Section Overview Video
Fractions Starts with parts and equivalence defining the denominator numerator and structure of a fraction. A 2/6 vs 1/3 animation illustrates. Counting fractions starts with a discussion of wholes and parts and features the Order Hi to Low Tool where students learn about relative size of fractions by comparing them to eachother. In easy mode numerators = 1 and only denominators need be compared. A help chart displays fractions side-by-side, it is a great teaching and learning aid.
Equivalence animates a circle half shaded hovering the fractions above further divides the circle illustrating the concept of equivalence and leading to a discussion about infinite equivalent fractions. The 3 Equivalent Fractions tool gives students the opportunity to be creative, by using an identity fraction to generate equivalent fractions. Instructors may start students in level/1 by using multiples of 10 to generate equivalents. students may revisit this tool in level2 using other multiples.
The Halves and Quarters tool generates a number between 1 and 100. In Easy mode the number generated Halves and Quarters into whole numbers. In Medium mode the number halves to a whole and quarters to a half and in hard mode the number halves to a half and quarters to one or three quarters.
Simplification features a tool generating 5 improper fractions to be converted to simplified mixed numbers. Detailed solutions show whole groups and remainders for each incorrect answer. A how to simplify tutorial starts with a 72/96 being simplified to 3/4 using prime factorization. A prime factorization tutorial showing factors of 96 and 97, and divisibility rules for 2 3 and 5 teach students about factoring. In easy mode the tool generates numbers made from 3 primes either 2s 3s or 5s. In Hard mode the number is generated from 5 primes possibly a 7 or an 11.
There are graphics defining 4 types of fractions, Proper Improper Identity and Reciprocals that instructors and students may review. The Fractional Operations tool generates two fractions and presents them in 4 operations add subtract multiply and divide. Detailed solutions showing steps for each operation help students study and learn. A tutorial for addition includes a common denominator graphic and an animation adding one half plus one third. A lowest common multiples tool is great for helping students find lowest common denominators. A single graphic shows the rules for multiplying and dividing fractions.
Easy Med Hard
Half:
0/0 0/0 0/0
Quarter:
0/0 0/0 0/0
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Easy Med Hard
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1/2 and 1/4 of 35
35
Think of ½ 35 as
Half of 30 + Half of 5
15 + 2 ½
Combined = 17 ½
Think of ½ of 17½ as
½ of 10 + ½ of 7 + ½ of ½
5 + 3 ½ + ¼
Combined = 8 3/4
Easy: Numbers half and quarter to whole numbers
Medium: Numbers half to wholes and quarter to halves
Hard: Numbers half to halves and quarter to quarters
Remember a Quarter is Half of a Half
Easy mode: generates a target number made from 3 prime numbers either 2s, 3s or 5s.
Hard mode: generates a target number made from 5 prime numbers either 2s, 3s or 5s and may include either a 7 or an 11.
Enter the prime factors in any order
Prime Factorization for
96 and 97
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Prime Factors of 96 and 97
Factor into Prime Numbers
Simplify
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Find Factors 2 3 5
Prime Factorization
Divisibility Rules for 2's 3's and 5's
If the number is even; 2 is a factor
If the number ends in 0 or 5; 5 is a factor
If the sum of digits is divisible by 3; 3 is a factor
Answer: 140.1111111... repeating
Written as: 140.1
Basketballs, are counted as whole things, 1,2,3 or more..., but we never have part of a ball, so we don't use fractions to count them.
Money is an example where we use fractions. When something costs $2.37 that means it costs 2 whole dollars and 37/100 of a third dollar, 37 is the numerator and 100 is the denominator.
Think about things we count in parts and things we count as wholes. Discuss and list 3 things that use fractions to count, and 3 that do not.
Halves and Quarters
Order Hi to Low
DENOMINATOR : on bottom tells how many total parts there are and names the fraction.
NUMERATOR : on top tells how many parts there are.
