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
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.