how to draw a model for dividing fractions
Introduction – Multiplying & Dividing Fractions
Tough creatures – The Fractions!
Fractions are considered to be one of the trickiest math concepts for young kids because it has different notations than whole numbers. It is an abstract notion that challenges the little rockstars to do better.
Operations on fractions add together to the complexity as it becomes strenuous for children to understand what these operations mean in concrete and therefore, they visualize them for better understanding. The multiplication and division of fractions might be contradictory to the already existing understanding of multiplying and dividing whole numbers.
For instance, multiplying 2 whole numbers ever results in a greater product, only this is not the case with multiplying fractions
Similarly, dividing two whole numbers usually results in a caliber that is smaller than the dividend, merely this is non the case with the dividing fractions.
Due to the lack of deep understanding of these concepts, even among teachers, students accept a hard fourth dimension agreement fractions. Information technology as well paves way for confusion and misconceptions among them.
The aim of this article is to provide engaging methods that would help children visualize multiplication and division concepts. Furthermore, we volition too try to ease the agreement of procedures involved in multiplying and dividing fractions through a simple methodology involving simply 4 steps.
Read on and make learning fractions piece of cake and pleasant!
Table of Contents
- Glossary
- Must-Knows
- Introduction to Multiplying Fractions
- First Step to Multiplying Fractions: Visual Modelling
- Multiplying Fractions: 4 Easy Steps
- Analysis: Multiplying FractionsVersus Whole Number Multiplication
- Introduction: Dividing Fractions
- First Step to Dividing Fractions: Visual Modelling
- Dividing Fractions: iv Like shooting fish in a barrel Steps
- Summary
- Frequently Asked Questions (FAQs)
Glossary
- Fraction – Function of a whole number written in the grade of – a/b
- Denominator – The bottom number on a fraction
- Numerator – The number on the top of a fraction
- Unit of measurement Fraction – A fraction with numerator 1
- Whole Number – Counting numbers (0, 1, 2, 3, 4…)
- Equivalent fraction – A fraction that has equal/same value as some other fraction
- Simplifying – Making a fraction more unproblematic
- Proper fraction – A fraction with a value less than 1 (numerator < denominator)
- Improper fraction – A fraction with a value greater than 1 (numerator > denominator)
- Mixed Number – A way of writing improper fractions using a whole number and a proper fraction
- Divisor – A number by which some other number is to be divided
- Dividend – A number that is to exist divided
- Quotient – The result of dividing ane number past some other
- Residue – The leftover later on division
Starting with the Multiplication & Partition of Fractions: Must-Knows
- Agreement of multiplication and division with whole numbers
- Understanding of fractions and their visual models
- Representing whole numbers as fractions
- Equivalent fractions
- Simplifying fractions to their everyman form
- Conversion of improper fraction into mixed number form and vice-versa
- Addition of fractions
Introduction: Multiplying Fractions
Before starting with the steps of multiplying fractions, information technology is imperative to develop a conceptual understanding of fraction multiplication. Children should be able to visualize multiplication and should know what it ways to multiply a fraction by a whole number or a fraction.
Quick Tip: It is suggested to offset with modeling multiplication or division involving only whole numbers. You tin then move on to partial numbers. This way kids' existing knowledge of multiplying or dividing whole numbers volition be refreshed and they would be able to connect it to amalgam the models for fraction multiplication or sectionalization.
Permit'due south first with Fraction Multiplication.
First Footstep to Multiplying Fractions: Modelling
Using visual models as a learning help makes the process of both didactics and learning more constructive, fun, and interactive. It is a student-centered approach and helps kids in visualizing key mathematical concepts, which further helps them to gain a deep conceptual agreement at a root level.
For the teachers, visual models tin trigger discussions of mathematical ideas and relations with previously known concepts. It helps them accept a amend understanding of students' thought processes about the concept.
For that reason, teaching fraction multiplication initially through models so proceeding towards standard procedures should be the ideal approach.
To begin with, Fraction Multiplication can take up 3 different forms.
Level 1A: Whole × Fraction
Level 1B: Fraction × Whole
Level 2: Fraction × Fraction
Please note: We will not be taking up mixed numbers equally a carve up instance because these are also fractions written in a different form. To help your kids learn most mixed numbers and improper fractions through fun games, you tin sign up here!
Level 1A: Whole × Fraction
Case 1: Tim used ¼ of the pumpkin to make one pumpkin pie.
She fabricated 3 pies. Let'southward find out how many pumpkins she used in total.
As she used one-fourth of the pumpkin 3 times, its multiplication expression would exist 3 × ¼
So,
3 × ¼ = 3/iv
And then, Tim used three-quaternary of the pumpkin to brand 3 pies.
Instance ii: If Tim had to brand 5 pies, how many pumpkins would she need?
5 × ¼ = 5/four
So, Tim would need 1 whole and a quarter piece of the pumpkin to make 5 pies.
Level 1B: Fraction × Whole
Visualizing the model for Fraction × Whole could be actually challenging for the kids.
To start with, the showtime number in the multiplication judgement denotes the number of groups or the number of times something is to be repeated. Merely, in the Fraction × Whole scenario, how do we form groups in a partial number?
