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Math Grade 4Mrs. Ennis
Equivalent Fractions Lesson Twenty
1. 3434 + D = 43102. 826 – 415 =
3. 5 x B = 20
4. L x 8 = 725. 36 ÷ 6 =
6. How many obtuse angles in this figure?
7. 100 cm = _________m
8. How many dimes in $1.65?
9. The concession stand at the ballpark sells hot dogs for $1.00 each. Their cost per hot dog is $0.25. If they sold 20 hotdogs, what was their profit?
10. The grocer places a case of canned tomatoes in a 3-shelf display. He puts 7 cans on each shelf and had 3 cans left over. How many cans in the case?
Fraction Notation
1
Numerator
Denominator
3
The fraction one-third is written like this:
The number above the bar is the numerator. The number below the bar is the denominator.
Equivalent Fractions
A fraction can have many different names.
½
2/4
6/12
5/10 4/8
3/6
In the picture we have ½ of a cake because a whole cake is divided into two congruent parts and we have only one of those parts.
But if we cut the cake into smaller congruent pieces, we can see that
2
1=
4
2
Or we can cut the original cake into 6 congruent pieces,
Now we have 3 pieces out of 6 equal pieces, but the total amount we have is still the same. Therefor
e,
2
1=
4
2
6
3
If you don’t like this, we can cut the original cake into 8 congruent pieces,
=
Then we have 4 pieces out of 8 equal pieces, but the total amount we have is still the same.
2
1 =4
2 =6
3 =8
4We can generalize this to:
2
1=
n
n
2
1 whenever n is not 0
Therefore,
2
1 =4
2 =6
3 =8
4
We can generalize this to
2
1=
n
n
2
1 (whenever n is not 0)
VocabularyEquivalent fractions are fractions that name the same amount.
24
= 48
5 x 1 = 5
23 x 1 = 23
37 x 1 = 37
7 x 1 = 7
17 x 1 = 17
What do you get when you multiply a number by 1? You get that number!
All these fractions = 1
4
4
33
33
5
5
2
2
7
7When the
numerator & denominator of a
fraction are the same, the fraction
equals 1.
What do you get when you multiply a fraction by 1?
You get AN EQUIVALENT
FRACTION
(This makes adding & subtracting fractions possible.)
• 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
35
x44
=1220
This fraction equals 1.
These fractions represent the same amount.
23
x33
=69
This fraction equals 1.
These fractions represent the same amount.
23
=69
Make An Equivalent Fraction
Find the Missing Numerator!
3x 3
x 3
49
=1636
Make An Equivalent FractionFind the Missing Numerator!
4x 4
x 4
58
=4572
Make An Equivalent FractionFind the Missing Numerator!
9x 9
x 9
27
= 621
Make An Equivalent FractionFind the Missing Numerator!
3x 3
x 3
67
=2428
Make An Equivalent FractionFind the Missing Numerator!
4x 4
x 4
37
=1228
Make An Equivalent FractionFind the Missing Numerator!
4x 4
x 4
78
=2124
Make An Equivalent FractionFind the Missing Numerator!
3x 3
x 3
13
= 515
Make An Equivalent FractionFind the Missing Numerator!
5x 5
x 5
24
=1020
Make An Equivalent FractionFind the Missing Numerator!
5x 5
x 5
45
=2430
Make An Equivalent FractionFind the Missing Numerator!
6x 6
x 6
45
= 810
Make An Equivalent FractionFind the Missing Numerator!
2x 2
x 2
If 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.
2835
÷ 7÷ 7
= 45
7/7 is equal to 1.28/35 is equivalent to 4/5.
If 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 3.
2130
÷ 3÷ 3
= 710
3/3 is equal to 1.28/35 is equivalent to 7/10.
If 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 5.
1525
÷ 5÷ 5
= 35
5/5 is equal to 1.15/25 is equivalent to 3/5.
2430
=1215
Make An Equivalent FractionFind the Missing Denominator!
2 ÷ 2
÷2
1824
=68
Make An Equivalent FractionFind the Missing Denominator!
