slide 2 / 114 fractions presentation part...
TRANSCRIPT
This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course materials to parents, students and others.
Click to go to website:www.njctl.org
New Jersey Center for Teaching and Learning
Progressive Mathematics Initiative
Slide 1 / 114
Fractions Presentation Part 1
www.njctl.org
2011-11-29
Slide 2 / 114
Fractions
Presentation 1
Slide 3 / 114
· Meaning of Fractions
· Equivalent Fractions
· Lowest Term Fractions
· Improper Fractions and Mixed Numbers
· Using Fractions in Measurement
· Adding Fractions with Common Denominators
· Adding Mixed Numbers with Common Denominators
· Subtracting Fractions with Common Denominators
· Subtracting Mixed Numbers with Common Denominators
· Finding Common Denominators
· Comparing Fractional Numbers
Table of Contents
Slide 4 / 114
· Adding Fractions with Unlike Denominators· Subtracting Fractions with Unlike Denominators· Adding Mixed Numbers with Unlike Denominators· Subtracting Mixed Numbers with Unlike Denominators· Multiplying Fractions
· Multiplying Fractions and Whole Numbers
· Multiplying with Mixed Numbers
· Dividing Fractions· Dividing with Whole Numbers and Mixed Numbers
Table of Contentsfor Presentation 2
Slide 5 / 114
Meaning of Fractions
Return toTable of Contents
Slide 6 / 114
Fraction - An expression that indicates the quotient ( ) of two quantities.
Numerator - The number above the fraction bar. The numerator answers the question"How many parts?"
Denominator - The number below the fraction bar. The denominator answers the question "How many total?"
Key Terms
Numerator 3 Denominator 7
Fraction = =
Slide 7 / 114
Proper Fraction - A fraction where the numerator (top number) is less than the denominator (bottom number)
5 7 11 9 13 17
Improper Fraction - A fraction where the numerator (top number) is greater than or equal to the denominator (bottom number)
8 12 9 3 7 9
Key Terms
Slide 8 / 114
Equivalent Fractions - Fractions that represent the same number or are equal to each other.
2 4 6 8 10 12 14 3 6 9 12 15 18 21
Mixed Number - A fraction with a whole number and a proper fraction.
5 1 2 2
= = = = = =
2
ImproperFraction
MixedNumber
Key Terms
Slide 9 / 114
Eighths
Slide 19 / 114
1 What fraction of the whole is shaded?
Slide 20 / 114
2 What fraction of the whole is white?
Slide 21 / 114
Internet links for more practice
Fractions Naming Model link
Fractions Parts of a Whole Model link
Slide 22 / 114
Equivalent Fractions
Return toTable of Contents
Slide 23 / 114
19
19
19
What do you notice about the denominators in each set of equivalent fractions?
Slide 24 / 114
Click below to use this interactive number line.
Slide 25 / 114
25
= ??
Use the multiplication table to make equivalent fractions.
Pull
Slide 26 / 114
To create equivalent fractions, multiply(or divide) the numerator and denominator by the same number.
2 x 3 6 x 2 12 x 3 36 7 x 3 21 x 2 42 x 3 126
36 / 6 6 / 3 2 126 / 6 21 / 3 7
= = =
= =
Slide 27 / 114
3 Which set of fractions is equivalent?
A
B
C
D
1 2 2 2
=
4 1 8 4
1 3 3 6
3 9 7 21
=
=
=
Slide 28 / 114
4 Write a fraction equivalent to 4 7
Slide 29 / 114
5 Which fraction is equivalent to ?
A
B
C
D
3 8
16 6
12 24
12 32
9 16
Slide 30 / 114
6 Which set of fractions is equivalent?
A
B
C
D
3 9 4 16
=
9 2 12 3
6 1 18 3
3 9 7 14
=
=
=
Slide 31 / 114
7 Write a fraction equivalent to 5 9
Slide 32 / 114
Lowest Term Fractions
Return toTable of Contents
Slide 33 / 114
Reducing Fractions to Lowest Terms
Once you complete operations with fractions, you must write your answer in lowest terms.
The easiest way to determine if your answer is in simplest form is to check:1. Do the numerator and denominator have any common factors? 2. If they do not, the answer is in simplest form. 3. If they do, divide both the numerator and denominator by common factors until there are none left.
40 10 4 2 2 220 10 22 2 11
= =
Slide 34 / 114
Remember: Whatever you do to the numerator, you must do to the denominator.
18 24
In this problem, 18 and 24 are divisible by 2, 3 and 6. If you divide by 6 (the GCF), you will reach the simplest form in one step.
18 6 3 24 6 4
=
Slide 35 / 114
If you divide by 2 and 3 (common factors), then you will reach the simplest form in two steps. Either way, the simplest form is the same.