2/6 is Not Simplified 1/3 is Simplified
2/6 and 1/3 are Equivalent Fractions
Equivalence
Counting Fractions
This tool generates two numbers and students find the lowest common multiple between them.
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Lowest Common Denominator
Same Two Fractions in 4 Expressions (+ - * ÷)
Easy Mode: Denominators 2, 3, 5; Numerators up to 7
Hard Mode: Denominators up to 7; Numerators up to 13
Simplify all Answers
Adding and Subtracting
Requires Common Denominators
1/2 + 1/2 = 2/2 = 1
1/4 + 1/4 + 1/4 = 3/4
Addition is Easy with Common Denominators
• Denominator remains the same
• Add or Subtract Numerators
What About Without Common Denominators
1/2 + 1/3 =
??ANSWER
1/2 + 1/3 = 5/6
3/6 + 2/6 = 5/6
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Find Lowest Common Denominators
Multiplication is Straight Across
Division requires a Second Term
Reciprocal then Multiplication
Remember to Simplify
Easy Hard
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Show Score Page
Add/Subtract ← how to → Multiply/Divide
Types of Fractions
Proper Fractions: Less than 1 such as: 1/2
Improper Fractions: Greater than 1 such as: 7/2
Identity Fractions: Equal 1 such as: 5/5 or 2x/2x
Reciprocals: Are Inverse Fractions, Product = 1
Improper Fraction and Mixed Numbers
are Greater than 1 or Less Than Negative 1
5/4 is an Improper Fraction
5/4 is equivalent to 4/4 plus 1/4
5/4 = 1¼
1¼ is a Mixed Number
It contains a Whole Number and a Proper Fraction
EASY: The denominators are less than or equal to 5, and the answers are up to 4 whole groups.
HARD: The denominators are less than or equal to 12, and the answers are up to 12 whole groups.
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How to Simplify4 Types of Fractions
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Easy Medium Hard
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x/x x/x x/x x/x x/x
Largest 5->4->3->2->1 Smallest
We could think of 1 dollar as the same as
100 pennies or 10 dimes or 20 Nickels or 4 quarters
One Penny = 1/100→one hundredth of a dollar
One Dime = 10/100→ten hundredths of a dollar
One Nickel = 5/100→five hundredths of a dollar
One Quarter = 25/100→twenty-five hundredths of a dollar
Count the Money
Equivalent Fractions & Simplification
50/100 = 5/10 = 1/2
50 25 5 1
−−− = −− = −− = −
100 50 10 2
½ + ½ = 1HOWEVER
1/2 + 1/3 = 5/6Use the IDENTITY property to find any common denominators
Adding and Subtracting Fractions requires Common Denominators
DECIMALS
1/10 = .1 1/100 = .01 1/1000 = .001
1/2 = .5 1/4 = .25 3/4 = .75
1/3 = .33333333333...
Any Fraction can be written as a Decimal
Long Division is a Prerequisite for This Section
Instructors and students work together making equivalent fractions using multiples of tens and negative numbers for example the Fraction:
3/7
Has Equivalent Fractions
30/70 .3/.7 -3/-7
Remember there are an infinite number of equivalents for each fraction.
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Use Reciprocals to Solve
Flip the Fraction
The Product Equals 1
when reciprocals are multiplied the product
is always 1 or Identity because numerators
and denominators equal each other
Reciprocals and Algebra
Proper Fractions are between -1 and 1
They may need to be simplified for example:
2/4 simplifies to 1/2
Identity Fractions = 1
Numerator = Denominator
5/5 3/3 .1/.1 2X/2X Y²/Y²
Any Fraction • Reciprocal = Identity
A/B • B/A = AB/BA = 1
Hover Fractions Equivalent to 1/2
1/2 2/4 3/6 4/8 6/12 12/24
One Half
Two Fourths
Three Sixths
Four Eighths
Six Twelfths
Twelve Twenty Fourths
How Many Fractions are Equivalent to 1/2 ?
INFINITY
Practice Making 3 Equivalent Fractions