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Fractions

Fun with Fractions

Jack Anderson

Bake a Cake with Fractions!

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A Great Way to Review Basic Concepts

Table of Contents

Expressing a Fraction as Part of a Whole

Classifying Fractions

Equivalent Fractions

Simplest Form of a Fraction

Fractions to Decimals

Let’s begin with a fun question to

get you ready for fractions.

*INTRODUCTION TO FRACTIONS *

*PicScience *

Answer: A

FRACTION

 A that names

of a whole

Or

of a group

GENERAL INFORMATION

 A fraction is always represented as a

with numerator and denominator

 Let’s Say

Or

 numerator (part chosen)

 denominator (total number of parts)

 Read as one-fourth.

EXAMPLES OF SOME FRACTIONS

1

Read as one-half.

2

3 Read as three-sevenths.

7

5

Read as five-eights.

8

FRACTIONAL REPRESENTATION

 A circle is divided into 8 equal parts with 2 parts shaded in red. What fraction of the circle is shaded?

 Red parts – numerator – 2

 Total parts – denominator – 8

2

 So the fraction is represented as

8

 Read: two-eighths of the circle is shaded

WHAT FRACTION OF THE CIRCLE IS

SHADED?

 5 parts are shaded in red

 The circle is divided into 8 equal parts

 Parts – 5 (red) – numerator

 Whole – 8 –denominator

5

 So the fraction is represented as 8

 Read: five-eighths of the circle is shaded

DRAW YOUR OWN FIGURE

 A rectangle divided into 5 equal parts with 2 of

the parts shaded in red. Write a fraction for the

part that is shaded.

 Parts – 2 (red) – numerator

 Whole – 5 –denominator

2

 So the fraction is represented as 5

 Read: two-fifths of the rectangle is shaded

CLASSIFYING FRACTIONS

 These fractions are similar because they all have

a denominator of 3.

1

2

3

3

3

3

1

2

 The fractions and are proper fractions.

3

3

3

 The fraction is an improper fraction.

3

CLASSIFYING FRACTIONS

EXAMPLES OF IMPROPER AND PROPER

FRACTIONS

*Fraction *

*Type *

*Words *

Proper

One-half

4

2

1

3

5

4 Improper

Four-thirds

1

2

Improper

Five-fifths

3

3

3

Proper

Two-thirds

3

CLASSIFYING FRACTIONS

The improper fractions above have a numerator that is equal to the denominator.

Each fraction above is equal to one whole, or one.

CLASSIFYING FRACTIONS

CLASSIFYING FRACTIONS

WRITE THE FRACTIONS AS A MIXED

NUMBER.

CLASSIFYING FRACTIONS

*Fraction *

*Words *

*Type *

Three-fourths

Proper

Five-halves

Improper

Two and one- fourth

Mixed number

One- third

Mixed number

Three and one- fifth

Mixed number

EQUIVALENT FRACTIONS

 These are equivalent fractions because they all

have the same value.

2

 The simplest form of all these fractions is .

3

EQUIVALENT FRACTIONS

EQUIVALENT FRACTIONS

Multiplying the numerator and the denominator of a fraction by the same nonzero whole number will change that fraction into an equivalent fraction but it will not change the value.

SIMPLEST FORM OF A FRACTION

 Simplest form – no common factors for numerator and denominator

 Factors – numbers that are multiplied to give a

product

BASIC CONCEPTS

 Any number multiplied or divided by doesn’t

change its value.

 Similarly dividing numerator and denominator by the same number won’t change the value of the fraction.

BASIC CONCEPTS

The value of the fraction

doesn’t change.

 Dividing the numerator and denominator by the same number is the same as dividing by 1.

FIND THE SIMPLEST FORM OF A FRACTION,

EXAMPLE 4

16

 First, find the common factors of the numerator

and denominator.

 Factors of 4: 1, 2, 4 (1 × 4 = 4; 2 × 2 = 4; 4 × 1 = 4)

 Factors of 16: 1, 2, 4, 8, 16 (1 × 16 = 16; 2 × 8 = 16; 4

× 4 = 16; 8 × 2 = 16; 16 × 1 = 16)

 Next, find the Greatest Common Factor.

 Greatest number that is a factor for both numerator and denominator.

 Here, it is 4.

S

4

IMPLEST FORM OF 16

 Divide the numerator and denominator by the

Greatest Common Factor.