18 3 6 2 3 24 3 8 2 4
= =
Slide 36 / 114
Slide 37 / 114
8 Simplify to lowest terms.
21 35
Slide 38 / 114
9 Simplify to lowest terms.
3 9
Slide 39 / 114
10 Simplify to lowest terms.
21 29
Slide 40 / 114
11 Simplify to lowest terms.
17 51
Slide 41 / 114
12 Simplify to lowest terms.
24 96
Slide 42 / 114
Internet links for more practice
Simplifying Fractions link(interactive at bottom of page)
Rename in Lowest Terms interactive
Slide 43 / 114
Return toTable of Contents
Improper Fractions and
Mixed Numbers
Slide 44 / 114
In a proper fraction, the numerator is always less than the denominator. The value of a proper fraction is always less than 1.
3 5
In an improper fraction, the numerator is equal to or greater than the denominator. The value of an improper fraction is equal to or greater than 1.
5 7 5 5
Proper or Improper?
Slide 45 / 114
An improper fraction can be expressed as a whole number and a fraction. This is called a mixed number.
"Seven Halves"
3 1 2
7 2 =
Seven halves can fill up 3 whole strips and of another whole strip. That's and we say "three and one half", meaning "three plus one half".
3 1 2
1 2
Mixed Numbers
Slide 46 / 114
Converting Improper Fractionsto Mixed Numbers
Remember, the fraction bar symbolizes division! Therefore:
· Divide the numerator by the denominator to see how many "wholes" there are.· Write the remainder over the denominator
Let's look at "seven halves" again.
7 2 3 1
2 7 2 =
32 7 -6 1
2
Slide 47 / 114
Let's look at another example.
Now try this one. 17 8
13 5
25 13 -10 3
5
2 3 5
13 5
=
Slide 48 / 114
Converting Mixed Numbersinto Improper Fractions
To do this, complete a multiplication problem.
· Multiply the whole number by the denominator to create an improper fraction (of the original whole number).· Add the new fraction to the original fraction (from the mixed number).
Let's look at "seven halves" again.
3 1 2
7 2
== 6 2
+ 1 2
Slide 49 / 114
Let's look at another example.
Now try this one.
4 2 3
14 3
== 12 3
+ 2 3
6 3 7
Slide 50 / 114
13 is a proper fraction.
True
False
8 5
Slide 51 / 114
14 Change to a mixed number.
1 7 8
A
15 8
2 7 8
B
1 3 8
C
Slide 52 / 114
15 Change this mixed number to an improper fraction.
1 3 4
Slide 53 / 114
16 Change this mixed number to an improper fraction.
3 9 10
Slide 54 / 114
17 Change this improper fraction to a mixed number.
28 6
Slide 55 / 114
Return toTable of Contents
Using Fractionsin Measurement
Slide 56 / 114
Each one inch segment on this ruler is like one strip folded into four parts. For every inch, there are , and inch markings. 1
4 1 2
3 4
1 4
1 4
1 4
1 4
Fraction Ruler
Slide 57 / 114
Move the pink arrows to two locations on the ruler. Then hit the large blue arrow for the distance between the arrows to be measured.
Slide 58 / 114
18 What is the length between the two arrows?
1 9 16
in.A 1 5 8
in.C
3 4
in.D1 3 4
in.B
Slide 59 / 114
19 What is the length between the two arrows?
1316
in.A 3 4
in.C
7 8
in.D1 in.B
Slide 60 / 114
Return toTable of Contents
Adding Fractionswith Common Denominators
Slide 61 / 114
Adding Fractions with Common Denominators
To add fractions with common denominators, add the numerators and leave the denominator the same. Make sure your answer is in simplest form.
The denominator indicates the number of parts of the whole. If the fractions have a common denominator, they are the same "size" so we can add the numerators (or number of parts).
2 6 3 6 5 6
+
Slide 62 / 114
Try these!Move the boxes to see work and answers.Be sure to simplify all answers.
2 4 1 4
3 4
+
3 7 1 7
4 7
+
5 12 4 12
9 12
+
3 4
11301330
2430
+
4 5
Slide 63 / 114
23 5 12
2 12
+
Slide 67 / 114
24 8 20
6 20
+
Slide 68 / 114
Return toTable of Contents
AddingMixed Numberswith Common Denominators
Slide 69 / 114
Adding Mixed Numbers withCommon Denominators
To add mixed numbers with common denominators, add the fractions then add the whole numbers. Make sure your answer is in simplest form.
2 1 6
+ 1 4 6
3 5 6
5 1 9
+ 2 2 9
7 3 9
= 7 1 3
Slide 70 / 114
25 Is the equation below true or false?
True False
1 1 4
+ 3 2 4
4 3 4
Slide 71 / 114
26 Is the equation below true or false?
True False
4 1 4
+ 4 1 4
8 2 4
Slide 72 / 114
27 Find the sum.
2 5 12
+ 3 2 12
Slide 73 / 114
28 Find the sum.
5 3 10
+ 7 5 10
Slide 74 / 114
Adding Mixed Numbers withCommon Denominators
Sometimes after you add the mixed numbers, the fraction is improper. When this occurs, you must rename the improper fraction as a mixed number and add it to the whole number.
