How To Multiply Divide Add And Subtract 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. Information technology is an abstract notion that challenges the fiddling rockstars to do better.

Operations on fractions add to the complexity as it becomes strenuous for children to understand what these operations hateful and therefore, visualizing them can lead to ameliorate comprehension of the concept. The multiplication and division of fractions might be contradictory to the already existing understanding of multiplying and dividing whole numbers.

For example, multiplying two whole numbers always results in a greater product, but this is not the case with multiplying fractions.

Similarly, dividing two whole numbers usually results in a quotient that is smaller than the dividend, merely this is not the case with dividing fractions.

Division of fractions is unlike than dividing two whole numbers

Due to the lack of proper understanding of these concepts, even among teachers, students have a difficult fourth dimension understanding fractions. It also causes confusion and misconceptions amid them.

The aim of this article is to provide engaging methods that would help children visualize the concepts of multiplication and division. Furthermore, we will besides endeavour to ease the agreement of procedures involved in multiplying and dividing fractions through a elementary methodology involving just 4 steps.

Read on and make learning fractions easy and pleasant!

Tabular array of Contents

• Glossary
• Must-Knows
• Introduction to Multiplying Fractions
• Outset Step to Multiplying Fractions: Visual Modelling
• Multiplying Fractions: 4 Easy Steps
• Assay: Multiplying Fractions Versus Whole Number Multiplication
• Introduction: Dividing Fractions
• Beginning Step to Dividing Fractions: Visual Modelling
• Dividing Fractions: 4 Like shooting fish in a barrel Steps
• Summary
• Oft Asked Questions (FAQs)

Glossary

• Fraction – Part of a whole number written in the form of a/b
• Denominator – The bottom number on a fraction
• Numerator – The number on the top of a fraction
• Unit Fraction – A fraction with numerator ane
• Whole Number – Counting numbers (0, 1, 2, three, 4 …)
• Equivalent fraction – A fraction that has equal/aforementioned value as some other fraction
• Simplifying – Making a fraction simpler
• Proper fraction – A fraction with a value less than one (numerator < denominator)
• Improper fraction – A fraction with a value greater than ane (numerator > denominator)
• Mixed Number – A way of writing improper fractions using a whole number and a proper fraction
• Divisor – A number by which another number is to be divided
• Dividend – A number that is to be divided
• Quotient – The outcome of dividing one number by another
• Remainder – The leftover after division

Starting with the Multiplication & Division of Fractions: Must-Knows

• Understanding 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 lowest form
• Conversion of improper fraction into mixed number and vice versa
• Addition of fractions

Introduction: Multiplying Fractions

Before starting with the steps of multiplying fractions, it is imperative to develop a conceptual understanding of fraction multiplication. Children should be able to visualize multiplication and should know what information technology ways to multiply a fraction by a whole number or a fraction.

Quick Tip: Outset with modelling multiplication or partition involving only whole numbers. You can then motion on to partial numbers. This way, the existing noesis kids have, of multiplying or dividing whole numbers, volition be refreshed and they would exist able to connect it to constructing the models for fraction multiplication or partition.

Let's beginning with fraction multiplication.

First Pace to Multiplying Fractions: Modelling

Using visual models as a learning aid makes the process of both instruction and learning more constructive, fun, and interactive. It is a student-centered arroyo that helps kids visualize central mathematical concepts, which farther aids them in gaining a deeper understanding of the concept at a root level.

For the teachers, visual models can trigger discussions of mathematical ideas and relations with previously known concepts. It helps them have a better agreement of the students' grasp on the concept.

For that reason, teaching fraction multiplication initially through models and and so proceeding towards standard procedures would be the ideal approach.

To brainstorm with, Fraction Multiplication can have upwards 3 dissimilar forms.

Level 1A: Whole × Fraction

Level 1B: Fraction × Whole

Level two: Fraction × Fraction

Please note: We will non exist taking up mixed numbers every bit a separate example because these are besides fractions written in a different class. To help your kids learn about mixed numbers and improper fractions through fun games, y'all can sign upwardly here!