 4 ÷ 4 = 1

 16 ÷ 4 = 4

4

1

 So, the simplest form of is .

16

4

FIND THE SIMPLEST FORM OF

 Common factors

 16 : 1, 2, 4, 8, 16

 84 : 1, 2, 4, 6, 7, 12, 14, 21, 42,84

 Once past the maximum value of the numerator there won’t be a common factor.

 Greatest Common Factor = 4

TOY CARS

 Alex has six toy cars. Three of the cars are blue.

How can you write a fraction for the blue cars in

simplest form?

 Fraction

 Common factors

 3 – 1, 3

 6 – 1, 2, 3, 6

6 FISH ARE GREEN AND 6 ARE BLUE, SO

OF THE FISH ARE BLUE.

1

6

 is the simplest form of

2

12

2

3

4

6

1

 , , and are other ways of representing 4

6

8

12

2

LET’S PLAY A GAME

This year, 100 people are playing the game. Of this number 30

people have never played before. How can you express this part of the group as a fraction and as a decimal?

 Write thirty-hundredths this way

 Ones Tenths Hundredths

30

 Of the 100 players, or 0.3 are new players.

100

30

 Simplest form of 100

 Factors of 30: 1, 2, 5, 6, 10, 15, 30

 Factors of 100: 1, 2, 4, 5, 10, 25, 50, 100

6 OF THE 100 DIDN’T FINISH THE GAME

 Fraction six-hundredths

 Ones Tenths Hundredths

 Hint: Read a decimal by reading the place value

of the last digit at the right.

FRACTIONS TO DECIMALS

 A decimal is another way of representing a

fraction.

 A decimal has no numerator or denominator.

 For example, the fraction can be expressed as a decimal,

 The period ( . ) represents the decimal point.

 Read as five-tenths.

FRACTIONS TO DECIMALS

 Examples:

 0.9 nine-tenths

 0.3 three-tenths

 0.25 twenty five-hundredths

 Hint: Numbers after decimals are read as tenths

and hundredths.

BASIC CONCEPTS

 Note:

 Multiples of 10 in the numerator – increase the final value

 Multiples of 10 in the denominator – decrease the

final value

WRITE A DECIMAL AND FRACTION FOR THE

SHADED PARTS.

WHICH OF THE FOLLOWING IS

EQUIVALENT TO

2 ?

5

 Because the answer has a decimal in tenths, let’s

find an equivalent fraction with 10 in the

denominator.

2

2

 Multiply by .

5

2

WHICH OF THE FOLLOWING IS

EQUIVALENT TO 0.83?

 Ones Tenths Hundredths

 The last digit, 3, is in the hundredths place.

 So, the denominator is 100.

WHICH DECIMAL IS EQUIVALENT TO

1 ?

4

 Because the answer has a decimal in hundredths,

let’s find an equivalent fraction with 100 in the

denominator.

Now that you’ve reviewed fractions, let’s see how

well you understand the basic concepts.

Download Bake a Cake with Fractions! to test your knowledge.

If you don’t ace the quiz, you can come back to this lesson for a quick review.

Bake a Cake with Fractions!

Get Your Free Copy Here

A Great Way to Review Basic Concepts


Fractions

Best viewed on a color device. This is an ideal lesson for the student who needs help with fractions. It is also a good review for the student who has already been introduced to fractions but needs a refresher on basic concepts. Each lesson builds on the information presented in the previous section. With careful study, the student comes away with a solid understanding of the fundamental concepts and how they relate to each other. The first section introduces the fraction as a number that expresses part of a whole. With colorful illustrations, the student visualizes shaded parts of a circle and a rectangle as parts of a whole. The next section explains how to classify fractions as proper, improper and mixed. Examples are provided with step by step explanations on how to write improper fraction as mixed numbers. The section on equivalent fractions begins with the definition and examples of how these fractions are related to each other. Sample problems show the student how to find equivalent fractions by multiplying the numerator and denominator by the same nonzero whole number. One way to express a fraction’s equivalent form is to find the simplest form of that fraction. Sample problems and solutions provide step by step guidance. Terms such as the greatest common factor are defined to help the student find the simplest form. The lesson concludes by showing the student how to express a fraction as a decimal. Examples and solutions show how to express the simplest form of a fraction in decimal form and how to find the equivalent fraction of a decimal.

  • ISBN: 9781311076649
  • Author: Jack Anderson
  • Published: 2016-02-18 17:20:11
  • Words: 1233
Fractions Fractions