3 3 5
+ 2 4 5
5 7 5
= 5 + 1 2 5
= 6 2 5
6 5 9
+ 1 7 9
7 12 9
= 7 + 1 3 9
= 8 1 3
Slide 75 / 114
29 Is the equation below true or false?
True False
1 8 12
+ 1 5 12
3 1 12
Slide 76 / 114
30 Find the sum.
2 4 9
+ 5 2 9
Slide 77 / 114
31 Find the sum.
3 3 14
+ 2 4 14
Slide 78 / 114
32 Find the sum.
4 3 8
+ 2 3 8
Slide 79 / 114
Return toTable of Contents
Subtracting Fractionswith Common Denominators
Slide 80 / 114
Subtracting Fractions withCommon Denominators
To subtract fractions with common denominators, subtract the numerators and leave the denominator the same. Make sure your answer is in simplest form.
The denominator indicates the number of parts of the whole. If the fractions have a common denominator, they are the same "size" so we can subtract the numerators (or number of parts).
5 6 4 6 1 6
Slide 81 / 114
Try these!Move the boxes to see work and answers.Be sure to simplify all answers.
2 4 1 4
1 4
3 7 1 7
2 7
11 12 3 12
8 12
2 3
19301330
6 30
1 5
Slide 82 / 114
33 7 8 4 8
Slide 83 / 114
34 7 10 3 10
Slide 84 / 114
Return toTable of Contents
SubtractingMixed Numberswith Common Denominators
Slide 88 / 114
Subtracting Mixed Numbers withCommon Denominators
To subtract mixed numbers with common denominators, subtract the fractions then subtract the whole numbers. Make sure your answer is in simplest form.
2 4 6
1 3 6
1 1 6
5 7 9
2 4 9
3 3 9
= 3 1 3
Slide 89 / 114
38 Is the equation below true or false?
True False
4 5 9
3 9
3 2 9
Slide 90 / 114
39 Is the equation below true or false?
True False
2 7 9
1 9
1 2 3
1
Slide 91 / 114
40 Find the difference.
4 7 8
2 3 8
Slide 92 / 114
41 Find the difference.
6 7 12
1 4 12
Slide 93 / 114
42 Find the difference.
13 5 8
5 2 8
Slide 94 / 114
Return toTable of Contents
FindingCommon
Denominators
Slide 95 / 114
How many halves make a whole circle?
Slide 96 / 114
How many fourths make half of this circle?
Slide 97 / 114
How many sixths make 1/3 of this circle?
Slide 98 / 114
How many eighths can fit in 1/4 of this circle?
Slide 99 / 114
How many different combinations can you make to fill the circle?Keep track of what pieces you use. (You may need to rotate your pieces.)
1/8
1/4
1/21/3
1/61/7
1/5
Slide 100 / 114
Fix the Sticks
You can use the set of Skip Counting Sticks to find common denominators for two fractions with unlike denominators. If you don't have a set of sticks, you can create them by listing the multiples of the denominator.
For the fractions and , line up the sticks this way for the denominator of each fraction:
Find the smallest number in the "denominator" sticks that is common in both fractions.
It's 12. The least common denominator of and is 12.
3 4
4 8 12 16 20 2428 32 36
6 1218 24 30 36 42 48 54
...
...
1 6
3 4 1 6
3 4
1 6
Slide 101 / 114
A quick way to find LCDs...
List multiples of the larger denominator and stop when you find a common multiple for the smaller denominator.
Ex: and
Multiples of 5: 5, 10, 15
Ex: and
Multiples of 9: 9, 18, 27, 36
2 5
1 3
3 4
2 9
Slide 102 / 114
43 Find the LCD of this pair of fractions.
2 4
1 6
Slide 103 / 114
44 Find the LCD of this pair of fractions.
5 6
3 8
Slide 104 / 114
Return toTable of Contents
Comparing Fractional Numbers
Slide 105 / 114
Comparing Fractional Numbers
Common DenominatorsWhen you have two fraction with common denominators, all you have to do is compare the numerators.
Unlike DenominatorsTo compare fractions with unlike denominators, you have to rewrite both fractions with a common denominator. Then compare the numerators.
> 8 9
7 9
2 3 7 10
2 3
2030
=
7 10
2130
=< 2
3 7 10
Slide 106 / 114
Compare the fractions
1. 4 2 7 5
4 7
2035
=
2 5
1435
=
4 2 7 5
>
2. 11 1317 17
11 1317 17
<
3. 4 3 5 4
4 5
1620
=
3 4
1520
=
4 3 5 4
>
Slide 107 / 114
45 True or false?
2 3
3 4
>
Slide 108 / 114
46 True or false?
5 6
5 8
>
Slide 109 / 114
47 Compare the two fractions.
A >
8 11
3 4
B <
C =
Slide 110 / 114
48 Compare the two fractions.
A >
3 12
1 4
B <
C =
Slide 111 / 114
49 Compare the two fractions.
A >
4 9
5 8
B <
C =
Slide 112 / 114
Internet links for more practice
Finding fractions on a number line link
Comparing Fractions Model
Slide 113 / 114
Slide 114 / 114