Level 1A: Whole × Fraction

Instance ane: Tim used ¼ of the pumpkin to make one pumpkin pie.

He made iii pies. Let's notice out how many pumpkins he used in total.

Every bit he used ane-fourth of the pumpkin 3 times, its multiplication expression would be 3 × ¼

3 times 1/iv is three/4

Then,

3 × ¼ =  _iii/iv

And then, Tim used three-quaternary of the pumpkin to brand 3 pies.

Case 2: If Tim had to make 5 pies, how many pumpkins would he demand?

v times one/iv is 5/4

5 × ¼ = _5/4

So, Tim would need one whole and a quarter piece of the pumpkin to make five pies.

Level 1B: Fraction × Whole

Visualizing the model for Fraction × Whole could be really challenging for kids.

To outset with, the outset number in the multiplication sentence denotes the number of groups or the number of times something is to exist repeated. Only, in the Fraction × Whole scenario, how do nosotros form groups in a fractional number?

Example: ¼ × eight

We can depict this expression in simple words as one-quaternary of eight . Mathematically, the discussion 'of' ways multiplication.

Let's draw a model for this expression.

Step 1:

Step 1 – Multiplication of fraction with whole numbers

Step 2:

Pace two – Multiplication of fraction with whole numbers

So, ¼ × 8 = two

Example ane: ¾ × 8

This means: three-fourth of viii

Example 1 – Multiplying fraction with the whole number

So, ¾ × 8 = 6

Let's endeavour a few more examples.

Example 2:  Jamie prepared 4 glasses of juice using 3 limes. Observe the number of lime fruits he used for each glass of juice.

This means he used a quarter of 3 limes to ready ane glass of juice.

Mathematical expression to be solved for this example: ¼ × iii

Let'due south consider the three limes to be A, B and C.

Example 2 – Multiplying fractions with whole numbers

Ane-quaternary of all times in each plate

Each plate represents one-4th or quarter of the whole lot, that is, iii limes.

How many fourths are there in 1 plate? Three-fourths

And so, ¼ × iii = ¾

Jamie used ¾ of lime in ane glass of juice.

Example 3: Detect out how many limes Jamie used for iii glasses of juice.

This means that nosotros demand to find out how much three-fourth of 3 limes is.

Mathematical expression to be solved for this situation: ¾ × 3

Finding out how many limes are used for three glasses of juice

Each plate represents one-fourth or quarter of the whole lot i.e three limes. And so, three plates will represent iii-fourths.

How many fourths are there in three plates? Nine-fourths

Summary of the last example

Then, ¾ × 3 = _9/4

Jamie used _9/4 limes in three glasses of juice.

What does Fraction 10 Whole denote?

Level 2: Fraction × Fraction

Multiplying a fraction with fraction is also a tricky form and students find it quite difficult to understand the application of multiplying two fractions.

We can now help them visualize this concept through this engaging and simple paper folding activity.

Example ane: Visualize and solve: ⅓ × ½

In general, this expression would mean one-3rd of the half . You can help your kid model this scenario using a canvas of paper.

Ask your little learner to follow these elementary steps:

1. Take a rectangular sheet of paper and fold it in half.
2. Next, fold the one-half into 3 equal parts.
3. Color one of the folded sides to testify i-third of the half.
4. Open up the sheet support.
5. Identify which fraction of the whole the shaded role represents.

Paper folding activity to understand multiplying fractions

⅓ × ½ = ⅙

MUST Endeavor More than!

Encourage your children to endeavor multiplying different fractions using the same technique.

Let'southward explore a few more examples:

The following models follow the same principle as in the newspaper folding activeness above. The principle mentioned is modelling ii fractions in one model.

Example 2: How much is ¼ × ½?

This represents a quarter of half.

Case ii – Multiplying fraction with fraction

Tip on multiplying fraction with fraction

Instance 3: _v/7 × ¾

Example 3 – Multiplying fraction with fraction

Example 4: _{1/three × 1⅗}

Example four – Multiplying fraction with fraction

After a few examples, yous tin can encourage your child to directly draw the combined model.

