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Fractions
Index• What is a fraction?• Equivalent Fractions• Making Equivalent Fractions by multiplying • Making Equivalent Fractions by dividing• Simplest Form • Uses of Fractions • Fractions Written as a Whole• Improper Fraction• Mixed Number• How to change from Improper Fraction to Mixed Number• How to change from Mixed Number to Improper Fraction • Comparing Fractions• Ordering Fractions • Ordering Fractions with Number Line• Adding Fractions
What is a Fraction?
3
2
I’m the NUMERATOR. I tell you the number of
equal parts you are looking at or have.
I’m the DENOMINATOR. I tell you the number of equal parts into which the whole is
divided.
A fraction is formed by dividing a whole into a number of parts
Uses of Fractions
• A fraction may represent division.
• Fractions can express probability.
• Fractions are used to compare two quantities as a ratio.
Student Reference Book p. 57-58
Equivalent Fractions
2
1
12
6
Equivalent fraction: fractions that have the same value
12
6
1 WHOLE 1 WHOLE4
26
3
• Multiply the numerator and denominator by the same number.
• You will get a new fraction with the same value as the original fraction.
• We are not changing the value of the fraction, because we are simply multiplying by a fraction that is equivalent to ONE.
To Make Equivalent Fractions
What do you get when you multiply a fraction by 1?
You get
AN EQUIVALENT FRACTION
that makes
adding & subtracting fractions
possible.
Make An Equivalent FractionFind the Missing Numerator!
Given the newdenominator, can you
find the missing numerator?
x 3
x 3
Make An Equivalent FractionFind the Missing Numerator!
Given the newdenominator, can you
find the missing numerator?
x 4
x 4
Make An Equivalent FractionIf you have larger numbers, you can make equivalent fractions using division. Divide by a common factor.
In this example,
we can divide both
numbers by 7.
÷ 7
÷ 7
2835
45
Fractions in Simplest FormFractions are in simplest form when the numerator and denominator do not have any common factors besides 1.
Examples of fractions that are in simplest form:
45
211
38
Writing Fractions in Simplest Form
• Find the greatest common factor (GCF) of the numerator and denominator.
• Divide both numbers by the GCF.
Example:
2028
201 x 20
2 x 10
4 x 5
281 x 28
2 x 14
4 x 7
20: 1, 2, 4, 5, 10, 20
28: 1, 2, 4, 7, 14, 28
Common Factors: 1, 2, 4
GCF: 4
We will divide by 4.
÷ 4÷ 4
= 57
Simplest Form
Fractions Written as a Whole
2
213
31
If a hexagon is worth 1, what are 5 trapezoids worth?
1 Whole
Trapezoid Trapezoid
TrapezoidTrapezoid
Trapezoid
2 Trapezoids = 1 Hexagon 1 Whole 1 Whole
½
We can report this as 2 ½ or 5/2 Trapezoid
Improper Fractionfractions that are equal to or greater than 1
5/2
is read as – five halves
Mixed Numbera whole number and a fraction written together
2 ½
is read as - two and one half
If a triangle is 1/3,what shape is ONE whole?
1/3
Remember: Numerator is what you have- 1.
Denominator is how many pieces your whole is cut into - 3.
How many more triangles do you need to make a whole?
1/31/3
What shape can we make?
1/3 + 1/3 + 1/3 = 3/3 or 1 Whole
Trapezoid1 Whole
If the triangle is 1/3, what is the rhombus?
If the rhombus is 1/3, what shape is the WHOLE?
Turn to MJ p. 124
If the rhombus is 1/3, what is the triangle?
If the triangle is ½, what shape is the WHOLE?
If the triangle is ½, what is the trapezoid?
Mixed Number
• A mixed number has a part that is a whole number and a part that is a fraction.
= 1 34
What is the mixed number?
= 3 34
What is the mixed number?
= 4 34
What is the mixed number?
= 5 12
Improper Fraction
• A fraction in which the numerator is greater than the denominator.
=84
What is the improper fraction?
= 154
What is the improper fraction?
= 194
What is the improper fraction?
= 112
How is the mixed number below related to the
improper fraction?
=112
=125
How to change an improper fraction to a mixed number
= 52
Divide the numerator by the denominator.
Put your remainder over the denominator.
How to change an improper fraction to a mixed number
= 52
2 ) 5 numerator
denominator
How to change an improper fraction to a mixed number
= 52
2 ) 5 numerator
denominator
2 r 1
How to change an improper fraction to a mixed number
= 52
2 ) 5 numeratordenominator 2
1
Put your remainder over the Denominator.
2
Change this improper fraction to a mixed number.
7
3= 3 ) 7
2 r 1
Put your remainder over the denominator.
= 213
Change this improper fraction to a mixed number.
8
3= 3 ) 8
2 r 2
Put your remainder over the denominator.
= 223
Change this improper fraction to a mixed number.
9
2= 2 ) 9
4 r 1
Put your remainder over the denominator.
= 412
Change this improper fraction to a mixed number.
