whole make up the fractional parts.

For exercise half of the class, 1/3 of a tray of eggs. Counters, marbles, cubes or any other set of objects that can be counted can be used as a manipulative to model fractions .

**How to Make Adding and Subtracting Fractions Easy**?

**Doing fractions > Learning fractions **

The first gear and foremost thing that students need to do whilst learning to add and subtract fractions is understand fractions better. They need to rehearse fractions to make connections to the real world, i.e, they need to fold papers, cut parts, color shapes, etc.

One major challenge with fractions is that it ’ s not always concrete. We start teaching fractions through visuals but when it comes to operations with fractions we switch to rules and procedures for the same. Rote memorization of the steps leads to more confusion.

In fraction accession, we add the numerators but not the denominators. But in fraction generation, we multiply the denominators angstrom well as the numerators. This puzzles the students even more.

It ’ second good advised to use ocular models to show the addition of fractions which will help students understand the steps rather than mugging the steps without conceptual clarity.

⅛ is one slit carved out of the total 8 slices ,

And 2/8 are 2 slices out carved of the entire 8 slices ,

now if we add or put together both the fractions/pizza slices, we get 3 slices of the 8 pizza slices which imply 3/8 .

**Concrete -> Contextual -> Computational **

To introduce a new and catchy concept like fractions, it is critical to provide students with ample opportunities to concretely absorb it. This means immerse students in experiences like paper abridge, newspaper fold, drawing, newspaper pizza, apples, chocolate bars, etc. merely by using such experiences will they be able to see, touch, and feel the concept of fractions and make their own discoveries .

Once students get enough of this concrete exposure, they would start making connections between these objects and the real worldly concern .

A bunch of time should be spent creating, exploring, pen up, and visualizing fractions before moving them to fractional problems involving plain numbers .

For exemplar : Before asking ¼ of 20 = ?, we can present a real-world scenario like this :

“ Ron had 20 dollars. He spent ¼ of it. How a lot money is he left with ? ”

This will help evening a scholar with little understanding of fractions to start making connections .

**Show them “WHY” the rules work**

If the notion of fractions as numbers is developed well then it is easier to understand operations on fractions besides. fair like we add and subtract numbers, fractions besides can be added and subtracted. It is important to emphasize conceptual understanding along with the procedural cognition of the steps .

For example :

We know, 1 apple + 1 apple = 2 apples

similarly, we can add fractions besides .

We besides know 2 apples + 3 apples = 5 apples

similarly, we can add fractions besides :

To know the kernel of 2/6 and 3/6 ; consider it as two one-sixths and three one-sixth which will add up to five one-sixth equitable like we add numbers .

immediately let ’ s take a subtraction exercise :

We know 5 apples – 2 apples = 3 apples

On exchangeable lines, we can subtract fractions besides :

In the encase of “ like fractions, ” we can merely add/subtract the numerators and keep the denominator the same. But we can ’ thyroxine add unlike fractions as we add like fractions .

The reason behind this is very elementary .

Just like we can ’ thymine add 2 apples and 3 oranges and say the sum is 5 applonges, we can ’ thymine total fractions with different denominators. It is, thus, important to first specify addition as the combination of two or more like-unit quantities. similarly, subtraction is taking away like-unit quantities .

so, how do we add/subtract unlike fractions ? Let ’ s attend into that adjacent !

**STEPS TO ADD AND SUBTRACT FRACTIONS**

now, let ’ s look at the steps we can follow to add or subtract fractions :

**Step 1** : Make denominators the same

**Step 2** : Add or Subtract the numerators ( keeping the denominator the same )

**Step 3** : Simplify the fraction

To add or subtract unlike fractions, the inaugural step is to make denominators the same so that numerators can be added equitable like we do for like fractions .

**STEP 1: SAME DENOMINATORS**

How do we make denominators the same?

In the lawsuit of like fractions, the denominators will already be the like, so you can skip Step 1 and move to Step 2 .

For Unlike fractions, there are 2 possibilities :

i ) If one denominator is a multiple of the other denominator

model : ½ + ¾

In this case – 4 is a multiple of 2. We can multiply 2 by 2 to make it 4 and as a consequence, the denominators will become the same. so, the larger phone number becomes the common denominator .

apply :

therefore the trouble now becomes :

If one denominator is a multiple of the other, we can multiply the smaller denominator by a total ( say k ) that creates the larger denominator. then the larger denominator becomes the common denominator .

two ) If both the denominators have no common factor

model : ¼ + ⅗

In this encase, 4 and 5 have no common factors. We can plainly multiply the denominators to get a common denominator.