3 ÷ 3
÷3
2025
=45
Make An Equivalent FractionFind the Missing Denominator!
5 ÷ 5
÷5
915
=35
Make An Equivalent FractionFind the Missing Numerator!
3 ÷ 3
÷3
1224
=12
Make An Equivalent FractionFind the Missing Numerator!
12
÷ 12
÷12
3640
=910
Make An Equivalent FractionFind the Missing Numerator!
4 ÷ 4
÷4
Fractions in Simplest Form (This is also known as
“reducing.”)Fractions 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
1 2
38
Writing Fractions in Simplest Form.
• Find the greatest common factor (GCF) of the numerator and denominator.
• Divide both numbers by the GCF.
Example:
20282
01 x 20
2 x 10
4 x 5
281 x 28
2 x 14
4 x 7
Common Factors: 1, 2, 4
GCF: 4We will divide by 4.
÷ 4÷ 4
= 57
Simplest Form
20: 1, 2, 4, 5, 10, 2028: 1, 2, 4, 7, 14, 28
Example:
27452
71 x 27
3 x 9
451 x 45
3 x 15
5 x 9
Common Factors: 1, 3, 9
GCF: 9We will divide by 9.
÷ 9÷ 9
= 35
Simplest Form
20: 1, 3, 9, 27
28: 1, 3, 5, 9, 15, 45
Example:
15181
51 x 15
3 x 5
181 x 18
2 x 9
3 x 6
Common Factors: 1, 3
GCF: 3We will divide by 3.
÷ 3÷ 3
= 56
Simplest Form
15: 1, 3, 5, 15
18: 1, 2, 3, 6, 9, 18
Example:
812 8
1 x 8
2 x 4
121 x 12
2 x 6
3 x 4
Common Factors: 1, 2, 4
GCF: 4We will divide by 4.
÷ 4÷ 4
= 23
Simplest Form
8: 1, 2, 4, 8
12: 1, 2, 3, 4, 6, 12
Online Practice
Flash Cards
http://www.helpingwithmath.com/resources/games/fraction_game4/equivalent01.html
http://www.mathplayground.com/fractions_reduce.html
http://mathematics.hellam.net/maths2000/fraction1.html
Math Fun:Fiona went to the produce market. She spent $1.20 for a bag of squash, which sold for $0.60 per pound. Her bag of 6 equally-sized apples weighed the same as their bag of 2 identical squash. Her 8 peaches, all about the same size, weighed as much as 3 apples and 1 squash. She also purchased a small pumpkin that weighed the same as 12 peaches. How much did the pumpkin weigh?
Answer:The pumpkin weighed 3 pounds.
Fiona bought 2 squash. Since she spent $1.20, with squash priced at $0.60 per pound, the 2 squash must have weighed 2 pounds.This means that 6 apples also weigh 2 pounds, and 3 apples weigh 1 pound. You also know that 8 peaches weigh 2 pounds, so 4 peaches weigh 1 pound and 12 peaches must weigh 2 + 1 = 3 pounds, which is also the weight of the pumpkin.
http://mathlearnnc.sharpschool.com/UserFiles/Servers/Server_4507209/File/Instructional%20Resources/G4WW1-4.pdf
http://nces.ed.gov/nceskids/grabbag/math_teasers/Challenge2.asp
Resources:
http://www.mrhammond.org/math/mathlessons/
www.nwlincs.org/nwlincsweb/EITCdata/Fractions/01EquivFrac.ppt
star.spsk12.net/math/5/equivalent_fractions.ppt
http://www.helpingwithmath.com/resources/games/fraction_game4/equivalent01.html
http://www.mathplayground.com/fractions_reduce.html
http://mathematics.hellam.net/maths2000/fraction1.html
1
1/2 1/2
1/3 1/3 1/3
1/4 1/4 1/4 1/4
1/5 1/5 1/5 1/5 1/5
1/6 1/6 1/6 1/6 1/6 1/6
1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8
1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9
1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10
1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12
Equivalent Fractions
Twelfths
Tenths
Ninths
Eighths
Sixths
Fifths
Fourths
Thirds
Halves
Whole
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