11
5= 5 ) 11
2 r 1
Put your remainder over the denominator.
= 215
Change this improper fraction to a mixed number.
10
5= 5 ) 10
2
If there is no remainderyour answer is a wholenumber.
= 2
Change this improper fraction to a mixed number.
16
4= 4 ) 16
4
If there is no remainderyour answer is a wholenumber.
= 4
How to change a mixed number to an improper fraction
• Multiply the whole number times the denominator.
• Add your answer to the numerator.
• Put your new number over the denominator.
412x
+=
92
Change this mixed number to an improper fraction
• Multiply the whole number times the denominator.
• Add your answer to the numerator.
• Put your new number over the denominator.
623x
+=203
Change this mixed number to an improper fraction
• Multiply the whole number times the denominator.
• Add your answer to the numerator.
• Put your new number over the denominator.
3 25x
+=175
Change this mixed number to an improper fraction
• Multiply the whole number times the denominator.
• Add your answer to the numerator.
• Put your new number over the denominator.
4 34x
+=194
Change this mixed number to an improper fraction
• Multiply the whole number times the denominator.
• Add your answer to the numerator.
• Put your new number over the denominator.
6 23x
+=203
Change this mixed number to an improper fraction
• Multiply the whole number times the denominator.
• Add your answer to the numerator.
• Put your new number over the denominator.
8 35x
+=435
Use >, <, or =.
5
33
29 10<
<
Cross Multiply or “Butterfly Method”
Comparing Fractions
Use >, <, or =.
10
34
112 10>
>
Cross Multiply or “Butterfly Method”
To order fractions you can draw a picture or
use the Least Common Denominator (LCD).
Ordering Fractions
One way to compare or order fractions is to
express them with the same denominator.
Any common denominator could be used. But the
Least Common Denominator (LCD)
makes the computation easier.
Use LCD
List the fractions in order from greatest to least.
3
2,9
5,
12
7,6
1
Use LCD
Step 1: Find a common denominator
3
2,9
5,
12
7,6
1
6, 12, 18, 24, 30, 36 ….
LCD = 36
Find the LCD:
12, 24, 36, 48, 60 …9, 18, 27, 36 …
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 …
Put the largest denominator first and write down the first 5 multiples
Then continue with the next denominator until you find a common digit…
Step 2: Write equivalent fractions.
6
1
36x 6
x 6 6 12
736x 3
x 321
9
536x 4
x 420 3
236x 12
x 1224
Step 3: Compare the numerators
6
136 6
12
73621
9
53620
3
23624
In order from greatest to least:
6
1,9
5,
12
7,3
2
PRACTICE: Use LCD
In order from greatest to least:
6
1,9
5,
12
7,3
2
Finding Fractions on a Number Line
• We can use number lines to help us order fractions.
Finding Fractions on a Number Line
• This number line breaks one whole into fourths.
• Where would ¼ be on the number line?
• What about 4/4?
4
1
4
4
Finding Fractions on a Number Line
• How many sections does this number line break one whole into?
• Can you locate where 1/8 would be?
• Name a fraction in eighths that is between ½ and ¾.
8
1
4
1
4
2 4
3
Finding Fractions on a Number Line
• What does this number line show?
• Where would 7/9 be?
• What fraction is between 1/9 and 2/9?
Finding Fractions on a Number Line
• How would you explain this number line using words?
• Can you find 3/5?
• Can you mark a fraction larger than 4/5 on the number line?
Finding Fractions on a Number Line
• What type of number line is this?
• Can you order 5/8, 1/4, 2/3, and 3/16 on this number line?
Adding Fractions with common denominators
8
4
8
3
8
7
Add these fractions
1/5
1/51/5
1/5
35
15
+ =45
1/5
Add these fractions
1/4
1/4
1/424
14
+ =3
4
Adding Fractions with different denominators
Problem:
You can’t add fractions with different denominators without getting them ready first. They will be ready to add when they have common denominators
Solution: Turn fractions into equivalent fractions with a
common denominator that is find the Lowest Common Multiple (LCM) of the two denominators
7, 14, 21, 28, 35…
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
2
1
7
3We need a common denominator to add
these fractions.
7, 14, 21, 28, 35…
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
REMEMBER the first number IN COMMONthat appears on both lists
becomes the common denominator
x 2
x 2
X 7
x 7 7
6
7 + 6 = 1313
2
1
7
3
14
14
14
5
17
3
We need a common denominator to add
these fractions.
5, 10, 15, 20, 25, 30, 35, 40, 45
7, 14, 21, 28, 35, 42, 49, 56, 63
x 7
x 7
X 5
x 5 15
7
15 + 7 = 22
22
35
35
35
7
3
5
1
Try These
A
F
EB
C
D
Answers On Next Slide
• Each click on the next slide reveals an answer.
• Check your papers.
• If you discover an incorrect answer, be able to explain your mistake.
Try These
A
F
EB
C
D1727
1920
109
4128
2621
1312
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