4 X 5 = 20 so 20 is the coarse denominator for both the fractions .

If there is no park component to both the denominators then you multiply both the denominators to get the coarse denominator .

Let ’ s see how we will get 20 as a coarse denominator for both the fractions :

If we multiply the denominator, we have to multiply the numerator equally well to get an equivalent fraction .

so the problem now becomes :

**STEP 2: ADD/SUBTRACT NUMERATORS**

This dance step is pretty simpleton and identical aboveboard. We have to add/subtract the numerators and the result of their sum/difference is the new numerator. The park denominator ( as discussed in Step 1 ) remains the same.

Read more: How to Tie a Tie: 7 Knots for All Occasions

Let ’ s take our previous examples and continue from there :

- ½ + ¾

After making the denominators the lapp, this trouble looks like this :

now, we need to add the two numerators together ( 2+3 =5 ) to get the new numerator while the denominator ( 4 ) remains the same .

So the answer will be 5/4 .

- ¼ + ⅗.

After making the denominators the same, this problem looks like this :

immediately, we need to add the numerators together ( 5 + 12 = 17 ) to get the new numerator while the denominator ( 20 ) remains the same .

So the answer will be 17/20 .

**STEP 3: SIMPLIFY THE FRACTION**

The answers we have derived above are discipline, but we may simplify the fraction far till there are no coarse factors in the numerator and the denominator other than 1.

The fraction can be reduced to its simplified mannequin by removing the common factors .

Let ’ s continue with our former examples :

And ,

In the above cases – 5/4 and 17/20 are already simplified fractions as the numerator and the denominator have no common factors.

Let ’ s take some examples of fractions that can be simplified :

4/12 is not simplified .

4 is a common factor in both the numerator and the denominator so it can be reduced to its simplified imprint as follows :

**Please note: ** We will not be taking up blend numbers as a separate case because these are besides fractions written in the different ( interracial ) shape .

Let ’ s summarize these steps by taking one exemplar of addition and subtraction each .

time to practice all three steps together !

addition Problem : 3/4 + 1/12

**Step 1: Make the denominators the same**

Denominators are 4 and 12. 12 is a multiple of 4 so the coarse denominator will be 12 .

**Step 2: Add/Subtract the numerators (keeping the denominator as same)**

**Step 3: Simplify the fraction**

To simplify 10/12, the coarse factor is 2

so 10/12= 5/6 ( in simplified form )

Hence, 3/4 + 1/12= 5/6

now let ’ s look at a subtraction trouble :

Example : 2/5 **–** 1/3

**Step 1: Make the denominators the same**

Common denominator will be 3 ten 5 = 15

**Step 2: Add/Subtract the numerators (keeping the denominator the same)**

**Step 3: Simplify the fraction**

1/15 is in its simplify form already as 1 and 15 have no coarse factors.

**The Butterfly Method **

A very interest and utilitarian method to promptly add/subtract fractions is the butterfly method .

In this method, we draw the chat up wings to imply which two numbers are to be multiplied together. We then go on to write the result in the respective antenna. The denominators are multiplied and the consequence of that is written below in the abdomen .

In the end, we just add/subtract the antenna and write it over the abdomen to get the result .

**Adding/Subtracting Fractions – Common Mistakes**

Teachers need to ensure that students are taken gradually from the concrete to the contextual to computational degree.

Students need to be given a lot of examples to help them get over some of the coarse mistakes and misconceptions :

**1. Adding/subtracting numerators and denominators**

One significant thing to pay close attention to while adding/subtracting fractions is the way students represent them :

The most common error in adding fractions is to add both the numerators and the denominators individually just as we add whole numbers .

For model : When adding 2/3 and 1/4, a coarse mistake is to represent each fraction as shown above and then put them together to form 3/7 as the answer.

When students add, combine or find the summarize by putting together the wholes and both the fractional parts, it entirely seems reasonable that they look at each fraction independently .

so, it is important to emphasize that fractional parts can not be manipulated independently from their unharmed .

That is why it is necessity to have a common denominator. In the case of a common denominator, the fractions can be interpreted on the lapp diagram and combined. Let ’ s spirit at this like model when done on the coarse solid .

In this case, the common denominator for 2/3 and 1/4 will be 12.

immediately consider the whole made of 12 parts .

immediately let ’ s find ⅔ and ¼ .

To find 2/3 first separate the whole into 3 equal parts :

2/3 will be 2 of these 3 equal parts :

2/3 = 8/12

similarly, to find 1/4 we need to divide the whole into 4 equal parts :

1/4 will be :

1/4 = 3/12

immediately to add 2/3 and 1/4 we can combine 8 parts and 3 parts whose summarize equals 11 parts.