Draw the model to multiply two fractions with these steps:

1. Draw a big rectangle.
2. Divide it into every bit many equal horizontal strips every bit the denominator of the beginning fraction. Shade parts to stand for the beginning fraction.
3. Next, carve up the same model into every bit many equal vertical strips as the denominator of the 2d fraction. Shade parts to represent the second fraction.
4. Identify the overlapping office in the model. The fraction it represents is the product of the 2 fractions.

Multiplying Fractions: 4 Easy Steps

Encourage kids to find the products derived from the models and also tell them which rule is being followed in the multiplication of fractions.

We can help them understand the process through these 4 easy steps of multiplying fractions.

1. Write both the numbers in fraction course.
2. Multiply the numerators. The product is the new numerator.
3. Multiply the denominators. The product is the new denominator.
4. Rewrite the answer in the lowest or mixed number form.

Check out a few examples.

Example i:

Example 1 – Steps of multiplying fractions

Example two:

Example 2 – Steps of multiplying fractions

Example 3:

Case 3 – Steps of multiplying fractions

Analysis: Multiplying Fractions versus Whole Number Multiplication

Question: Do nosotros always get a greater product on multiplying two numbers?

Detect the following multiplication problems.

6 × 4 = 24
2 × 9 = xviii
iii × 1 = iii
5 × seven = 35
10 × viii = lxxx
19 × 1 = 19
8 × 0 = 0
vii × eleven = 77
sixteen × 2 = 32

Do you recall the same question holds for multiplication with fractions as well?

The respond to that is 'sometimes'.

Permit'southward check out a few cases to better understand them.

Case 1: When one of the multiplicands is 0

The product will also be a zero regardless of what the other fraction is.

_{¼ × 0 = 0/4 = 0}

_{⅗ × 0 = 0/5 = 0}

_{7/2 × 0 = 0/2 = 0}

Case 2: When one of the multiplicands is a fraction less than ane

The product volition be smaller than the other fraction.

_{3/4 × 7/3 = 21/12 = 7/4 (< seven/3)}

_{1/4 × vii/8 = seven/32 (< vii/8)}

_{3/4 × ane/9 = 1/12 (< 1/9)}

Case iii: When 1 of the multiplicands is a fraction equivalent to 1

The product will be the same every bit the other number.

_{1 × vii/8 = vii/8}

_{6/half dozen × nine/5= 54/30= 9/5}

_{6/6 × 3/5= 18/30= iii/5}

Case 4: When one of the multiplicands is a fraction greater than 1

The product is will be greater than the other fraction.

_{8/3 × two/5= 16/15 (> 2/5)}

_{six/10 × ix/5= 54/50= 27/25 (> 6/10)}

_{9/6 × one/vii= nine/42= 3/14 (> 1/7)}

Case five: When both of the multiplicands are fractions greater than 1

The product will be greater than both the fractions.

_{8/3 × 3/two  = 4 (> 8/3, 3/2)}

_{6/4 × 5/2= 30/8 (> 6/4, 5/2)}

Dividing Fractions in Existent Life: Introduction

We come beyond situations in our solar day-to-day lives where we apply the concept of fraction division. Fraction partition can be made interesting and the concept can be fully instilled in kids' minds if they are challenged to solve scenarios from real life.

This would help the kids visualize and make sense of fraction partitioning.

Instance: Suppose yous have 3 apples, each cut in half. Among how many people tin you distribute these 3 apples if each gets one-half a piece?

Allow's film this situation and solve information technology. After all, an apple a solar day volition certainly keep the math blues away!

Dividing three apples between half-dozen people

The trouble tin can be further extended by modifying the fraction.

For example, what if y'all decide to give each person a quarter piece? How many people can be served now?

Understanding fraction division

Understanding Fraction Division

Or what if you decide to give each person 3 quarters? How many people can be served now?

Conceptual Understanding of Fraction Division

Conceptual Understanding of Fraction Division

Comprehending a problem and then modelling it is a crucial step in whatsoever problem-solving scenario of fraction sectionalisation. Encourage students to effort visualizing the scenario and and so look for its solution.

Draw and Solve!

A group of friends bought a pizza. They shared the pizza every bit and finished it.