Example: ¼ × eight
We tin can depict this expression in simple words as one-fourth of eight . Mathematically, the discussion 'of' means multiplication.
Let'due south draw a model for this expression.
Step i:
Step 2:
So, ¼ × 8 = 2
Instance 1: ¾ × viii
This means: three-fourth of eight
So, ¾ × eight = 6
Allow's endeavor a few more than examples.
Example 2: Jamie prepared four glasses of juice using 3 limes. Find the number of lime fruits he used for each glass of juice.
This means he used a quarter of 3 limes to prepare one drinking glass of juice.
Mathematical Expression to exist solved for this example: ¼ × 3
Let'due south consider the three limes to be – A, B & C
Each plate represents one-4th or quarter of the whole lot, that is, 3 limes.
How many fourths are there in ane plate? Three-fourths
So, ¼ × 3 = ¾
Jamie used ¾ of lime in one glass of juice.
Instance iii: Find out how many limes did Jamie apply for 3 glasses of juice.
This means that we need to find how much is 3-quaternary of iii limes.
Mathematical Expression to exist solved for this situation: ¾ × 3
Each plate represents one-4th or quarter of the whole lot i.e iii limes. So, 3 plates will correspond iii-fourths.
How many fourths are there in three plates? Nine-fourths
So, ¾ × 3 = 9/four
Jamie used 9/4 limes in three glasses of juice.
Level two: Fraction × Fraction
Multiplying Fraction with Fraction is also a catchy form and students find it quite hard to understand the application of multiplying two fractions.
We can now help them visualize this concept through this engaging and simple newspaper folding activity.
Example 1: Visualise and Solve: ⅓ × ½
In general, this expression would hateful one-third of the one-half . You can help your child model this scenario using a canvass of newspaper.
Ask your little learner to follow these simple steps:
- Take a rectangular sheet of paper and fold it into one-half.
- Next, fold the half into 3 equal parts.
- Colour 1 of the folded sides, to show i-third of the half.
- Open upwards the canvas
- Identify what fraction of the whole does the shaded part stand for
⅓ × ½ = ⅙
MUST TRY More than!
Encourage your children to endeavor multiplying unlike fractions using the aforementioned technique. Let's explore a few more examples:
The following models follow the same principle equally in the paper folding action to a higher place. The principle mentioned is modeling two fractions in one model.
Instance 2: How much is ¼ × ½
This represents a quarter of half.
Example three: 5/7 × ¾
Case 4: ane/iii × 1⅗
After a few examples, you can encourage your kid to straight describe the combined model.
Describe the model to multiply two fractions with these steps:
- Describe a big rectangle.
- Divide it into equally many equal horizontal strips equally the denominator of the start fraction. Shade parts to stand for the first fraction.
- Next, carve up the same model into as many equal vertical strips every bit the denominator of the second fraction. Shade parts to represent the 2nd fraction.
- Place the overlapping part in the model. The fraction it represents is the product of the two fractions.
Multiplying Fractions: 4 Like shooting fish in a barrel Steps
Encourage the kids to find the products derived from the models along with telling what rule is beingness followed in the multiplication of fractions.
Nosotros can help them understand the process through these 4 easy steps of multiplying fractions.
- Write both the numbers in fraction course.
- Multiply the numerators. The product is the new numerator.
- Multiply the denominators. The product is the new denominator.
- Rewrite the answer in the everyman or mixed number class.
Check out a few examples.
Case 1:
Example 2:
Case three:
Analysis: Multiplying Fractions versus Whole Number Multiplication
Question: Exercise we always get a greater product on multiplying 2 numbers?
Observe the following multiplication problems.
6 × 4 = 24
2 × ix = 18
three × 1 = iii
five × 7 = 35
x × 8 = 80
19 × i = 19
8 × 0 = 0
7 × xi = 77
16 × 2 = 32
Do you think the same question holds for multiplication with fractions too?
The answer to that is 'sometimes'.
Permit's bank check out a few cases to understand those use cases in a ameliorate capacity.
Case 1: When one of the multiplicands is 0
The product will also be a nix regardless of what the other fraction is.
¼ × 0 = 0/iv = 0
⅗ × 0 = 0/v = 0
7/ii × 0 = 0/2 = 0
Case two: When one of the multiplicands is a fraction less than 1
The product will exist smaller than the other fraction.
3/4 × 7/three = 21/12 = 7/4 (< seven/3)
one/4 × 7/8 = 7/32 (< 7/8)
three/4 × ane/9 = 1/12 (< one/9)
Case 3: When 1 of the multiplicands is a fraction equivalent to 1
The product volition exist the same as the other number.
1 × 7/8 = 7/8
half-dozen/6 × 9/5= 54/thirty= 9/5
6/vi × three/5= xviii/30= 3/v
Case four: When 1 of the multiplicands is a fraction greater than one
The production is will be greater than the other fraction
eight/3 × 2/5= sixteen/fifteen (> two/5)
6/ten × 9/five= 54/50= 27/25 (> 6/ten)
9/6 × 1/7= nine/42= 3/14 (> 1/vii)
Instance v: When both of the multiplicands are fractions greater than i
The product will exist greater than both the fractions.