2/3 + 1/4 = 8/12+ 3/12 = 11/12

similarly, this lapp err is observed in subtracting fractions american samoa well. Both the numerators and the denominators are subtracted individually good as we subtract wholly numbers.

For example : 5/6 – 1/3 = ( 5-1 ) ( 6-3 ) = 4/3

Let ’ s find the right room of solving 5/6 – 1/3 = ?

In this sheath, the common denominator for 5/6 and 1/3 will be 6 ( common multiple ).

now consider the unharmed made of 6 parts :

5/6 will be :

For 1/3 we divide the whole into 3 equal parts :

1/3 will be one of these three equal parts :

1/3 = 2/6

nowadays to subtract 1/3 from 5/6, we will take away 2 parts from the 5 parts of the lapp solid.

5/6 – 1/3 = 5/6 – 2/6 = 3/6

**2. Adding/subtracting numerators while ignoring the denominators**

As students struggle to see fractions as different operations, they frequently treat them as whole numbers.

12/13 + 7/8 = 19, because 12 + 7 = 19

12/13 – 7/8 = 5, because 12 – 7 = 5

The key here is to make their understanding of fractions concrete, right from the very begin .

**3. Adding/subtracting denominators while ignoring the numerators**

Some students add only the denominators and ignore the numerators. They look at the denominators as two unharmed numbers and add/subtract them.

12/13 + 7/8 = 21, because 13 + 8 = 21

12/13 – 7/8 = 5, because 13 – 8 = 5

**Interesting Activities for Addition and Subtraction of fractions**

Incorporate simple activities like cutting real-world objects to develop sake and a better grip of fractions. Activities like Tic tac toe, BINGO, or matching activities can be done to make fractions problems more fun .

**Fraction in Everyday Life**

Parents should encourage talking about fractions with kids in casual life. Encourage kids to apply fractions in daily tasks like equal division of things, in measurement, or while cooking their darling new recipes. We can besides include fractions while talking about time or the marks kids scored in school !

Talking about fractions evades the fear of it and kids are more likely to enjoy practicing them.

**Games on Fractions**

Games encourage students to drill a distribute of questions which they broadly don ’ thyroxine like doing differently. Check out these fun fraction games at SplashLearn

**Fractions Models/Manipulatives**

Using manipulatives like fraction strips, area models, lego blocks and numeral lines make fractions interesting and engaging for the kids. These manipulatives help kids visualize fractions and hence understand them better .

**Fraction Word problems**

Solving contextual problems helps students relate divide learning to real-life situations. They understand the significance, the need, and importance of fractions and how to apply them to solve problems. You can check out these divide word problems games on SplashLearn and make fractions a lot simple !

**To Summarize:**

- It’s important for students to recognize that fractions are beyond shading and coloring.
- Fractions are numbers that are used to represent the numbers between any two consecutive whole numbers.
- Help students practice fractions by cutting, pasting, coloring to help them understand fractions better and have fun with them.
- Use fraction models to help them visualize and grasp addition and subtraction of fractions.
- Make sure they know why the steps of adding/subtracting fractions work rather than just blindly applying the steps.
- As a parent,use fractions in everyday conversations, relate fractions to real-life contexts and provide them instances from daily life activities like cooking, baking, time and measurement.

**Teach Fractions with SplashLearn **

Loved by 40+million parents, SplashLearn is a one-stop solution for your kids ’ mathematics and read travel. You can make your short learners play games on adding and subtracting fractions or learn through worksheets. With curriculum-aligned teach, SplashLearn provides a personalized experience that adapts to every child ’ sulfur needs .

## Frequently Asked Questions (FAQs)

## 1. What are fractions?

Fractions are numbers between the wholly numbers ( 0,1,2,3,4 ). They represent a portion/part of an entire thing. A divide has two parts – numerator and denominator .

## 2. What are the steps for adding and subtracting fractions?

**Step 1** : Make denominators the like

**Step 2** : Add/Subtract the numerators ( keeping the denominator as same )

**Step 3** : Simplify the fraction

## 3. How do you add and subtract fractions with different denominators?

Fractions with different denominators can be added by converting them to fractions with the same denominators with the help of equivalent fractions .

## 4. How do you add and subtract mixed numbers?

first, write the interracial numbers as fractions. now add/subtract just like you do with fractions. In the end, don ’ t forget to convert the answer ( fraction ) to a desegregate total !

## 5. How do you add and subtract negative fractions?

minus fractions can be considered as fractions with numerators as negative. The steps to add and subtract the negative fractions remain the same as fractions except now kids would need to add negative or incontrovertible numerators .