Try identifying how many friends there were if each of them got:

one-eighth of the pizza		two-8th of the pizza
8 friends		four friends
So, i ÷ ⅛ = 8		Then, 1 ÷ two/8 = four

Outset Footstep to Dividing Fractions: Modelling

Just similar multiplication, once students gain expertise in modelling sectionalisation problems for fractions, and then the method to find the answer is a cakewalk.

Therefore, for the division of fractions as well, an arroyo from visual to the non-visual method is suggested. For students, such an arroyo is more plausible as it lays a strong conceptual foundation.

Let's see a few examples.

Whole Number ÷ Fraction

Case 1:

Example 1 – Division of Whole Numbers with Fractions

Example 2:

Example 2 – Segmentation of Whole Numbers with Fractions

Quick Tip: When a divisor is a fractional number – it helps to draw the partition 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 mitt with more ease.

Fraction ÷ Whole

Agreement partitioning of fraction with whole numbers

Fraction ÷ Fraction

Agreement division of fraction with a fraction

Mixed Number ÷ Fraction

Understanding division of mixed numbers with fractions

Dividing Fractions that Involve the Remainder

Example 1

Example 1 – Fraction partition involving remainder

Case 2:

Example 2 – Fraction division involving remainder

Some Mutual Struggles in Dividing Fractions

1. Students often struggle to understand the departure between dividing past 2 and dividing by ½.

The following models can help them easily visualize the difference.

Struggles in fraction segmentation

Struggles in fraction sectionalization

2. Students often struggle to understand that division of fractions will non always upshot in a smaller quotient.

Dividing Fractions: 4 Easy Steps

It's imperative that we encourage children to observe the quotients derived from the models and tell them which rule is being followed in the multiplication of fractions. Doing such activities with them can help in developing inference and reasoning skills.

Help them learn the process through these 4 easy steps to divide fractions.

1. Flip the divisor fraction.
2. Modify sign from ÷ to ×
3. Multiply the fractions.
4. Simplify.

Steps to dividing fractions

Fundamental to Excel—Practice More

Understanding fractions and their operations becomes a lot easier in one case children gain expertise in visualizing the problem and knowing what needs to exist calculated. Simply to proceeds such confidence, they need to practise a lot of math problems. It'south necessary that they model the problem and then solve them.

You can refer to these worksheets on SplashLearn, which are easily downloadable and printable, to help solidify your kid's agreement of multiplying fractions.

To sum up

• For deeper understanding of the concept, brand sure to provide kids with an environment conducive to experiential learning.
• You can use your kids' previous and existing knowledge of multiplying and dividing whole numbers to build new noesis of multiplying and dividing fractions.
• Encourage your kids to visualize problems and model them. Brand them feel comfortable with request questions.
• It'south imperative to focus less on answering accurately and more on the reasoning and thought process of the child.
• As a parent, chronicle the mathematical problems with real-life situations and provide instances from day-to-day activities.

Make Fractions Easy with SplashLearn

With interactive games and rewards to boost your child's confidence and scores, you lot can now brand learning piece of cake and seamless. Join our community of 40+ million fearless learners today!

Often Asked Questions (FAQs)

Q1 – How to multiply fractions step by stride?

1. Write both the numbers in fraction form.
2. Multiply the numerators.
3. Multiply the denominators.
4. Simplify or rewrite the respond in mixed number class.

Q2 – How to divide fractions step by step?

1. Flip the divisor fraction.
2. Change sign from ÷ to ×.
3. Multiply the fractions.
4. Simplify.

Q3 – How do you place if multiplication past a fraction will event in a greater or a smaller product?

Compare the numerator and denominator of the fraction to cheque whether the production will be greater or smaller than the number to which they are multiplied.

Greater Product → Numerator > Denominator. Examples: iii/two, 4/3, 8/5, and then on.

Smaller Production → Numerator < Denominator. Examples: iii/4, 4/7, 5/ix, and so on.

How To Multiply Divide Add And Subtract Fractions,

Source: https://www.splashlearn.com/blog/how-to-multiply-divide-fractions-steps-with-visual-models/

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