8/3 × 3/two = 4 (> 8/three, 3/2)
6/4 × 5/two= 30/8 (> 6/four, 5/2)
Dividing Fractions in Real Life: Introduction
Nosotros come up across situations in our day-to-24-hour interval lives where we use the concept of fraction division. Fraction division can exist made interesting and the concept can be fully instilled in our kids' minds if they are challenged to solve scenarios from real life.
This would assist the kids to visualize and make sense of fraction division.
Example: Suppose you have 3 apples, each cut in one-half. To how many people can yous distribute these 3 apples, if each gets one-half a piece?
Let's moving picture this situation & solve it. Also, an apple a day will definitely keep the math blues away!
The trouble can be further extended by modifying the fraction.
For example, what if you lot decide to requite each person a quarter piece? How many people can be served now?
Or what if yous make up one's mind to give each person three quarters? How many people can exist served now?
Comprehending a problem and then modeling information technology is a crucial stride in any trouble-solving scenario of fraction partitioning. Encourage students to try visualizing the scenario and then look for its solution.
Describe and Solve!
A group of friends bought a pizza. They shared the pizza equally and finished it.
Attempt identifying how many friends were there if each of them got—
| one-eighth of the pizza | two-8th of the pizza | |
 |  | |
| 8 friends | iv friends | |
| Then, 1 ÷ ⅛ = 8 | Then, ane ÷ two/viii = 4 |
Kickoff Step to Dividing Fractions: Modelling
Just like multiplication, once students gain expertise in modeling division bug for fractions, and so the procedural method to discover the answer is a cakewalk.
Therefore, for the division of fractions equally well, information technology'south suggested to use the approach from visual to non-visual method. For students, such an approach is more plausible equally it lays a strong conceptual foundation.
Let's see a few examples.
Whole Number ÷ Fraction
Case one:
Case ii:
Quick Tip: When a divisor is a fractional number – it helps to draw the division statements as 'How many groups of (divisor) can be formed from the (dividend)?' or 'How many groups of the (divisor) are there in the (dividend)'. These descriptions help children to visualize the situation at hand with more ease.
Fraction ÷ Whole
Fraction ÷ Fraction
Mixed Number ÷ Fraction
Dividing Fractions that Involve Remainder
Case 1
Instance 2:
Some Common Struggles in Dividing Fractions
- Students often struggle to empathize the difference between dividing past two and dividing by ½
Following models can help them easily visualize the deviation.
- Students oft struggle to understand that it is non necessary that division of fractions will ever result in a smaller quotient.
Dividing Fractions: iv Easy Steps
Information technology'south imperative that we encourage the children to detect the quotients derived from the models and tell what dominion is being followed in the multiplication of fractions. Such activities with them help in developing inference and reasoning skills.
Help them memorize the procedure through these 4 like shooting fish in a barrel steps to divide fractions.
- Flip the divisor fraction
- Alter sign from ÷ to ×
- Multiply the fractions
- Simplify
Key to Excel— Do More
Understanding fractions and their operations become a lot easier one time children gain expertise in visualizing the problem and know what needs to be calculated. Merely to gain such conviction, they need to practice a lot of problems. It'south necessary that they model the problem and then solve them.
You tin can refer to these worksheets on SplashLearn which are easily downloadable and printable, to aid solidify your child's understanding of multiplying fractions.
To sum up,
- For deeper understanding of the concept, make sure to provide kids with the environment for experiential learning.
- You can use your kids' previous and existing knowledge of multiplying and dividing whole numbers to build the new knowledge of multiplying and dividing fractions.
- Encourage your kids to visualise problems and model them. Make them feel comfortable with asking questions.
- It's imperative to focus less on answering accurately and more on reasoning and thought procedure of the child
- As a parent, relate the mathematical problems with existent life situations and provide instances from twenty-four hours-to-mean solar day activities.
Make Fractions Easy with SplashLearn
With interactive games and rewards to boost your kid's confidence and scores, you can at present make learning piece of cake and seamless. Bring together our community of 40+ million fearless learners today!
Frequently Asked Questions (FAQs)
Q1 – How to multiply fractions step by step?
- Write both the numbers in fraction form.
- Multiply the numerators.
- Multiply the denominators.
- Simplify or rewrite the answer in mixed number grade.
Q2 – How to separate fractions pace by step?
- Flip the divisor fraction.
- Change sign from ÷ to ×.
- Multiply the fractions.
- Simplify.
Q3 – How do you lot identify if multiplication by a fraction will result in a greater or a smaller production?
Compare the numerator and denominator of the fraction to cheque whether the product will exist greater or smaller than the number to which they are multiplied.
Greater Production → Numerator > Denominator. Examples: 3/two, four/3, 8/5, and so on.
Smaller Product → Numerator < Denominator. Examples: 3/4, 4/7, 5/nine, and so on.
Source: https://www.splashlearn.com/blog/how-to-multiply-divide-fractions-steps-with-visual-models/
Posted by: jolleycapecontabir.blogspot.com
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